Foreword The 6th International Gravel-Bed Rivers Workshop (GBR6) was held at St. Jakob/ Defereggental, near Lienz in Austria, between 5th and 9th September 2005. It was organised by a European scientific committee composed of Austrian, British, French, German, and Italian representatives with pre- and post-tours in the Austrian, French, German, and Italian Alps. This workshop was designed in continuity with previous GBR meetings, open to invited scientists and post-graduate students, with the goal of providing a forum for the review and discussion of research and developments in the preceding five years of all aspects of gravel-bed river sciences. Previous Gravel-Bed Rivers Workshops took place in:
England, Gregynog, Newtown, Wales, June 1980; USA, Pingree Park, Colorado, August 1985; Italy, Poggio a Caiano, September 1990; USA, Gold Bar, Washington, August 1995; and New Zealand, Christchurch, August–September 2000.
The subject of GBR6, ‘‘From process understanding to river restoration’’, is concerned with recent progress in the understanding of gravel-bed river morphology and sediment transport, as well as new developments in restoration. There was a particular emphasis on scaling aspects of gravel-bed river processes and patterns. GBR6 focused on mountain rivers of the Alps and their surroundings, and specifically addressed the European challenge in terms of ecological improvement in a cultural landscape where natural hazards are critical. In the host country of Austria, the issue of natural hazards is of immediate relevance due to floods in August 2002 and August 2005 – the latter immediately prior to the conference – that had recurrence intervals of more than 1000 years and induced significant morphological changes in many gravel-bed rivers, including threeto four-fold increases of the river bed width and metamorphosis from single thread to braided rivers. The implementation of the European Water Framework Directive strives to achieve a ‘‘good ecological status’’ of all running waters by the year 2015. River basin management is crucial in this respect because gravel-bed river behaviour is determined by a complex interaction of large- and small-scale processes and patterns. In general, Alpine rivers have undergone significant changes over the last two centuries. Human activities have modified their geometry through engineering measures to gain land for agricultural purposes and settlements, as well as through active mining to exploit gravel resources. Their sediment and water transfers have also been altered by hydropower plant construction, torrent control works, and catchment land-use changes. The resulting river morphological changes have led to abiotic (e.g., river bed
vi
Foreword
degradation and narrowing) and biotic (e.g., longitudinal and lateral disconnection) disruption. In river basins in the Alps, where rivers are not steady-state but follow long-term trajectories of changes related to multiple human driven parameters, the current management situation has been made critical by channel instability problems, flood effects and biodiversity decrease, and river restoration is a major issue. Early attempts at river restoration mainly focused on small-scale measures. Today, successful restoration projects in high-energy and bedload transport-dominated conditions must include the full spectrum of scales and initiate self-forming morphodynamics. Three sessions of GBR6 dealt with scales, ranging from ‘‘scales of analysis for gravel-bed rivers’’, ‘‘analysis of processes at point and local scale’’, and ‘‘basin scale: sediment delivery and storage’’. One session treated ‘‘channel change and instability’’, another session covered ‘‘ecohydrology and ecohydraulics’’ and the last session focussed on ‘‘management and restoration’’. Furthermore, an extended PhD session was held. Each session was designed to contain one geomorphologist, one engineer and one ecologist in order to promote interdisciplinary discussion and to stimulate future interrelations and collaborations across the fields. Traditionally, intensive fieldwork is undertaken during GBR events, where practical questions dealing with gravel-bed river processes and management are exposed to the participants and discussed. During GBR6, several specific reaches of the Isel River, the Upper Drau River, and torrential tributaries were considered in terms of three themes: sediment sources and torrent control; sediment input, transfer and river management; and river restoration design based on hydromorphological trends. Tour guides provided additional information to the participants. The final discussion of the fieldwork was incorporated into a Carinthian BBQ that took place along the Drau River. This book presents invited papers that were at least double-blind reviewed, thus maintaining the high standard of earlier gravel-bed river books. The book is organized into six parts:
Introductive contributions deal with the scale of analysis, with particular focus on scaling processes by M. Church, reach characterisation by R. Ferguson, and hydrodynamics and turbulence by V. Nikora. The second part is devoted to the analysis of the river processes at the point and local scales, with disciplinary questions in hydraulics, physics and fluid mechanics. Specific contributions open discussions on bedload transport by P. Diplas, surficial and sub-surficial velocity by M. Detert and his colleagues, and velocities between the stream and the hyporheic zone by I. Seydell and her colleagues. At local scales, themes include bifurcation in braided rivers by M. Tubino and W. Bertoldi, geomorphic effects of floods by E. Mosselman and K. Sloff and by E.Wohl, bank erosion modelling by M. Rinaldi and S. Darby, and grain size responses to hydrological patterns by G. Parker and his colleagues. The third part focuses on the basin scale, including sediment delivery and storage, with specific discussions on sediment delivery and climate change by T. Coulthard and his colleagues, sediment delivery and human controls by M. Page and his colleagues, catchment responses to human activities and climate change by J. Pizzuto and his colleagues, sediment transport and its link to sediment supply by S. Ryan and M. Dixon, sediment organisation at the basin scale by J. Hoyle and her
Foreword
vii
colleagues, evolution of sediment waves by T. Lisle, and sediment storage and transport in coarse-bed streams by M. Hassan and his colleagues. The fourth part introduces more applied questions related to channel change and instability. Specific contributions concern a review of ecological responses due to human pressures by F. Nakamura and his colleagues, channel incision by B. Wyz˙ ga, vegetation encroachment of braided rivers by M. Hicks and his colleagues, and the effects of extreme floods on channel processes and stability by M. Jaeggi. The fifth part deals with ecohydrology and ecohydraulics, linking hydraulic and geomorphic processes with ecological demands and providing scientific knowledge for river managers. The chapters include reservoir operation and ecosystem losses by K. Jorde and his colleagues, hydraulic effects on macroinvertebrate communities at the local scale by S. Rice and his colleagues, hydraulic geometry and ecological implications by N. Lamouroux, and gravel bars as key habitats for vegetation by D. Gilvear and his colleagues. The sixth part concludes the book with clearly applied contributions to river management and restoration, providing a large set of gravel-bed river examples, with a review of restoration experiences in the Alps and their surroundings by H. Habersack and H. Pie´gay, a discussion on uncertainty in river restoration by D. Sear and his colleagues, the evolutionary scenario and its use for the development of a conservation and restoration strategy for the Willamette River by S. Gregory, and the ecological assessment of restoration on the Drau River, Austria by S. Muhar and her colleagues.
Following this peer-review book publication, submitted poster papers, after successful review, have also been published in special sister issues in Earth Surface Processes and Landforms and Geodinamica Acta. Special thanks go to Peter Ergenzinger and Trevor Hoey as members of the organizing committee, Hugo Seitz for coordinating the local workshop organisation, Fre´de´ric Lie´bault and Jacqueline Dupuis for their active participation in the scientific organisation, John Laronne for very valuable inputs during the genesis of the workshop and also his constant attention to guide us in the right direction with respect to the contributors, all the colleagues involved in the pre- and post-conference tours, the sponsors of the workshop, the Austrian Ministry of Agriculture, Forestry, Environment and Water Management, the regional water authorities of Tyrol and Carinthia, the village of St. Jakob/Defereggental, the company ‘‘Interconvention’’ for all administrative support, convenors of the pre- and post-study excursions, chairmen of the sessions and many students for helping to prepare and convene the workshop. Due to the excellent contributions and fruitful discussions, the workshop was of very high quality. The venue’s Austrian mountain scenery, combined with the smallvillage atmosphere, wonderful weather and social activities, will hopefully firmly implant GBR6 in the memories of the participants and entice some to return to explore these Alpine gravel-bed rivers and their environments in more detail. Helmut, Herve´, Massimo Developments in Earth Surface Processes
Invited Participants in the 6th Gravel-Bed Rivers Conference 2005
Contents Foreword List of contributing authors
v xiii
Scales of analysis for gravel-bed rivers 1 2 3
Multiple scales in rivers Michael Church Gravel-bed rivers at the reach scale Rob Ferguson Hydrodynamics of gravel-bed rivers: scale issues Vladimir Nikora
3 33 61
Analysis of processes at point and local scales 4
Pressure- and velocity-measurements above and within a porous gravel bed at the threshold of stability Martin Detert, Michael Klar, Thomas Wenka and Gerhard H. Jirka 5 Evaluating vertical velocities between the stream and the hyporheic zone from temperature data Ina Seydell, Ben E. Wawra and Ulrich C.E. Zanke 6 Bifurcations in gravel-bed streams Marco Tubino and Walter Bertoldi 7 The importance of floods for bed topography and bed sediment composition: numerical modelling of Rhine bifurcation at Pannerden Erik Mosselman and Kees Sloff 8 Review of effects of large floods in resistant-boundary channels Ellen Wohl 9 Modelling river-bank-erosion processes and mass failure mechanisms: progress towards fully coupled simulations Massimo Rinaldi and Stephen E. Darby 10 Adjustment of the bed surface size distribution of gravel-bed rivers in response to cycled hydrographs Gary Parker, Marwan A. Hassan and Peter Wilcock 11 Bed load transport and streambed structure in gravel streams Panos Diplas and Hafez Shaheen
85
109 133
161 181
213
241 291
Contents
x Basin scale: sediment delivery and storage 12
13
14
15
16
17
18
Non-stationarity of basin scale sediment delivery in response to climate change Tom J. Coulthard, John Lewin and Mark G. Macklin Changes in basin-scale sediment supply and transfer in a rapidly transformed New Zealand landscape Mike Page, Mike Marden, Mio Kasai, Basil Gomez, Dave Peacock, Harley Betts, Thomas Parkner, Tomomi Marutani and Noel Trustrum Two model scenarios illustrating the effects of land use and climate change on gravel riverbeds of suburban Maryland, U.S.A. Jim Pizzuto, Glenn Moglen, Margaret Palmer and Karen Nelson Spatial and temporal variability in stream sediment loads using examples from the Gros Ventre Range, Wyoming, USA Sandra E. Ryan and Mark K. Dixon Sediment organisation along the upper Hunter River, Australia: a multivariate statistical approach Joanna Hoyle, Gary Brierley, Andrew Brooks and Kirstie Fryirs The evolution of sediment waves influenced by varying transport capacity in heterogeneous rivers Thomas E. Lisle Sediment storage and transport in coarse bed streams: scale considerations Marwan A. Hassan, Bonnie J. Smith, Dan L. Hogan, David S. Luzi, Andre E. Zimmermann and Brett C. Eaton
315
337
359
387
409
443
473
Channel change and instability 19
20
21
22
Ecological responses to anthropogenic alterations of gravel-bed rivers in Japan, from floodplain river segments to the microhabitat scale: a review Futoshi Nakamura, Yoˆichi Kawaguchi, Daisuke Nakano and Hiroyuki Yamada A review on channel incision in the Polish Carpathian rivers during the 20th century Bart!omiej Wyz˙ga Contemporary morphological change in braided gravel-bed rivers: new developments from field and laboratory studies, with particular reference to the influence of riparian vegetation D. Murray Hicks, Maurice J. Duncan, Stuart N. Lane, Michal Tal and Richard Westaway The floods of August 22–23, 2005, in Switzerland: some facts and challenges Martin Jaeggi
501
525
557
587
Contents
xi
Ecohydrology and ecohydraulics 23
24
25 26
Reservoir operations, physical processes, and ecosystem losses Klaus Jorde, Michael Burke, Nicholas Scheidt, Chris Welcker, Scott King and Carter Borden Movements of a macroinvertebrate (Potamophylax latipennis) across a gravel-bed substrate: effects of local hydraulics and micro-topography under increasing discharge Stephen P. Rice, Thomas Buffin-Be´langer, Jill Lancaster and Ian Reid Hydraulic geometry of stream reaches and ecological implications Nicolas Lamouroux Gravel bars: a key habitat of gravel-bed rivers for vegetation David Gilvear, Robert Francis, Nigel Willby and Angela Gurnell
607
637 661 677
River management and restoration 27
28 29
30
River restoration in the Alps and their surroundings: past experience and future challenges Helmut Habersack and Herve´ Pie´gay Uncertain restoration of gravel-bed rivers and the role of geomorphology David A. Sear, Joseph M. Wheaton and Stephen E. Darby Historical channel modification and floodplain forest decline: implications for conservation and restoration of a large floodplain river – Willamette River, Oregon Stanley Gregory Restoring riverine landscapes at the Drau River: successes and deficits in the context of ecological integrity Susanne Muhar, Mathias Jungwirth, Gu¨ nther Unfer, Christian Wiesner, Michaela Poppe, Stefan Schmutz, Severin Hohensinner and Helmut Habersack
Subject index
703 739
763
779
809
List of contributing authors Note: Bold names indicate the corresponding authors. Walter Bertoldi Dipartimento di Ingegneria Civile e Ambientale, University of Trento, Trento, Italy Harley Betts
Landcare Research, Palmerston North, New Zealand
Carter Borden
Center for Ecohydraulics Research, University of Idaho – Boise, USA
Gary Brierley School of Geography and Environmental Science, University of Auckland, Auckland, New Zealand Andrew Brooks Centre for Riverine Landscapes, Griffith University, Nathan, Queensland, Australia Thomas Buffin-Be´langer Module de ge´ographie, De´partement de biologie, chimie et ge´ographie, Universite´ du Que´bec a` Rimouski, Canada Michael Burke
Center for Ecohydraulics Research, University of Idaho – Boise, USA
Michael Church Department of Geography, University of British Columbia, Vancouver, British Columbia, Canada,
[email protected] Tom J. Coulthard Department of Geography, University of Hull, Hull, UK,
[email protected] Stephen E. Darby
School of Geography, University of Southampton, Highfield, UK
Martin Detert Institute for Hydromechanics (IfH), University of Karlsruhe, Germany,
[email protected] Panos Diplas Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, USA,
[email protected] Mark K. Dixon USA
USDA Forest Service, Rocky Mountain Research Station, Fraser,
Maurice J. Duncan
NIWA, Christchurch, New Zealand
List of contributing authors
xiv
Brett C. Eaton Department of Geography, The University of British Columbia, Vancouver, British Columbia, Canada Rob Ferguson Department of Geography, Durham University, Durham, UK,
[email protected] Robert Francis London, UK
Department of Geography, Kings College London, Strand.
Kirstie Fryirs Department of Physical Geography, Macquarie University, North Ryde, NSW, Australia David Gilvear School of Biological and Environmental Sciences, University of Stirling, UK,
[email protected] Basil Gomez Geomorphology Laboratory, Indiana State University, Terre Haute, Indiana, USA Stanley Gregory Department of Fisheries & Wildlife, Oregon State University, Corvallis, Oregon, USA,
[email protected] Angela Gurnell
Department of Geography, Kings College London, London, UK
Helmut Habersack Institute of Water Management, Hydrology and Hydraulic Engineering, Department of Water, Atmosphere and Environment, BOKUUniversity of Natural Resources and Applied Life Sciences, Vienna, Austria,
[email protected] Marwan A. Hassan Department of Geography, The University of British Columbia, Vancouver, British Columbia, Canada,
[email protected] D. Murray Hicks
NIWA, Christchurch, New Zealand,
[email protected] Dan L. Hogan British Columbia Ministry of Forests, PO Box 9519, Station Provincial Government, Victoria, British Columbia, Canada Severin Hohensinner Institute of Hydrobiology & Aquatic Ecosystem Management, Department of Water, Atmosphere & Environment, BOKU – University of Natural Resources and Applied Life Sciences, Vienna, Austria Joanna Hoyle Department of Physical Geography, Macquarie University, North Ryde, NSW, Australia,
[email protected] Martin Jaeggi River Engineering and Morphology, Ebmatingen, Switzerland,
[email protected] List of contributing authors Gerhard H. Jirka Germany
xv
Institute for Hydromechanics (IfH), University of Karlsruhe,
Klaus Jorde Center for Ecohydraulics Research, University of Idaho – Boise, USA,
[email protected] Mathias Jungwirth Institute of Hydrobiology & Aquatic Ecosystem Management, Department of Water, Atmosphere & Environment, BOKU – University of Natural Resources and Applied Life Sciences, Vienna, Austria Mio Kasai Australia
Department of Physical Geography, Macquarie University, NSW,
Yoichi Kawaguchi Aqua Restoration Research Center, Public Works Research Institute, Gifu, Japan Scott King USA
Center for Ecohydraulics Research, University of Idaho – Boise,
Michael Klar Robert Bosch GmbH; formerly, Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg, Germany Nicolas Lamouroux CEMAGREF, UR Biologie des Ecosyste`mes Aquatiques, Lyon, France,
[email protected] Jill Lancaster Institute of Evolutionary Biology, School of Biological Sciences, University of Edinburgh, Edinburgh, UK. Stuart N. Lane
Department of Geography, University of Durham, Durham, UK
John Lewin Institute of Geography and Earth Sciences, University of Wales, Aberystwyth, UK Thomas E. Lisle USDA Forest Service, Pacific Southwest Research Station, Arcata, California, USA,
[email protected] David S. Luzi Department of Geography, The University of British Columbia, Vancouver, British Columbia, Canada Mark G. Macklin Institute of Geography and Earth Sciences, University of Wales, Aberystwyth, UK Mike Marden
Landcare Research, Gisborne, New Zealand
Tomomi Marutani Japan
Graduate School of Agriculture, Hokkaido University, Sapporo,
List of contributing authors
xvi
Glenn Moglen Department of Civil and Environmental Engineering, University of Maryland, College Park, USA Erik Mosselman Delft University of Technology & WL|Delft Hydraulics, Delft, The Netherlands,
[email protected] Susanne Muhar Institute of Hydrobiology & Aquatic Ecosystem Management, Department of Water, Atmosphere & Environment, BOKU – University of Natural Resources and Applied Life Sciences, Vienna, Austria,
[email protected] Futoshi Nakamura Graduate School of Agriculture, Hokkaido University, Sapporo, Japan,
[email protected] Daisuke Nakano Japan
Graduate School of Agriculture, Hokkaido University, Sapporo,
Karen Nelson Department of Entomology, University of Maryland, College Park, USA Vladimir Nikora Engineering Department, Kings College, University of Aberdeen, Aberdeen, UK,
[email protected] Mike Page Institute of Geological and Nuclear Sciences, Lower Hutt, New Zealand,
[email protected] Margaret Palmer
UMCES Chesapeake Biological Laboratory, Solomons, USA
Gary Parker Department of Civil and Environmental Engineering and Department of Geology, University of Illinois, Urbana, USA,
[email protected] Thomas Parkner Graduate School of Agriculture, Hokkaido University, Sapporo, Japan Dave Peacock
Gisborne District Council, Gisborne, New Zealand
Herve´ Pie´gay University of Lyon, CNRS-UMR 5600 EVS, Site Ens-lsh, Lyon, France,
[email protected] Jim Pizzuto Department of Geology University of Delaware, Newark, USA,
[email protected] Michaela Poppe Institute of Hydrobiology & Aquatic Ecosystem Management, Department of Water, Atmosphere & Environment, BOKU – University of Natural Resources and Applied Life Sciences, Vienna, Austria Ian Reid
Department of Geography, Loughborough University, UK
List of contributing authors
xvii
Stephen P. Rice Department of Geography, Loughborough University, UK,
[email protected] Massimo Rinaldi Dipartimento di Ingegneria Civile e Ambientale, Universita` di Firenze, Firenze, Italy,
[email protected] Sandra E. Ryan USDA Forest Service, Rocky Mountain Research Station, Fort Collins, USA,
[email protected] Nicholas Scheidt USA
Center for Ecohydraulics Research, University of Idaho – Boise,
Stefan Schmutz Institute of Hydrobiology & Aquatic Ecosystem Management, Department of Water, Atmosphere & Environment, BOKU – University of Natural Resources and Applied Life Sciences, Vienna, Austria David A. Sear soton.ac.uk
School of Geography, University of Southampton, UK, D.Sear@
Ina Seydell Institute of Hydraulic and Water Resources Engineering, University of Technology Darmstadt, Germany,
[email protected] Hafez Shaheen
An-Najah National University, Palestine
Kees Sloff Delft University of Technology & WL Delft Hydraulics, Delft, The Netherlands Bonnie J. Smith Department of Geography, The University of British Columbia, Vancouver, British Columbia, Canada Michal Tal St Anthony Falls Laboratory, National Center for Earth-Surface Dynamics, University of Minnesota, Minneapolis, MN, USA Noel Trustrum Zealand
Institute of Geological and Nuclear Sciences, Lower Hutt, New
Marco Tubino Dipartimento di Ingegneria Civile e Ambientale, University of Trento, Trento, Italy,
[email protected] Gu¨nther Unfer Institute of Hydrobiology & Aquatic Ecosystem Management, Department of Water, Atmosphere & Environment, BOKU – University of Natural Resources and Applied Life Sciences, Vienna, Austria Ben E. Wawra Institute of Hydraulic and Water Resources Engineering, University of Technology Darmstadt, Germany
List of contributing authors
xviii Chris Welcker USA
Center for Ecohydraulics Research, University of Idaho – Boise,
Thomas Wenka Federal Waterways Engineering and Research Institute (BAW), Karlsruhe, Germany Richard Westaway UK Joseph M. Wheaton
Halcrow Group Limited, Burderop Park, Swindon SN4 0QD,
School of Geography, University of Southampton, UK
Christian Wiesner Institute of Hydrobiology & Aquatic Ecosystem Management, Department of Water, Atmosphere & Environment, BOKU – University of Natural Resources and Applied Life Sciences, Vienna, Austria Peter Wilcock Department of Geography and Environmental Engineering, Johns Hopkins University, Baltimore, USA Nigel Willby Stirling, UK
School of Biological and Environmental Sciences, University of
Ellen Wohl Department of Geosciences, Colorado State University, Fort Collins, CO, USA,
[email protected] Bart#omiej Wyz˙ga krakow.pl
Polish Academy of Sciences, Kracow, Poland, wyzga@iop.
Hiroyuki Yamada Japan
Graduate School of Agriculture, Hokkaido University, Sapporo,
Ulrich C.E. Zanke Institute of Hydraulic and Water Resources Engineering, University of Technology Darmstadt, Germany Andre E. Zimmermann Department of Geography, The University of British Columbia, Vancouver, British Columbia, Canada
Gravel-Bed Rivers VI: From Process Understanding to River Restoration H. Habersack, H. Pie´gay, M. Rinaldi, Editors r 2008 Elsevier B.V. All rights reserved.
3
1 Multiple scales in rivers Michael Church
Abstract Rivers are characterized by multiple scales of length and time. A viable theory of river behaviour must reconcile the various processes that occur at different scales. Scales of turbulent fluid motion are determined by the properties of the fluid, while the texture of boundary materials formally scales criteria for resistance to flow and sediment entrainment. The macroscale limit of turbulent motion is the scale at which the flow detects its confining boundaries. The size of the channel is determined by how much water the channel must pass and is summarized by channel width. Channel scales also depend on the nature and magnitude of sediment fluxes and the valley gradient down which they must be passed, while the evolution of channel morphology is directed by its interaction with the persistent secondary circulation. From these conditions a set of scales is derived that define the channel state. At scales between that of channel width and some limit scale set by the larger landscape, river channel pattern may exhibit scale-free (self-similar) behaviour while, at still larger scales, river systems are subject to topographical constraints set by valley form and bedrock structure. The latter conditions are mainly externally set and contingent. Superimposed on these physical scales is a set of ecological scales expressed by aquatic organisms. These are derivative insofar as life is evolutionary and adaptive but, in this area, there remains a great deal to learn.
1.
Introduction
Rivers are the product of turbulent stream flow over myriad granular elements, vegetable matter, and solid refractory materials under strong, irregular forcing on effective timescales that range from seconds to centuries. They are complex systems because they are characterized by multiple scales of time and length that define a tightly integrated hierarchical set of subsystems, each of which exhibits some range of scale-free behaviour. A viable theory of river behaviour must reconcile processes that occur at different scales. It must also reconcile intrinsic dynamical scales – ones E-mail address:
[email protected] ISSN: 0928-2025
DOI: 10.1016/S0928-2025(07)11111-1
Michael Church
4
associated with process – with extrinsic scales imposed by the materials that make up the river boundary. A successful analysis must demonstrate the consistency of fluvial processes across scales whilst providing us with a satisfactory basis for understanding. Rivers surely represent one of the more difficult problems in physical science. The purpose of this paper is to explore the hierarchy of scales that must be addressed in order to make progress toward understanding rivers and to examine some of the connections amongst them. These scales pose certain constraints to practical modes of analysis. Some constraints arise from the state of our technology, but others appear to be quite fundamental insofar as they are connected with the information that it appears possible to have about the river. The discussion will remain elementary: the study of scales in fluvial phenomena has remained almost entirely empirical, and it appears most important to focus attention on what might be the fundamental scales of interest. First, we must establish what is a scale in a physical problem.
2.
Scales, scaling, and parameterization
The ‘‘scale’’ of a phenomenon is widely but informally recognized as the (order of) magnitude, in length and time, of the principal elements and/or processes involved. In particular problems, other dimensions – for example, mass – may also be relevant. By this definition, we recognize the scale of turbulent phenomena, for example, to fall approximately within the range 104–101 m, while stream channels fall characteristically within the range 100–103 m (in width). More formally, ‘‘scaling’’ a problem entails the selection of intrinsic reference quantities (scales) so that each term in the dimensional equations that describe the problem is transformed into the product of a constant factor that closely estimates the term’s order of magnitude and a dimensionless factor of order 1.0. An ‘‘intrinsic’’ reference quantity is one that is endogenous to the problem, that is, one that arises directly from the physical properties of the medium and is therefore universal. The length scale, n/u, in which n is the kinematic viscosity and u the shear velocity, represents an intrinsic reference quantity for problems associated with the small scales of turbulence – the limit of turbulent motions set by fluid viscosity. The laminar sublayer, for example, is scaled as uys/n, where ys is the dimensioned sublayer thickness. It is increasingly recognized that many phenomena occupy some range of scales specified by separate upper and lower limits. Within that range, the phenomena may exhibit essentially scale-free or ‘‘scaling’’ behaviour. The identification of ranges of self-similar behaviour has also come to be known as ‘‘scaling’’. Scaling behaviour has received much attention lately, but it seems that the more fundamental knowledge about a phenomenon remains with the defined limit scales. It is not always obvious how to choose scales. Whilst it appears most appropriate to choose them in the fundamental dimensions of mass, length and time, it is often convenient to select derivative quantities, such as reference velocities or fluxes. Very often, problems in fluvial hydraulics are not completely specified by known equations, and dimensional analysis is used to make a formal selection of appropriate
Multiple scales in rivers
5
parameter groups that include suitable scaling quantities. Dimensional analysis guarantees the requirement that properly scaled terms be rational (dimensionally balanced). ‘‘Parameterization’’ is the selection of a convenient (i.e., easily measured) surrogate variate that tracks the behaviour of a more fundamental variate of interest. The substitution is commonly effected via approximate theoretical arguments or by study of empirical correlations. Such procedures may be adopted to avoid the complications of analyzing complex subsystems. It is possible that such procedures can be used to discover appropriate scaling quantities. In this paper, most of the scales are descriptive and geometrical ones since we are seeking, in the main, to identify characteristic length and time scales of fluvial processes. They have mostly been identified by empirical or formal means rather than from rational theory.
3.
The scales of turbulent flow
The classical construction of turbulent flow holds that the phenomenon is essentially random and the description of it, necessarily statistical. Two important length scales have been associated with this view, a turbulent microscale – the limit scale for turbulent motion at which viscous dissipation of kinetic energy becomes dominant – and an integral length scale, or macroscale, the largest scale at which spatial correlation persists in the flow. A microscale pertinent to fluvial processes is n/u, noted above. (This quantity corresponds with neither of the usually quoted energetic turbulent microscales.) The usual point velocity measurement technique R k leads to an approximation of the macroscale via the integral timescale T E ¼ o RðtÞdt, where R(t) denotes the correlation of velocity (or of some other property of the flow) at increasing temporal intervals, t, k is defined by the condition R(k)E0, and subscript E an Eulerian reference frame. Adopting the ‘‘frozen turbulence’’ convention (Taylor, 1935), so that a space-for-time substitution may be effected, LE ¼ ou4 TE then gives the macroscale, where ou4 is the temporal mean flow velocity. This scale has been interpreted as the maximum dimension of a turbulent eddy in the direction of the measurement (usually downstream). Unlike the microscale, it betrays no overt clue about the reason for its existence. In the 1950s, ideas began to circulate about large-scale structure in supposedly random turbulence. In the west, early work consisted of attempts to interpret the macroscale in physical terms, and it was motivated by the desire to understand the compound form of turbulent velocity profiles (for a review of early work see Cantwell, 1981). On the basis of correlation studies and visualization work, Townsend (1970, 1976) proposed relatively early on that large-scale turbulent structures took the form of inclined contra-rotating cylinders of circulating water, or inclined cones, that extended through the water column. The latter conception acknowledges that structures originating in the near-bed region of high shear might grow in size as they move away from the boundary. Velikanov (1949) proposed a sequence of depth-scaled roller eddies. Later Russian work (Dement’ev, 1962; Makaveev, 1964; see Shvidchenko and Pender, 2001, for a brief summary of
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Michael Church
additional work) apparently confirmed this interpretation, but found that the features were streamwise elongated. American experimental work focused on the near-wall region where turbulent kinetic energy production was found to be concentrated (Klebanoff, 1954) and led to the ‘‘Stanford model’’ (Kline et al., 1967; Corino and Brodkey, 1969) of bursting streaks. The model of uplifted (‘‘ejected’’), paired streaks of low-velocity water, which are replaced by an inrushing ‘‘sweep’’ of high-velocity water, was initially supposed to control the net production of turbulent energy in shear flow and to be a wall-associated phenomenon governed by the turbulent microscale. It was therefore a major shock when Rao et al. (1971) reported that the burst period scales with outer region variates uN and d, the free stream velocity and boundary layer thickness, with the mean dimensionless time between bursts being given by uNT/dE5. Moreover, this scaling appeared to be characteristic throughout the depth of the flow and the large eddies appeared to be advected at a rate comparable with the mean flow, so their spacing and, conceivably, their size should be approximately LE5d. Grass (1971), in a critical contribution that compared turbulence characteristics over smooth and rough walls (the latter comprising 9 mm pebbles), showed that ejections and inrushes were present regardless of surface roughness. The near-wall flow over a fully rough boundary must be substantially different from that over a smooth wall, yet the basic organization of the fluid motion appears to remain largely unchanged. One is forced to the conclusion that the bursting process occurs in turbulent shear flow irrespective of the boundary condition. One speculates that the reservoir of slow-moving fluid resident in the laminar sublayer of smooth-wall flows is replaced by reservoirs of low-momentum fluid trapped amongst the elements of rough walls (Kirkbride, 1993). So the burst model has become a standard representation for momentum transfer and structure throughout turbulent shear flows (see, e.g., Jackson, 1976; Yalin, 1992; Best, 1993), with the implication that the wall-based phenomena associated with turbulent energy production control the character of the entire turbulent flow. This appearance raises the questions whether the scaling of Rao et al. represents a suitable turbulent macroscale, and what is its relation to LE. Subsequent experimental studies and initial field studies have yielded additional estimates of the scale of coherent structures, a summary of which is given in Table 1.1. The results must be appraised with considerable reservation. First, d is flow depth, d, not boundary layer depth. Since most rivers have truncated boundary layers (i.e., depth is not sufficient for the boundary layer to fully develop), the true value of d remains unknown. Similarly, u mostly is U, the profile averaged mean velocity of the flow, rather than uN. The effects of these two biases tend to mutually cancel, but the underestimate of depth likely is generally the greater so that computed values may be fractionally high. Most of the values listed for L/d fall in the range 2–7, which is comparable with the range 3–7 that has been reported (Jackson, 1976). A more fundamental problem is that turbulent bursts and large eddies actually occur intermittently and the distribution of their recurrence period is skewed (see Fig. 1.1) – in fact, exhibits a scaling range. So it is not clear, on the analysis of the complete velocity record, just what may be true ejection events, hence just what is the actual frequency of the burst cycle. Investigations might fail to detect certain events – inflating the time and length scales – or may mix various derivative eddies with the bursts, producing negatively biased estimates.
Multiple scales in rivers Table 1.1.
Data of macroturbulent eddy scales. ua
db
Dc
L/dd
Remarks
0.07 0.73 0.38–0.98
0.04 0.12 0.03–0.10
– 4.8 2–8
2.1 3.0 4.770.2
0.3 m wide flume 0.6 m wide flume 0.3 m wide; n ¼ 18
0.36 0.34
0.35–0.40 0.28
33 30–50
6.7–6.9 9.6
Gravel-bed river Gravel-bed river
0.45–0.67
0.35–0.60
30–45
2–6e
Gravel-bed river
1.5–1.7
1.7–2.1
6.470.1
Jackson (1976)
0.64–1.42
0.55–5.6
7.871.5
Kostaschuk et al. (1991)
1.0
11
3.9–4.6
n ¼ 3; 1 datum deleted 0.2 m dunes; n ¼ 14 2 m dunes
Source Flume studies Komori et al. (1982) Cellino and Graf (1999) Shvidchenko and Pender (2001) Gravel-bed rivers Buffin-Be´langer et al. (2000) Paiement-Paradis et al. (2003) Roy et al. (2004) Sand-bed rivers Korchokha (1968)
a
7
1
Values in m s ; should be uN, but most values are mean velocities, Jackson and Kostaschuk values are surface velocities. b Values in m; all values are flow depths. c Values in mm; values are D50 of mixture or size of homogeneous material. d Calculated by writer as uT/d. T is time between successive observed structures or mean duration for passage of a structure. e Full range is 1–10 due to two excentric values. Many determinations were made from data collected by three independent methods. See source for details.
The scaling of Rao et al. is in fact very closely allied with the Strouhal number, the scaled interval for eddy shedding from a bluff object (in which the classical constant is 2p, but the figure is lower at high Reynolds number). Eddies certainly are shed from individual protruding objects on rough beds, and so it appears quite possible that the apparently universal phenomenon of macroturbulent bursting represents a general phenomenon of eddy production over a rough boundary – the consequence of a sort of ‘stick and slip’ motion of the fluid over the surface. Jackson (1976) investigated the relation between evident bursting frequencies and the Eulerian macroscale using the turbulence measurements collated by McQuivey (1973) and concluded that they are essentially equivalent. On that evidence, it appears that L ¼ uNT might represent a suitable turbulent macroscale. A deeper issue is presented by the appearance, in Fig. 1.1, that the occurrence of turbulent eddies is scale-free over the range between the scale of their generation near the bed and some multiple of channel depth. This reinforces the notion that channel depth functions in some way as a meaningful limit scale for turbulent eddies. (Most studies of macroturbulent structure to date have been conducted in essentially 2-D flows; on the other hand, available information on the eddies’ lateral structure also implicates d as a suitable unit scale.) The balance of evidence suggests that 3rL/ dr6, perhaps, but it is possible that the upper limit value should be preferred, which would tend to confirm or magnify the original estimate of Rao et al. (1971), and this would no longer be a ‘‘characteristic’’ scale, but the limit of a scaling range.
Michael Church
8 103
NUMBER OF EVENTS
102
101
100
10-1 -2 10
10-1
100
101
DURATION (S) Figure 1.1. Frequency distribution of the duration of burst-type events in a shallow flow in a gravel-bed river over 30–45 mm cobbles (R. Eaton Nord, Que´bec, Canada; data from Roy et al., 2004). Closed symbols indicate the record of all events initiated by an upward passage of the velocity past ou4; open symbols indicate the same record restricted to events initiated when velocity exceeds ou4+1.3su, the standard deviation of velocity. The plot can be scaled to eddy length by multiplying by the mean velocity, 0.62 m s1. At the low-frequency end, the two plots merge: it is most likely that eddies at this scale reflect the burst period. (Reproduced with permission from Cambridge University Press.) Similar data have been presented by Jackson (1976) and by Lapointe (1992) for flows in sand-bed rivers with dunes. The plots always exhibit significant ranges of self-similarity.
4.
Roughness scales
Turbulence production in river channels is complicated by the fact that river flows are shear flows over a more or less rough boundary. In gravel-bed rivers, the boundary certainly is rough; that is, the individual clastic elements forming the boundary represent a significant source of resistance to the flow. This fact is important when one considers the application of theoretical and experimental results on turbulence to flows over gravels. Most experimental studies of turbulence have been conducted over smooth boundaries because the chief motivation has been to
Multiple scales in rivers
9
understand flows over surfaces such as airfoils, turbine blades, and other machinery. The capacity of the rough boundary to generate eddies directly at scales determined by the scale of the boundary elements creates circumstances that may be significantly different from those investigated in most fluid mechanical experiments. In the region immediately above a rough surface, the mean profile of turbulent shear flow has been found to take the form u 1 30y (1.1) ¼ ln un k ks pffiffiffiffiffiffiffiffi in which kE0.41 is a constant (von Ka´rma´n’s constant), un t=r a velocity scale (the shear velocity), and ks a roughness length scale. This equation is Prandtl’s ‘‘law of the wall’’ and shows that velocity is proportional to roughness-scaled distance (y) from the wall. When D/d-1.0, D being a characteristic bed material grain diameter, the description breaks down as the flow becomes a series of jets between the large roughness elements. Conversely, when the flow becomes deep, an outer layer develops above the wall layer. The logarithmic wall layer is often asserted to apply to the lower 15–20% of the flow but, over high roughness, logarithmic dependence often extends right to the surface, but with modified scaling (Fig. 1.2). The division of the flow profile is related to the phenomena of turbulent eddy production and dispersion in the flow. Production is concentrated at the base of the wall layer, but eddies remain highly coherent within the wall layer before dispersing upward, giving rise to a near-uniform distribution of fluid shear within the wall layer. Near the bed, the flow ‘‘sees’’ only the eddies produced locally but, higher up, the flow is influenced by advected and dispersing eddies generated from a more extended upstream area. The roughness of the bounding material of the channel has classically been scaled by reference to bed material grain size. The roughness length, ks, can be related to a zero-plane displacement, y0 – the distance above the entirely solid bounding plane at which the velocity becomes zero. If we scale distance by y0, we have y0 ¼ ks/30. On granular boundaries, both ks and y0 are difficult to define physically so that, conventionally, ks is parameterized as kD, k being a constant of proportion or ‘‘grain size multiplier’’. Gravel beds consist of a spectrum of grain sizes, the larger of which protrude significantly into the flow, so it is usual to adopt some large grain size (e.g., D84; D90) as the appropriate surrogate scale. This long-adopted practice is supported by the observation that the large grains support a high proportion of the entire shear stress exerted on the channel bed. van Rijn (1982) found from literature review that, for D90, the range of values assigned to k varies from 1 to 10. Clifford et al. (1992) demonstrated from measurements that the commonly quoted value ks ¼ 3.5D84 yields reasonable results over a relatively featureless gravel bed. However, no single constant is apt to be robust, since the effective roughness depends on not only grain protrusion but also the net effect of aggregate grain structures, so there is no welldefined single scale. k is, in effect, a scale adjustment to cover a number of complexities of the boundary. Integration of equation (1.1) yields U 1 11d (1.2a) ¼ ln un k ks
Michael Church
10 10 surface
5.0
y - ks (cm)
2.0
1.0
1.9 cm above bed
0.5
1/20
1/16
0.2
1/8 1/80 1/12 0.1 10
20
30
40
U (cm/s) Figure 1.2. Velocity profiles over channel beds with high roughness (after Nowell and Church, 1979): experimental data using regularly arrayed roughness elements of 0.9 cm height and variable spacing. Fractions given for the individual profiles represent roughness density. In this representation, roughness length was assumed to be 0.9 cm. The profiles clearly show two segments, the lower of which corresponds with a zone of uniform shear for roughness densities41/48. Arbitrary adjustment of the roughness length can straighten the profiles, which yields a single velocity scale, but there is no physical reason to perform such an adjustment. The alternative is to accept distinct velocity scales, u, for the wall region and the outer region.
Multiple scales in rivers
11
and this result was further specified by Keulegan (1938) for a trapezoidal channel of finite width as U 1 12:2R (1.2b) ¼ ln un k ks in which R is the hydraulic radius. This equation specifies the resistance to flow over the rough boundary by specifying the scaled mean velocity, again in relation to the roughness length scale. The roughness scale is closely allied with the relative roughness, R/ksd/D, which is a somewhat special quantity insofar as it forms the ratio of two important system scales. In gravel-bed rivers, grain size appears to scale significant bed structures that further modify the resistance to flow. Most of the time, bed material moves in gravelbed rivers in a regime of size-selective partial transport (Wilcock and McArdell, 1993). The finer materials are preferentially transported in comparison with the larger materials. The largest grains of all may rarely be entrained. Those large clasts become keystones for imbricate accumulation of grain clusters (Brayshaw, 1984) which may ramify into lines (Laronne and Carson, 1976) and irregular reticulate networks (Church et al., 1998; from which the following description is taken). Most of the clasts that form such structures are larger than D84 of the bed material, and the keystones might correspond with some size of order D90 or larger. The ratio of structure spacing (diameter) to constituent clast diameter is of order 10:1, implying that the constituent stones occupy between 15% (linear features) and 25% (stonebound circles) of the bed. These values correspond with the fractional area (approximately 0.12oao0.25) indicated by Rouse (1965) from analysis of experimental results (and observed in the data of Fig. 1.2) to contribute most of the boundary frictional resistance to flow. These figures represent the range of concentrations for dominant roughness elements to produce intense wake interactions and strong turbulence production (Nowell and Church, 1979). The features appear to play a role in gravel-bed channels similar to primary bedforms in sand-bed channels. However, the latter appear to be scaled by d or d: the basis for scaling these emergent channel bed features probably is quite different in the two cases. An important distinction between them is sediment transport intensity – in the case of primary sandy bedforms, full bed mobility is achieved. In unusually powerful flows, full mobility is achieved in gravel-bed channels, and then similar, depth-scaled bedforms develop, but usually with only low amplitude relative to wavelength. Roughness scales have characteristically been estimated in terms of an equivalent grain size, D, since this is the most obvious length scale associated with the rough boundary. It is evident, however, that the real complexity of the boundary prevents any single, unequivocally identifiable scale from emerging. In light of this, some investigators have adopted a spectral approach to determining roughness scales (early work is summarized in Nikora et al., 1998). It has emerged that the standard deviation of bed elevation – in effect, the vertical dimension of bed roughness – is a robust length scale for homogeneously rough beds (Aberle and Nikora, 2006) and is a viable scale for estimating flow resistance even when D/d-1.0 (Smart et al., 2002; Aberle and Smart, 2003). But a significant portion of flow resistance – parameterized heretofore only through the use of the grain size multiplier – is associated with large
Michael Church
12
bedforms and with the channel geometry itself, so the problem of determining resistance to flow is, of itself, a problem with multiple scales.
5.
Scaling sediment transport
The significant fraction of stream sediment, for purposes of understanding alluvial channel form, is the bed material, the sediment that forms the bed and lower banks of the channel. Movement and deposition of this material alters the form of the channel. In gravel-bed channels, the displacement of bed material essentially corresponds with the movement of bedload. There is still no wholly rational theory from which to predict bed material or bedload movement. Since we require rational statements in order to study scaling, we follow many prior analysts in resorting to dimensional analysis. We consider the relevant variates r, the fluid density; rs, the sediment density; n, fluid viscosity; D, sediment particle diameter; d, water depth; t, the shear force per unit area imposed by the flow on the bed; g, the acceleration of gravity; and gb, the mass sediment transport rate per unit channel width. These variates yield five dimensionless groups: Re ¼ uD/n, the grain Reynolds number; t ¼ t/gr(s1)D, the Shields number; c ¼ gb/g1/2r(s1)D3/2, Einstein’s transport intensity; s ¼ rs/r, the sediment specific weight; and D/d, the relative roughness. s is effectively a material constant, and it is known from experiment that Re does not vary significantly within the range of gravel sizes. Hence, we have D (1.3) c ¼ f tn ; d t is, in effect, shear stress scaled according to D via the submerged particle weight, sediment specific weight remaining constant, which expresses the grain inertia. The important scale is, accordingly, the sediment grain scale (a reasonable result, but it emerges from the essentially arbitrary choice of D as a repeating variate in the dimensional analysis). In a fully alluvial channel, D constitutes an intrinsic scale of the system although, in many cobble- and boulder-bed channels, grain size of bed material is extrinsically imposed by material delivered from overbank by mass wasting. There exist a significant number of specific realizations of equation (1.3), in most of which the term in relative roughness is, at best, implicit. An important part of specifying this equation in bulk calculations is selecting the appropriate grain scale. The values usually chosen to scale t have been the central measures Dm and D50, mean and median size respectively, the latter being preferred perhaps because it is not so sensitive to the variable skewness of grain size distributions. It has been shown (Wilcock and Southard, 1989) that, for purposes of estimating a bulk measure of bedload transport, D50 fairly represents the texture of sediment mixtures. An alternative approach to estimating sediment transport, which has the merit of relating the phenomenon directly to the deformation of the channel, is to consider the distance of transport and the volume (or mass) of sediment taking part in the process.
Multiple scales in rivers A simple, empirically scaled characterization of this process is u d s s C ¼ ðs 1Þð1 pÞ ou4 D
13
(1.4)
in which C is sediment fractional volumetric concentration, us ¼ xp/t the sediment virtual velocity (i.e., the distance traveled, xp, per unit time, including rest periods), ds the depth of the active layer taking part in the transport, and p the bed porosity but can also be adjusted to account for the reduced spatial density of partial transport. The scales ou4 and D are both accessible. ds is not easily measured, but it is possible that it is approximately constant at dsED90 (Wilcock and McArdell, 1997). This transport scaling has not been investigated. The characteristic step length of bed material in transport has received far less attention than it deserves. The first systematic investigation was by Einstein (1937), who regarded particle displacement as a random process and conducted experiments to show that distributions of step lengths followed a gamma-related probability distribution. Tracing grains in natural streambeds is tedious and difficult, and it is only in recent years that a number of observing programs have returned results that can be interpreted to reasonably reflect the displacement of the material. Pyrce and Ashmore (2003a) summarized results and have shown (Pyrce and Ashmore, 2003b) that, under weak transport, the distribution of displacements is, indeed, local and stochastic, as Einstein supposed but, under stronger transport, grains cluster and the characteristic distance correspond with the pool-riffle spacing (Fig. 1.3) – that is, with the channel scale of transverse oscillation (discussed in the following section). This much makes elementary sense; bars are nothing more than aggregations of episodically mobile sediments. Nikora et al. (2002) have analyzed grain paths in more detail. Borrowing ideas from nonlinear statistical mechanics, they have defined local, intermediate, and global ranges of displacement. Local displacement refers to a single trajectory between two points of collision with the bed, whilst an intermediate displacement refers to a sum of local displacements without intervening rest. Global displacements describe the sum of more than one intermediate displacement with intervening rest periods. They presented a dimensional analysis of the problem that issued in the formal relation xp D tun ¼ f tn ; Ren ; ; (1.5) ks D D wherein, oxp4 is the mean distance traveled by a particle, t the travel time (including rest periods for the global range), and the balance of the terms are earlier defined. Ignoring Re, as usual, and supposing that ksED, or some constant proportion of it, as before, we obtain oxp4/D ¼ f[t, tu/D] with scale D, as one would expect. (Nikora et al. were actually interested in particle diffusion, hence in the higher moments of the particle position, but the scaling is similar.) Available data are restricted to experiments at fixed flows, hence fixed values of t, and fixed observing period, T, so that oxp4/D ¼ f[tu/D]. This scaling has not been investigated, but the results of Pyrce and Ashmore (2003b) indicate that there are ranges of behaviour in a manner analogous to those defined by Nikora et al. in the time domain.
Michael Church
14 0.15 a) very weak transport (n = 160)
0.10
RELATIVE AMOUNT OF TRACER MATERIAL
0.05
0.00 0.15 b) intermediate transport (n = 1264)
0.10
0.05
0.00 0.15 c) strongest transport (n = 670)
0.10
0.05
0.00 0.00
0.25
0.50
0.75
1.00
1.25
1.50
DISTANCE DOWNSTREAM, (λ;meander wavelength) Figure 1.3. Distributions of bed material displacements, scaled by l, under variable flow strength (ideal functions after Pyrce and Ashmore, 2003b; n ¼ number of experimental observations upon which the displayed distribution is based).
To this point, no distinction has been made amongst different grain sizes. Nikora et al. (2002) noticed that particle velocities do not vary systematically, at least over a restricted range of sizes, but systematic differences in travel distance have been demonstrated from field data (presumably for intermediate and global ranges) amongst grains that initially were unconstrained (Church and Hassan, 1992). GrainsoD50 tend to show only moderate variation in travel distance, but travel distance of larger grains declines rapidly with size. This behaviour likely reflects the effect of the scaled size D/D50, smaller grains being liable to be trapped by larger ones resident on the bed, whereas the travel of larger grains is limited mainly by their inertia in relation to flow strength. One supposes, then, that modulation of travel
Multiple scales in rivers
15
distance by grain size is a phenomenon of the partial transport regime. Church and Hassan showed that, as one would expect, the effects become stronger for grains that are restrained by clast structures.
6.
Channel scale
Once the flow detects the boundary, it is steered by the boundary and, in turn, it may shape the boundary by erosion, transfer and deposition of the sediments of which it is formed. This gives rise to ‘‘pinned’’, therefore persistent, secondary circulations. These circulations scale with the channel dimensions. Channel width is scaled by the flow that the channel must transmit, that is, by hydrology, and by bank materials. Therefore it is at least in part an extrinsic scale imposed on the fluvial system. (By an ‘‘extrinsic scale’’, I mean one established by processes – such as watershed hydrology – that do not establish a universal scale for the fluvial processes.) Water discharge represents one of the principal governing conditions imposed on river channels, the others being the quantity and caliber of sediment supplied to the channel from the drainage basin and the topographic gradient down which the fluxes of water and sediment must be passed. Together, these conditions establish the hydraulic geometry of the channel, including the depth and mean velocity. Fundamental connections exist between the channel scale and the scales of turbulent flow since the flow and channel gradient (specifically, the product rgQS, in which Q is the water discharge, and S the energy gradient of the stream) establish the rate at which potential energy must be transformed into kinetic energy and dissipated in the turbulent flow. Channel depth is arguably a more fundamental scale than width but it is not an intrinsic scale since the ratio of width to depth (the aspect ratio, w/d) again depends on material properties, in this case the bulk strength of the channel boundaries. Depth, however, appears to control the turbulent macroscale. Channel scale dynamics, in particular the phenomena associated with secondary circulations, are arguably the least well-understood aspect of fluvial processes, probably because measurements remain logistically demanding, hence difficult. The control of channel size by the flow is recognized in the well-established regime relation w p Q1/2 (Leopold and Maddock, 1953), which is easily the most consistent of the oft-quoted equations of hydraulic geometry. This suggests w as an extrinsic channel scale, and the equation has been called a ‘channel scale relation’. It is, indeed, an empirical scaling relation, but an incomplete correlation. The complete set of independent governing conditions for river channel form informs the hydraulic geometry. The strength of the bed and bank materials is independently effective principally through bank materials, which may be affected by cohesion, cementation, or vegetable material. A rational theory of river regime must encompass all of these factors. Approaches to river regime have been essayed by many authors (see Ackers, 1988; Huang and Nanson, 2000; Griffiths, 2003; Eaton et al., 2004, for varying recent approaches). In the present context, the analysis by Eaton et al. is interesting since results are presented in a general, scaled form. They solved available equations specifying flow continuity, flow resistance, sediment transport, and bank strength
Michael Church
16
subject to the condition that flow resistance be maximized and obtained a description of alluvial channel state in the scaled variates w/d, D/d, and t (Fig. 1.4). The length scales evidently are d and D. (It should be remarked that Eaton et al. made specific choices for parameterizing flow resistance, sediment transport, and bank strength. The choices were guided by a desire to characterize gravel-bed channels, but the form of the solution space is unlikely to depend specifically on those choices.) In the theory constructed by Eaton et al., equations of hydraulic geometry for given boundary materials (i.e., on a plane of constant bank strength) are approximately functions of Q, S, and D. The appearance of D reflects the dependence of channel form, within the constraints set by the governing conditions, on processes worked out at the scales of turbulent flow and sediment transport, which determine the channel dimensions within which the energy of the water is dissipated whilst passing the imposed sediment load. This dependence works through the total resistance to flow. There is no general analysis for form resistance and the usual means of parameterizing it has been to adopt a multiplier for grain size, as discussed in the last section. Flow that is steered by the boundary gives rise to ‘‘pinned’’ eddies. These are the persistent secondary circulations that have been classically described (see review in Leliavsky, 1956) but are still not well analyzed. Eddies with transverse axes are potentially limited in their growth to order d, while those with vertical axes might grow to order w. Initiated by velocity gradients near the banks that give rise to pressure gradients within the flow, the combination of these motions gives rise to
0.25 φ' = 60o
0.20 0.15
φ' = 50o
* 0.10
φ' = 40o
0.05 1
320 0.1
220
D/d 120 0.01
W/d
20
Figure 1.4. Alluvial state diagram (Eaton et al., 2004). j0 represents bank strength as measured by the effective friction angle. Each point on a plane of constant j0 represents an alluvial state characterized by unique Froude number, gradient (S), and sediment concentration (Qb/Q). The roles of t and S are equivalent and they may substitute for each other (reproduced with permission from John Wiley and Sons).
Multiple scales in rivers
17
helical circulations of channel scale with downstream axial orientation. These features may persist for some distance along the channel whilst having a subordinate dimension of order d, but their streamwise scale has not been independently established. They are delimited by channel geometry, but they simultaneously direct the currents that modify the geometry. The visually dominant form of deformation in all channels with erodible boundaries is lateral oscillation, whether it is expressed by a pool-riffle sequence (Thompson, 1986) with wavelength l/2 or by more or less regular meanders with wavelength l. Superficially, oscillatory behaviour, in the range 5wolo15w (Leopold et al., 1964), scales reasonably with channel width, which means that it can also be related to discharge. However, the origin of this scaling – indeed the question whether it is an appropriate scaling – remains obscure. The origin must be hydrodynamical since the homologous scale is present even in purely erosional channels in ice or bedrock (Leopold and Wolman, 1960) where, furthermore, the phenomenon can exhibit a 3-D, ‘‘corkscrew’’ character. But, since alluvial channel deformation entails sediment mobilization and redistribution, the scale in such channels must in some way be associated with sediment transfer, as demonstrated by the analyses of Pyrce and Ashmore. The scaling does not, evidently, arise directly from turbulent scales. Yalin (1977) proposed the existence of width-scaled eddies (or secondary flows) originating from bank drag, by analogy with bed-generated eddies, for which a Strouhal-type shedding frequency might be appropriate, but the idea has not been much pursued (see, however, Clifford, 1993). Lateral diffusion of communicated information – in this case, represented by bed material transfer – may provide a physical basis to understand the expression of channel deformation. The most rapid pffiffiffiffiffiffi communication of information in the flow occurs as a gravity wave with vg ¼ gd , where vg denotes a cross-channel wave velocity. Suppose (see Eaton et al., 2006) that the net lateral spread of sediments proceeds at the rate vp ¼ avg, 0oao1. Then the material propagates across the channel with angle tan1(vp/oa0 u4) ¼ tan1(a00 /Fr), where Fr is the Froude number, and a0 , a00 are also fractional constants. If material originates in a scouring zone near one bank, and spreads to the opposite bank after a distance l/4 (realizing that the pool-riffle spacing is l/2 and that entrained material will, on average, move half that distance), then, from geometry, w/(l/4) ¼ a00 /Fr and l ¼ (4Fr/a00 )w. This result may be compared with that from a linear stability analysis presented by Parker and Anderson (1975) and modified by Ikeda (1984) which pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gave l ¼ (5Fr/B)w, in which B ¼ Sðw=dÞ. These speculations provide a possible approach to investigate whether bed material diffusion is directly associated with the establishment of riffle scaling distance, but there are, at present, few data with which to pursue the matter. Investigating the ratio l/w ¼ 4Fr/a00 (which confines attention to simple channels), limited data of Lewin (1976) and of Eaton and Church (2004) suggest that, for FrE0.85, aE0.5, l/ wE6.8, while experiments by Garcia and Nino (1993) in which l/wE9 suggest that a00 varies with Fr. These results are consistent with empirical experience on planform oscillation of rivers. Nevertheless, the arguments remain essentially formal and the underlying assumption is not established. A special case arises when D/d-1, so that individual large sediment grains or aggregations of a few grains are major, semi-stable form elements of the channel
Michael Church
18
boundary. This situation occurs most frequently on relatively steep gradients where large clasts are introduced into the channel by mass wasting from the adjacent valleyside slopes. The large grains control most or whole of the drop in the water surface, creating step-pool features with a natural scaling LED/S, in which L is steppool length and both D and S are imposed.
7.
Channel pattern
Channel units occur repeatedly in homogeneous reaches and exhibit elements of scale-free behaviour within specifiable limits. The evolution of channel form depends strongly on prior configuration through its influence on sediment-directing circulation, so that an element of contingency enters into the analysis of a particular channel and reach-length river channel geometry does not exhibit a single, simple scale. This fact has been recognized in freely meandered rivers for a long time (Speight, 1965). Introduction of the concept of fractal geometry (Mandelbrot, 1977) opened a novel means to analyze scale-transcending geometry. Both the superposed sequence of bends in single-thread channels (Snow, 1989) and the nested sequence of bars in braided channels (Sapozhnikov and Foufoula-Georgiou, 1996) exhibit fractal ranges of dimension. But whereas mathematical fractals have no defined scale limits, the scale-free (self-similar or self-affine) behaviour of real objects has distinct limits imposed by material or energy constraints, or by larger scale features. The limits of selfsimilar scaling ranges may be more meaningful than the fractal character itself since these may suggest significant limit scales for landscape processes (and certainly for modeling them). Nikora (1991) suggested that channel and valley width define the lower and upper limits of fractal ranges for river planform geometry. The lower limit is self-evident; the upper presumably defines a limit beyond which the planform is constrained in its mean direction of development hence, while larger structures might remain selfaffine, they could not remain self-similar. Beauvais and Montgomery (1996) found that the largest meander wavelength present bounds the possible self-similar scaling domain; in many instances, this waveform is, in turn, bounded by valley width. They also found that valley width appears to influence the magnitude of the fractal dimension itself. In narrow valleys, it is not possible for the planform to become strongly nonlinear. They discovered in some of their rivers an intermediate scale at which the fractal property changed (so the planform exhibited two distinct scaling ranges), and found that this was determined by meander amplitude. In general, three scaling regions might be defined (Nikora et al., 1993). Near the physical lower limit, the channel often is nonfractal, or ‘‘smooth’’, in its behaviour. This region would normally correspond with the pool-riffle sequence. At larger scales, the pattern passes into a fractal scaling region, which ultimately is limited by larger scale landscape constraints on pattern development. Beyond that, behaviour may be self-affine, so long as the river remains under the influence of similar governing conditions. Empirical scales for delimiting these domains might be w and Wv, the latter denoting valley floor width, but entirely unconfined channels do not exhibit an infinite fractal range.
Multiple scales in rivers
19
Divided channels present a dramatically different morphology than do singlethread ones but questions related to the scaling of channel pattern remain rather similar. Since the basic building blocks of alluvial channel pattern are, in all cases, bars and pools, this is not surprising. Ashmore (2001) emphasized the affinities between single thread and braided channels and identified mean braid bar length as a fundamental scale analogous to pool-riffle length (or meander length) in singlethread channels. But a range of bar scales is obviously present. Self-affinity of bar and channel geometry in braided channels is summarized in Paola and FoufoulaGeorgiou (2001). A self-similar range has been identified by Walsh and Hicks (2002) with upper limit of order Wb, the braidplain width. At the lower end, meaningful channel division would be limited by some multiple of grain size (which would limit the occurrence of aggregate sediment deposits) and by stream competence, hence possibly by relative roughness. At the upper end, a limit in downstream affinity is apt to be set, as for meanders, by topographic space. An interesting study by Sapozhnikov and Foufoula-Georgiou (1997) demonstrates that time scaling across changes in length scale in a developing braided channel network is characterized by tr ¼ l 1=2 r , in which tr and lr are the time and length ratios of the compared examples, respectively. That is, changes at different scales in a self-similar or self-affine channel obey Froude scaling. Within limits posed by the governing conditions – particularly, in this case, limits posed by the boundary materials – comparisons across scales within the channel network constitute classical Froude models of each other. This observation goes some considerable way to explain the strongly suggestive outcomes of many early river modeling exercises that were not formally scaled at all. At the still larger scales of the drainage basin, stream channels are organized into tree-like, hierarchical drainage networks. Since water flows follow the line of steepest accessible descent, the drainage network is subject to topographical constraints set by landscape geometry, bedrock structure, hydroclimate, and drainage basin size. These conditions are mainly externally set and contingent in nature. Nonetheless, fractal self-similarity of drainage networks has been demonstrated (Tarboton et al., 1988; Rodrı´ guez-Iturbe and Rinaldo, 1997). Such appearances can be justified in terms of the necessarily space-filling behaviour of channel networks in order to drain the land surface, and can be simulated using various rules for drainage extension or network composition. At the scale of processes in river channels, however, one is concerned with individual confluences and with the distance between successive significant confluences (the limit length for a homogeneous reach). Over longer reaches the channel network structure is likely to be determined by landscape history – by inheritance – rather than by contemporary processes. The valley networks within which rivers run have long, complex histories that are not usually dominated by the contemporary river. A new set of landscape scales may be constructed to define valley networks, but these take us beyond the scope of this paper and will not be pursued.
8.
Ecological scales in rivers
A river appears, superficially, to be a relatively hostile environment for most life. The incessant, strongly turbulent flow requires strong rooting to resist, or significant
20
Michael Church
expenditure of energy to withstand. Aquatic organisms seek means to minimize the necessary expenditure of energy to maintain position and to conduct their activities. Beyond anatomical features such as streamlined shape, holdfast mechanisms, and low-resistance surfaces, their evolved behaviour patterns lead them to seek out special environments and to adapt their life-cycle activities to certain seasons and conditions of the river so that energy may be conserved. In these activities, aquatic animals, in particular, demonstrate adaptations at scales that correspond with the physical scales we have been studying (Statzner and Higler, 1986; Hart and Finelli, 1999). In this section, we give only a brief introduction to these adaptations and their scale associations. Many bottom-dwelling aquatic insects are dorso-ventrally flattened in order to be able to live ‘‘under the turbulence’’ in the laminar sublayer. In gravel-bed rivers, this would amount to seeking out the sublayer on individual clasts. Filter-feeding insects, whose foraging behaviour entails intercepting drift material passing in the turbulent flow, and certain scrapers have developed strong claws or hooks in order to be able to position themselves on exposed surfaces. Most preferentially inhabit areas of accelerating flow with favourable pressure gradients, where destabilizing turbulent stresses are smaller. Nevertheless, they inhabit only the lowest few millimeters of flow, where velocities remain relatively small. Many others conduct their lives in the lee of the larger clasts; most live primarily under the surface clasts where they are protected both from strong currents and from open-water predators. The body scaling of these insects is similar to the sublayer thickness, ys, or to characteristic bed pore size. The latter is an ecologically important measure that we have heretofore ignored, which is closely allied with D. For closely packed sediments pore opening, D0 E0.4D, but D will be some relatively small fraction in the size distribution. Accordingly, embedded substrate – a gravel bed with abundant fines blocking the clast interstices – represents poor habitat. More generally, the connectivity of subsurface openings is critical both for incubation of buried eggs and for the life patterns of hyporheic fauna. Like surface networks, there is accumulating evidence for the fractal nature of pore size openings and connections. Important animal interactions occur at scales comparable with bed grain size, since individual clasts may define significant habitat units for insects, for the fry of some fish species, and even for some larger fishes over suitably coarse substrates. Competitive interactions and density variations may be evident only at the small scales that represent actual habitat units (Downes et al., 1993). Stable clasts and clast aggregations are particularly important as refugia during strong flows (Biggs et al., 1997; Matthaei et al., 2000). At a larger scale, then, stable riffles are disproportionately important sites. Seasonal and/or life-cycle movements of many invertebrates are controlled at the turbulent macroscale or depth scale of the river, or at the scale of pool-riffle spacing. Many species, particularly crawlers, move only on the order of meters over periods of weeks (Malmqvist, 2002). Life-cycle requirements lead some species to move from riffle to pool habitats, from riffles to shallows, or to off-channel areas (Bilton et al., 2001). For others, seasonal movements represent a survival strategy in face of strong seasonal variations in flow. Some species follow a shifting zone of constant depth, while others seek relatively constant velocity or shear stress (Rempel et al., 1999).
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Locomotive abilities influence the movements of many species but, of course, some species travel long distances by drifting in the turbulent flow. Fishes are altogether more mobile than most waterborne insects. Habitat preferences have been categorized directly with depth and flow velocity (Stalnaker et al., 1989), but these preferences are usually expressed by the fish through selection for specific morphological units of the channel. Such units may be associated with grainto riffle-scaled features in gravel-bed rivers and are often associated with irregularities of the stream edge which afford suitable water, hiding room, and foraging possibilities. A wide range of such local habitats has been identified (Bisson et al., 1981; Padmore et al., 1998; Church et al., 2000) with typical dimensions comparable with w. In small channels, they may largely be equivalent to channel morphological units, but in large channels, they are much smaller units. When they travel, fish interact significantly with flow at the turbulent macroscale. It has recently been demonstrated (Liao et al., 2003) that upstream-swimming fish use vertically oriented eddies – typically ‘‘vortex streets’’ – to reduce swimming energy requirements by moving always into the upstream-directed side of the vortices. In effect, they slalom between successive eddies. Because vortex streets are shed from bluff bodies and bank protrusions, fish often swim in narrowly defined ‘‘pathways’’ along steep channel edges or from object to object. Long distance swimmers take advantage of larger eddy structures as well. Upstream migrating salmonids systematically cross the stream to swim in the ‘‘inner’’ bank slack water or separation eddy. Aquatic communities are structured at the habitat scale and, more loosely, at the river reach scale. Some species move more readily than others, according to foraging strategy, but some individuals of a particular species may also be more mobile than others. Channel pattern types are apt to be ecologically distinctive because they offer distinctive physical conditions and ranges of variance (e.g., Davey and Lapointe, 2007). Communities are defined, then, within the reach scales of the channels that hold them. Aquatic communities survive, however, within larger physical systems that are strongly directed by water and nutrient flow, and so food webs may extend to span an entire catchment (Woodward and Hildrew, 2002). Within the catchment, there are strong contrasts in nutrient recruitment, with abundant addition and possibly initial processing of carbonaceous materials in headwaters and successive stages of instream processing and reproduction of nutrient materials downstream. Gravel-bed channels that are found in the mid-reaches of many upland draining catchments are often richest in aquatic resources as the consequence of abundant nutrient delivery, the persistence of a varied range of habitats created by the diversity of gravel accumulations, and the moderate but persistent level of disturbance driven by low rates of bed material transport.
9.
Discussion
In this paper, I have sought to identify significant scales in length and time of processes that lend character to gravel-bed rivers. Attention has been focused on classical scales associated with the flow at turbulent and channel scales, and with channel morphology at unit and reach scales. Intrinsic turbulent length scales include
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a well-established microscale, n/u, and a macroscale, uNTEou4T, in which T is the timescale of large coherent structures. But the latter remains controversial, in part because the true nature of large coherent structures in the turbulent shear flow remains uncertain. The smallest scale of morphological significance in gravel-bed rivers is the boundary grain scale, D, which is seen to scale both resistance to flow and processes associated with bed material transport. Grain sizes fall within the range of scales spanned by turbulence, and so the bed elements interact directly with the flow to create turbulent structures. For the channel, evident length scales appear to include d, w, and xp, the latter being understood to be a characteristic bed particle step length typically approaching l/2. These are all simple geometric scales and, since boundary materials constrain channel shape, only xp might be intrinsic. It appears to be related to dynamical features of the flow, but the nature of those features remains unclear. A special case occurs when D-d (D/d-1.0) since, then, individual grains become significant morphological elements of the channel. In this case, the dominant morphological scale of the channel is set by the relation between grain size and channel gradient. Most channel reaches are constrained by the valley within which the river runs. Some rivers escape notable lateral constraints on alluvial fans and when flowing into large sedimentary basins, but there is usually a length constraint in such cases. Accordingly, the scales of repeating patterns in river channels are limited by w and by Wv, within the limits of which there may be no singular morphological scale. A strongly impressed scale, however, is meander wavelength or, equivalently, dominant braid bar wavelength. Some such scale is present even in fully confined channels. These scales are closely set by xp, and so do not convey additional information (but they are much more easily measured). A diagram that associates dominant features of the flow and morphology of rivers with characteristic dimensions of length and time is given as Fig. 1.5. There is an increasingly obvious fundamental problem underlying the selection of all of the morphologically significant scales. Each scale is more and more obviously not a singular reference dimension, but is merely representative in some way of a range of phenomena. We observe the scaling range of turbulent structures (Fig. 1.1), limited at the lower end by the near-boundary generating mechanism and, seemingly, at the upper end by the size of the ‘‘container’’. Hence, the association of large coherent structures with flow depth. Much of the intervening scaling range may be occupied by shearline eddies created within the flow. However the scaling range is created, we are left with scales that delimit the range of turbulent flow structures, while the interesting phenomena associated with energy transfer and dissipation, and with sediment entrainment and transport, occur at all scales within that range. Bed material also presents a range of sizes – a range created by cycles of entrainment and deposition of the sediments. This sorting process does not possess strict limits. Entrainment and disentrainment can be thought of as distinctly leaky filters operating on the streambed, leaky in part, at least, because the bed itself interferes with the transport over it so that grains are variously hidden from entrainment, or trapped and prematurely disentrained. Grain resistance to flow, which helps to set mean flow velocity, is disproportionately affected by the large sizes present on the bed, whereas sizes apt to be transported (hence suitable to scale the transport
Multiple scales in rivers
23 -1
0 10
1012
m
a
-1
drainage
tectonics
0
1010
neotectonics
m
y da
10
basin -1
=ν
108
reach
0
T
-1
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L
2
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TIME SCALE (m)
106
molecular diffusion 1 day
104
channel subchannel morpholog y
1 hour
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channel secondary
102
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s
flows
1 minute
turbulent
dynamic scale ranges LT
-2 =
g
100
10-2
10-2
100
102 104 LENGTH SCALE (m)
106
Figure 1.5. Representation of scale ranges in L– T space. Range limits are set by the scales of molecular diffusion and gravity waves. Trajectories in this space define characteristic system velocities. A typical velocity of 1 m s1 for water intersects turbulent and channel scales, while a long-term virtual velocity of 102 m a1, perhaps typical of mobile sediment, intersects scales from channel to tectonics. Subchannel morphology (granular accumulations such grain clusters, or ripples and dunes) would be associated with velocities, measured in the short-term, on the order of 10 m day1.
process) are, in gravels, usually much smaller. Grains on the streambed can form aggregate structures and do form larger, bar-form accumulations that add additional resistance to flow, so there is not a true simple scale here at all. A roughness length that incorporates the total resistance to flow can be back-calculated from knowledge of stream velocity, but it is a conceptual length scale only, not susceptible of independent measurement.
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Two scales that apparently are clearly defined are channel depth and channel width. They are set by the governing conditions of water supply, boundary materials, and stream gradient. But complications lurk here, as well, because flows in rivers are more or less continuously varied, so the problem arises of defining an appropriate reference flow, and with it a ‘‘regime’’ width and depth. This is a very old problem, but it is no closer to resolution for that. Experimental evidence suggests that grain paths in transport do have a characteristic length scale, and the reason for it must be associated with some aspect of the flow, as is seen by the occurrence of equivalent length scales impressed into ice or bedrock by purely erosional flows. The association appears to lie with large, streamwise vortical structures that are themselves shaped by the channel and ultimately pinned by the channel deformation they induce (hence, are not, properly, turbulent structures), but the chain of cause and effect has not entirely been worked out and the observed water circulation in alluvial channels could be a trailing phenomenon. Furthermore, it is evident that the characteristic path length, giving rise to the poolriffle sequence, or to the dominant meander dimension, is again a limit value. Actual path lengths cover a wide distribution and we commonly observe only the integral outcome of the transport process. Further elaboration of this picture will require more careful definition of timescales and particle step sequences, something that is still difficult because of measurement limitations. Whilst particle path length might be expected to give rise to a well-defined channel morphological scale, it turns out that channel morphological units repeat in selfsimilar (or self-affine) fashion over a range of scales. Why does this happen? In the case of braided channels, which repeat bar and channel features, local variations in sediment transport and sedimentation must be associated with the scale variation. This effect was demonstrated in a simple simulation model by Murray and Paola (1994) and is consistent with measurements by Ashmore (1988) of variable sediment transport at constant flow rate in a braided system. Paola and Foufoula-Georgiou (2001) claim that the effect is the consequence of the nonlinearity of sediment transport relations and connect this behaviour with the characteristic behaviour of self-organized critical systems, which typically store sediment (or energy) up to some critical limit after which they adjust over all possible length scales. There is, of course, an element of contingency introduced at channel scales, within which sediment accumulations persistently reflect the recent history of flow and sediment influx, so self-organized conditional stability might be a more apt description of channel state. In single-thread channels, the origin of sediment-driven self-similarity is perhaps more subtle since the physical sediment queue is more nearly linear. Single-thread channels contend with banks of variable strength that may give rise to variations in both channel form and local sediment mobilization, given nonlinear forcing. Certainly, variations in sediment transport have been documented over a range of scales varying from seconds to months or years (summaries are given by Reid et al., 1985, and Gomez, 1991). A consequent range in xp, hence in channel unit lengths scales, would not be surprising in such a circumstance. Beyond that, one must contend with the quite different temporal forcing of water and of sediment supply to stream channels, a circumstance that has been relatively little considered because of the long dominant
Multiple scales in rivers
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fiction that bed material transport in alluvial channels must proceed according to some functionally fixed hydraulic capacity. In the longer term, it appears that recognition of the scaling range of many of the most important features of flow, sedimentation, and morphology of river channels will compel a more detailed examination of almost all aspects of river processes, one consequence of which will be a radical rethinking of what are the fundamental scales, or scale limits, of river processes and forms. I hope that this paper might prompt a more systematic investigation of the issues.
Acknowledgements I thank Paul Jance for producing the drawings on very short notice, Brett Eaton for collaboration on river channel scales, and three reviewers for helpful insights that forced me to clarify many of my statements.
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Discussion by C.D. Rennie The author should be commended for presenting a stimulating review of the full spectrum of scales in rivers. Based on the work of Pyrce and Ashmore (2003a, 2003b, 2005), the author suggests that meander wavelength scaling in rivers is fundamentally related to sediment transfer. Pyrce and Ashmore (2003b) observed that particle step length during channel forming flows was symmetrically distributed with a mean equal to the pool-bar spacing. Sediment was eroded from pool locations and deposited on the subsequent bar, suggesting that sediment transfer determines the meander wavelength scale. However, it must be recognized that Pyrce and Ashmore observed particle step lengths after pool-bar meander morphology was established. It is entirely sensible that sediment was eroded from zones of flow convergence in the pool and deposited on the subsequent zone of flow divergence on the bar. This does not necessarily mean that the meander geometry was established by the sediment transfer. Flow in a sinuous channel consists of periodically reversing helical flow characterized by twin surface convergent helical cells of alternating strength. The mechanics of meander initiation has engrossed researchers for over a century (Thomson, 1878). The essential question is if meandering is a result of the flow field, sediment transport, or an interaction of the two. A meander initiation theory must explain how localized points of erosional bank attack alternate from side to side of the channel. An argument in favour of flow field theories is that meandering is observed in other fluid flows in the absence of sediment transport, such as ocean currents (Leopold and Wolman, 1960), supraglacial meltwater channels (Leopold and Wolman, 1960), water rivulets on inclined smooth plates (Gorycki, 1973), channels in sedimentary deposits of deep sea turbidity currents (Coterill et al., 1998; Parker, 1998), pollutant plumes (Etling, 1990), and tropical cyclone paths (Holland and Lander, 1993). This general tendency to meander suggests that meandering is a fundamental characteristic of fluid flow, associated with shear and vorticity production at density interfaces. Admittedly, however, it is presumptuous to assume that similar meander form in these flows suggests similar underlying processes (Knighton, 1998). Parker (1976) argued that in all meandering flows, a ‘third effect’ beyond potential (inertial and gravitational) and frictional forces is required to cause meandering (e.g., sediment transport, Coriolis acceleration, heat differences, or surface tension). However, it appears that this hypothesis remains largely untested. In general, meander development theories based on the flow field (e.g., Einstein and Shen, 1964; Quick, 1974), or on flow–sediment interactions (e.g., the bar-bend models of Johannesson and Parker, 1989 and Seminara and Tubino, 1989), require an initial perturbation in the bed surface to generate reversing helical flow and/or alternating zones of erosion and deposition. In natural rivers, initial perturbations could be generated by large woody debris or large clasts, but spatially differential sediment transport is usually evoked. In the two bar-bend models, feedback mechanisms between the flow and sediment result in the final meander form. It seems likely that meandering form in rivers, and thus the meander wavelength scale, is the result of interactions between an initial perturbation, reversing helical flow structure,
30
Michael Church
and sediment transport. Importantly, the experimental results of Pyrce and Ashmore do not necessarily eliminate the role of the flow field.
References Coterill, K., Coleman, J., Marotta, D., et al., 1998. Sinuosity in submarine channels; scale and geometries in seismic and outcrop indicating possible mechanisms for deposition (abstract). Am. Ass. Pet. Geol. Bull. 82 (10), 1904. Einstein, H.A., Shen, H.W., 1964. A study on meandering in straight alluvial channels. J. Geophys. Res. 69 (24), 5239–5247. Etling, D., 1990. On plume meandering under stable stratification. Atmos. Environ. 24A (8 Part 2), 1979–1985. Gorycki, M.A., 1973. Hydraulic drag: A meander initiating mechanism. Bull. Geol. Soc. Am. 84, 175–186. Holland, G.J., Lander, M., 1993. The meandering nature of tropical cyclone tracks. J. Atmos. Sci. 50 (9), 1254–1266. Johannesson, H., Parker, G., 1989. Linear theory of river meanders. In: Ikeda, S. and Parker, G. (Eds), River Meandering. American Geophysical Union, Washington, DC, pp. 181–213. Knighton, D., 1998. Fluvial forms and processes: A new perspective. Arnold, London. Leopold, L.B., Wolman, M.G., 1960. River meanders. Geol. Soc. Am. Bull. 71 (6), 769–793. Parker, G., 1976. On the cause and characteristic scales of meandering and braiding in rivers. J. Fluid Mech. 76, 457–480. Parker, G., 1998. Flow and deposits of turbidity currents and submarine debris flows (abstract). Am. Ass. Pet. Geol. Bull. 82 (10), 1948–1949. Pyrce, R.S., Ashmore, P.E., 2003a. Particle path length distributions in meandering gravel-bed streams: Results from physical models. Earth Surf. Process. Landf. 28 (9), 951–966. Pyrce, R.S., Ashmore, P.E., 2003b. The relation between particle path length distributions and channel morphology in gravel-bed streams: A synthesis. Geomorphology 56 (1–2), 167–187. Pyrce, R.S., Ashmore, P.E., 2005. Bedload path length and point bar development in gravel-bed river models. Sedimentology 52 (4), 839–857. Quick, M.C., 1974. Mechanism for streamflow meandering. J. Hydraul. Eng. 100 (HY6), 741–753. Seminara, G., Tubino, M., 1989. Alternate bars and meandering: Free, forced and mixed interactions. In: Ikeda, S. and Parker, G. (Eds), River Meandering. American Geophysical Union, Washington, DC, pp. 267–320. Thomson, J., 1878. On the origin of windings of rivers in alluvial plains, with remarks on the flow of water round bends in pipes. Proc. R. Soc. London, Ser. A. 25, 114–127.
Discussion by A. Roy I would like to raise three points concerning the turbulent scale. The author questions the usefulness of the integral length scale (LE) for determining the upper limit of turbulence. Because it is based on the integration of the autocorrelation function of the whole velocity signal, LE represents the scale of both the turbulent events and the ambient fluid. LE provides a very conservative estimate of the size of the turbulent flow structures. Our data from a range of gravel-bed rivers and of flow conditions show that LE for the streamwise velocity component averages around 0.9d with a standard deviation of 0.3. This scaling is the lowest estimate of eddy size when compared to values obtained from other methods that emphasize the scale of individual events. These latter methods should be preferred in establishing the maximum scale of turbulent eddies.
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and sediment transport. Importantly, the experimental results of Pyrce and Ashmore do not necessarily eliminate the role of the flow field.
References Coterill, K., Coleman, J., Marotta, D., et al., 1998. Sinuosity in submarine channels; scale and geometries in seismic and outcrop indicating possible mechanisms for deposition (abstract). Am. Ass. Pet. Geol. Bull. 82 (10), 1904. Einstein, H.A., Shen, H.W., 1964. A study on meandering in straight alluvial channels. J. Geophys. Res. 69 (24), 5239–5247. Etling, D., 1990. On plume meandering under stable stratification. Atmos. Environ. 24A (8 Part 2), 1979–1985. Gorycki, M.A., 1973. Hydraulic drag: A meander initiating mechanism. Bull. Geol. Soc. Am. 84, 175–186. Holland, G.J., Lander, M., 1993. The meandering nature of tropical cyclone tracks. J. Atmos. Sci. 50 (9), 1254–1266. Johannesson, H., Parker, G., 1989. Linear theory of river meanders. In: Ikeda, S. and Parker, G. (Eds), River Meandering. American Geophysical Union, Washington, DC, pp. 181–213. Knighton, D., 1998. Fluvial forms and processes: A new perspective. Arnold, London. Leopold, L.B., Wolman, M.G., 1960. River meanders. Geol. Soc. Am. Bull. 71 (6), 769–793. Parker, G., 1976. On the cause and characteristic scales of meandering and braiding in rivers. J. Fluid Mech. 76, 457–480. Parker, G., 1998. Flow and deposits of turbidity currents and submarine debris flows (abstract). Am. Ass. Pet. Geol. Bull. 82 (10), 1948–1949. Pyrce, R.S., Ashmore, P.E., 2003a. Particle path length distributions in meandering gravel-bed streams: Results from physical models. Earth Surf. Process. Landf. 28 (9), 951–966. Pyrce, R.S., Ashmore, P.E., 2003b. The relation between particle path length distributions and channel morphology in gravel-bed streams: A synthesis. Geomorphology 56 (1–2), 167–187. Pyrce, R.S., Ashmore, P.E., 2005. Bedload path length and point bar development in gravel-bed river models. Sedimentology 52 (4), 839–857. Quick, M.C., 1974. Mechanism for streamflow meandering. J. Hydraul. Eng. 100 (HY6), 741–753. Seminara, G., Tubino, M., 1989. Alternate bars and meandering: Free, forced and mixed interactions. In: Ikeda, S. and Parker, G. (Eds), River Meandering. American Geophysical Union, Washington, DC, pp. 267–320. Thomson, J., 1878. On the origin of windings of rivers in alluvial plains, with remarks on the flow of water round bends in pipes. Proc. R. Soc. London, Ser. A. 25, 114–127.
Discussion by A. Roy I would like to raise three points concerning the turbulent scale. The author questions the usefulness of the integral length scale (LE) for determining the upper limit of turbulence. Because it is based on the integration of the autocorrelation function of the whole velocity signal, LE represents the scale of both the turbulent events and the ambient fluid. LE provides a very conservative estimate of the size of the turbulent flow structures. Our data from a range of gravel-bed rivers and of flow conditions show that LE for the streamwise velocity component averages around 0.9d with a standard deviation of 0.3. This scaling is the lowest estimate of eddy size when compared to values obtained from other methods that emphasize the scale of individual events. These latter methods should be preferred in establishing the maximum scale of turbulent eddies.
Multiple scales in rivers
31
As noted by the author, defining unambiguously a true turbulent event (e.g., ejection) from velocity time series is a prerequisite to any scaling or frequency analysis. It is interesting to note, however, that the detection of turbulent events from velocity records may be quite robust. It is known that the application of various methods used to detect individual flow structures to velocity data will yield different results. In spite of this variability and using thresholds for each method that have been developed from studies in laboratory flumes, it appears that the frequency of events in gravel-bed rivers remains relatively constant among the various detection schemes. For instance, Roy et al. (1996) reported that average bursting frequency (T) for four commonly used burst detection schemes varies between 0.30 and 0.35 event per second. In gravel-bed rivers, bursting frequency is not very sensitive to height above the bed. This suggests that the phenomenon under study may be quite robust in its global properties or that the large-scale events that dominate the turbulent flow field in gravel-bed rivers are equally well detected by the schemes. It is important, however, that detection schemes be used consistently and that similar threshold values be applied across various studies. The selection of adequate thresholds may be guided by flow visualization. Bursting frequency in gravel-bed rivers is often quite low with reported values typically between 0.2 and 0.6 depending on the thresholds used in the detection schemes. This indicates that the turbulent structures are quite large. Using Rao et al.’s formula, such low T values would imply that measurements were taken in shallow and/or fast currents. If one supposes that the size of the ejections scale with depth (say 5d) and one samples flows of different depth but with similar flow velocity, then T as estimated by uNT ¼ 5d would increase with increasing depth while the size of the structures would also increase. If larger structures take more time than smaller ones to fully develop and if they advect roughly at the mean flow velocity, it is difficult to imagine that bursting frequency would also increase. It seems to me that it may be difficult to reconcile both scalings as in L ¼ 5d ¼ uNT in many contexts encountered in gravel-bed rivers.
References Roy, A.G., Buffin-Be´langer, T., Deland, S., 1996. Scales of turbulent coherent flow structures in gravel-bed rivers. In: Ashworth, P.J., Bennett, S.J., Best, J.L., and McLelland, S.J. (Eds), Coherent Flow Structures in Open Channels. Wiley, Chichester, pp. 147–164.
Reply by the author I thank Rennie and Roy for their helpful amplification of some points in the paper. Together, the discussions emphasize that the essential connections between the flow field and the resulting channel morphology remain an important unresolved problem. Rennie points out that the demonstration by Pyrce and Ashmore (2003b) of a preferred riffle–riffle step length for sediment grain movements was made with
Multiple scales in rivers
31
As noted by the author, defining unambiguously a true turbulent event (e.g., ejection) from velocity time series is a prerequisite to any scaling or frequency analysis. It is interesting to note, however, that the detection of turbulent events from velocity records may be quite robust. It is known that the application of various methods used to detect individual flow structures to velocity data will yield different results. In spite of this variability and using thresholds for each method that have been developed from studies in laboratory flumes, it appears that the frequency of events in gravel-bed rivers remains relatively constant among the various detection schemes. For instance, Roy et al. (1996) reported that average bursting frequency (T) for four commonly used burst detection schemes varies between 0.30 and 0.35 event per second. In gravel-bed rivers, bursting frequency is not very sensitive to height above the bed. This suggests that the phenomenon under study may be quite robust in its global properties or that the large-scale events that dominate the turbulent flow field in gravel-bed rivers are equally well detected by the schemes. It is important, however, that detection schemes be used consistently and that similar threshold values be applied across various studies. The selection of adequate thresholds may be guided by flow visualization. Bursting frequency in gravel-bed rivers is often quite low with reported values typically between 0.2 and 0.6 depending on the thresholds used in the detection schemes. This indicates that the turbulent structures are quite large. Using Rao et al.’s formula, such low T values would imply that measurements were taken in shallow and/or fast currents. If one supposes that the size of the ejections scale with depth (say 5d) and one samples flows of different depth but with similar flow velocity, then T as estimated by uNT ¼ 5d would increase with increasing depth while the size of the structures would also increase. If larger structures take more time than smaller ones to fully develop and if they advect roughly at the mean flow velocity, it is difficult to imagine that bursting frequency would also increase. It seems to me that it may be difficult to reconcile both scalings as in L ¼ 5d ¼ uNT in many contexts encountered in gravel-bed rivers.
References Roy, A.G., Buffin-Be´langer, T., Deland, S., 1996. Scales of turbulent coherent flow structures in gravel-bed rivers. In: Ashworth, P.J., Bennett, S.J., Best, J.L., and McLelland, S.J. (Eds), Coherent Flow Structures in Open Channels. Wiley, Chichester, pp. 147–164.
Reply by the author I thank Rennie and Roy for their helpful amplification of some points in the paper. Together, the discussions emphasize that the essential connections between the flow field and the resulting channel morphology remain an important unresolved problem. Rennie points out that the demonstration by Pyrce and Ashmore (2003b) of a preferred riffle–riffle step length for sediment grain movements was made with
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Michael Church
developed riffles. It is difficult to see how it could be otherwise since the riffles themselves are simply the consequence of such a preferred scale for grain displacements. The problem recurs in all situations in which more or less regular accumulations are observed in sediment transport systems – for example, in the production of aeolian ripples. Rennie reviews farther the largely speculative literature on the possible origin of channel scale regular deformation. I agree that the origin must lie in the flow for reasons that we both have both adduced. But whilst our mathematical theories require some initial, imposed perturbation, it is not at all clear that nature does. Roy has, I think, misunderstood my discussion of the turbulent integral length scale. I do not intend to criticize its role in describing the syndrome of turbulence, but to question whether it can illuminate the undoubted connection between the flow and the consequent scales of fluvial morphology. In any case, as the balance of his discussion makes clear, the significant scaling of turbulent events itself remains a subject for additional work.
Gravel-Bed Rivers VI: From Process Understanding to River Restoration H. Habersack, H. Pie´gay, M. Rinaldi, Editors r 2008 Elsevier B.V. All rights reserved.
33
2 Gravel-bed rivers at the reach scale Rob Ferguson
Abstract Reaches extending for tens or hundreds of channel widths along a river are normally seen as stable and homogeneous from a regime perspective, but other approaches emphasise channel change and within-reach spatial variability in flow and physical habitat. Tensions between different perspectives are discussed, with particular emphasis on limitations of traditional regime approaches. Cross-cutting issues include reconciling different scales of self-organisation in gravel-bed rivers, the need to treat bed characteristics as a degree of freedom, and within-reach spatial variability and temporal fluctuation. New ways to tackle these and other issues have been enabled by ever-increasing computing power. Non-uniform and/or unsteady fluvial processes can be modelled numerically, and remote-sensing methods have been developed to acquire dense spatially distributed measurements. But neither models nor observations are infallible, and models of different complexity need to be compared and assessed carefully.
1.
Introduction
The term ‘reach’ is widely used in the fluvial literature but seldom defined. It refers to a stretch of river channel not a specific locality, but a stretch much shorter than the full distance from headwaters to sea. Sometimes the limits of a study are set by data availability or the geographical limits of a management plan, but usually the ‘reach’ is perceived to be homogeneous in some way. My dictionary gives ‘a straight uniform stretch of river’ but this is too restrictive. A possible working definition of ‘reach scale’ is the length scale over which relevant characteristics of a river remain essentially the same. Thus a reach might have a certain channel pattern, support a certain ecosystem, be incising, or whatever. This implies lower and upper limits to the length of a reach. An individual pool or meander bend is not a reach, because its physical and ecological properties differ systematically from the adjacent riffle or crossover. The lower limit of ‘reach scale’ is therefore the wavelength of bed macroforms: 101 E-mail address:
[email protected] ISSN: 0928-2025
DOI: 10.1016/S0928-2025(07)11112-3
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channel widths. The upper limit is the distance over which changes in channel properties become unacceptably large for the purpose of the investigation, for example because major tributaries add significant discharge and load. This upper limit depends on both study purpose and network-scale properties of the river system, but is usually 4102 channel widths. Reaches therefore extend over tens or hundreds of widths. This is also the length scale at which disequilibrium due to environmental change or human activity becomes most obvious: channel widening or incision at a single cross section might relate only to bar or bend growth, but systematic change in width or bed elevation over a series of sections tells us the reach is not in equilibrium. More generally, the reach scale is where generic understanding of fluvial processes has to be reconciled with the contingency of particular landscapes and their forcing by climate and human activity. The literature on gravel-bed rivers at reach scale is large, ever-growing, multidisciplinary, and very varied, but four longstanding perspectives can be distinguished:
Engineers, and some geomorphologists, are interested in channel regime: what a channel must be like to remain in equilibrium. Geomorphologists, and many land managers and engineers, are aware of channel change: dynamic aspects of river behaviour such as meander migration, incision, and aggradation. Sedimentologists, geomorphologists and engineers have studied the key process of bedload transport and its interactions with bed characteristics and sediment supply. Ecologists, and subsequently geomorphologists, have focused on physical habitat diversity as a key aspect of in-stream ecology and a prerequisite for successful river restoration. Some riverine ecology deals with phenomena at sub-reach scale (e.g., animal movement within the hyporheic zone) but overall habitat characteristics are a reach property.
I begin this overview by highlighting some inconsistencies and tensions between these traditional perspectives. Things that are emphasised in some are largely ignored in others, suggesting that our science is not fully joined up. Because bedload transport and floodplain ecology are the subjects of detailed reviews elsewhere in this volume I base my discussion around the regime and channel-change themes, with links to the other two. The rest of the paper is inspired by the view that science is ‘the art of the soluble’ (Medawar, 1967). Recent technical and methodological developments, underpinned by the inexorable rise in computer power and the ingenuity of numerate fluvial scientists, have greatly increased our ability to measure, describe, or predict fluvial phenomena. This makes it possible to describe specific river reaches in far more detail than before, and to evaluate general explanatory hypotheses which were previously untestable. The key advances relevant to reach-scale research are the rapid development of methods for acquiring spatially distributed data, and the extension of modelling from one-dimensional (1-D, i.e., width-averaged) to 2-D and 3-D situations. I summarise these developments and discuss the problem of deciding what faith we can put in numerical models.
Gravel-bed rivers at the reach scale 2.
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Some limitations of present theory
Certain tensions between the four perspectives identified in Section 1 are obvious. For example, the shift of management focus away from the engineering stability of rivers towards their ecological health necessitates a concern for spatial and temporal variability, whereas regime theory deals with averages. Other less-apparent tensions can be identified by considering three cross-cutting topics: scales of self-organisation, the bed as a degree of freedom, and within-reach spatial and temporal variability. Sections 2.1–2.3 explore these topics, note inconsistencies between traditional approaches, and draw attention to work which may help resolve some of the tensions.
2.1.
Self-organisation in gravel-bed rivers
Rivers are gutters which drain the landscape and transfer sediment from source areas to alluvial basins, but they are gutters with deformable boundaries. Channel configuration controls flow and sediment transport in the short term but is eventually altered by them. Self-organisation occurs at four scales of which the first and last do not concern us here: the development of a drainage network, channel regime, planform development, and depth-scaled bedforms. The regime concept is that river channels adjust towards a dynamic equilibrium in which, averaged over a period of years, the channel is just able to convey the water and sediment supplied from upstream. The key adjustable property is bed elevation, which affects transport capacity through channel slope. Gilbert recognised over a century ago that local aggradation or degradation diffuses up and downstream to provide negative feedback. Channel slope can also be adjusted via sinuosity, and transport capacity also depends on width, so the essence of regime theory is to determine the equilibrium slope and width for given values of water discharge, bedmaterial load, and channel boundary materials. Early work by Lacey, Blench, and others used empirical correlations, as did the geomorphological reinvention of the approach by Leopold and Maddock (1953). Since the late 1970s the search has been for a ‘rational’ regime theory that is physically based (e.g., Parker, 1979), though in many cases closed only by an extremal hypothesis (e.g., Eaton et al., 2004). Regime theory helps us understand how a hierarchical system of fewer but bigger gutters works to remove water and sediment from the landscape, but it has several limitations stemming from simplifying assumptions that are made. The first issue is that potentially significant controls or responses are omitted. Channel pattern is either ignored, with a disclaimer that attention is restricted to straight channels, or valley slope is taken as independent with sinuosity and channel slope free to adjust. The characteristics of the river bed are represented by a single grain diameter which is assumed fixed and independent, contrary to what many bedload specialists think (Section 2.2). The evident role of bank strength has usually been ignored and a versatile treatment of it has only recently been developed (Millar and Quick, 1998; Eaton et al., 2004). A second issue relates to temporal variability (Section 2.3): regime theory, originating as it did in attempts to design irrigation channels to convey steady flows, collapses the flood magnitude-frequency spectrum into a
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dominant discharge. This ignores the non-linearity of the relation between flood magnitude and geomorphic work done; the effects of extreme floods are instead regarded as disruptions to regime. Third, channels are assumed to be uniform, which ignores the spatial variability created by small-scale self-organisation. This provides a poor basis for ecological research and calls into question the calculations of bedload transport in regime theories (see Section 2.3). One strand of channel-change research is complementary to regime research: the documentation of systematic channel incision, widening, etc over decades or longer. Such changes are normally regarded as shifts to a new regime following some natural or human-induced change in circumstances, and explicable in terms of discharge and sediment supply using qualitative schemes proposed by Lane (1955) and Schumm (1969). Research of this kind has revealed region-wide trends (e.g., Lie´bault and Pie´gay, 2002; Rinaldi, 2003) and provided valuable input to catchment management plans. But interpretations and predictions are subject to two of the same doubts as regime theory (neglected degrees of freedom, possible effect of major floods) and predictions carry further limitations: regime theory may mis-predict the eventual equilibrium if degrees of freedom are neglected (Wyzga, 2001), and it does not predict rates of adaptation. Case studies of response to major floods (e.g., Pitlick, 1993) suggest that different properties have different relaxation times so that complex response is possible. In a period of unprecedented human influence on river basins, and climate variability at a range of timescales, transient change may be the norm not the exception (Lewin et al., 1988). It may be triggered not only by step changes but by shocks (e.g., floods or landslides), pulses (e.g., gravel extraction), ramp changes (e.g., deforestation), or quasi-cyclic perturbations (e.g., those in flood magnitude induced by atmospheric teleconnections). To move forward from the limitations of regime and regime-change approaches we need quantitative as well as qualitative models of transient change in rivers. Such models will be numerical, not analytical, for flexibility and to deal with multiple, non-linear, and interacting processes. The sediment routing models mentioned below (Section 2.2) provide a starting point, but ought to allow time-varying discharge and to include a sub-model for width adjustment as discussed by Darby et al. (1998). The other tension between regime theory and alternative approaches to channel behaviour relates to scales of self-organisation. Regime and regime-change approaches are implicitly concerned with self-organisation over fairly extended time and space scales. The mechanisms through which this happens are not treated by regime theory, which seeks only an equilibrium solution, but they evidently comprise erosion and deposition of the bed and banks. Regime theory assumes uniform channel geometry, but channel erosion and deposition normally involve self-organisation at a local scale into characteristic repeating bed forms and patterns. The typical outcome in gravel-bed rivers is a bar-pool-riffle morphology, usually accompanied by local sediment sorting and often by a meandering or braided planform. The development of these repeating forms is studied in another branch of the channel-change perspective. It is a fundamentally different kind of self-organisation from what is envisaged in regime change: much more local, and involving positive feedbacks between the non-uniformity of the morphology, flow field, and transport field. Positive feedback makes for rapid evolution, in contrast to the diffusive character of
Gravel-bed rivers at the reach scale
37
bed aggradation or degradation. As the amplitude of the repeating forms increases negative feedbacks set in. These too are mainly local, as when meander growth is terminated by chute or neck cutoffs. This is reminiscent of self-organised criticality, as Stolum (1998) and Fonstad and Marcus (2003) have noted in connection with meandering and bank erosion respectively. Both morphology and flow remain intrinsically non-uniform at the within-reach scale. As a result, although the style of morphology is usually persistent and can be seen as part of the regime of a reach, it is at best a statistical equilibrium within which there is more or less frequent change at a local scale. This is the main source of disturbance in the riverine ecosystem, and helps sustain high diversity (Ward et al., 2002; Van der Nat et al., 2003). A challenge for future research is to investigate the coupling between the two scales of self-organisation in river reaches. Insight into the development of repeating forms has been gained mainly from laboratory experiments (e.g., Ashmore, 1991) and mathematical stability analysis of small perturbations of a uniform bed (reviewed by Rhoads and Welford, 1991). Both approaches show that barely perceptible irregularities grow into freely migrating quasi-periodic bedforms; flow deflection towards the banks leads to incipient meandering which locks migrating forms into place; then there is either a simplification of the pattern within a meandering planform, or ongoing instability if fixed bars are dissected by chutes which generate new free bars and a braided planform. Reach-scale channel pattern thus emerges from small-scale non-uniformity, in the way that is characteristic of systems with interacting nonlinear processes. But from the perspective of many field workers the channel pattern and aggradational or degradational tendency of a reach control the migration of bars and riffles and determine which locations experience bank erosion (e.g., McLean and Church, 1999). Is the apparent inconsistency between bottom-up and top-down views of channel behaviour just a matter of scale of interest?
2.2.
The bed as a degree of freedom
As well as a tension between regime-analysis and channel-change schools of thought, there is an inconsistency between regime-analysis and bedload-transport schools concerning the degrees of freedom a river has when adapting to change. Rational regime theory uses a characteristic bed grain size in resistance and transport calculations and treats it as fixed, but it is well known that some kinds of river adjustment are accompanied by changes in bed grain size distribution (GSD hereafter). Degrading channels usually become armoured, for example below dams or in flumes with no sediment feed. As with adjustment of width or slope this reduces the imbalance between bedload transport capacity and sediment supply, but through change in critical shear stress (tc) rather than flow shear stress (t). It is instructive to see how powerful this regulating mechanism can be. A river’s width-averaged bedload capacity can be written using the Meyer–Peter & Muller relation as Qs pwt1:5 c
t tc
1:5 1
(2.1)
R. Ferguson
38
in which t p dS, tc p D, and w, d, S, D denote width, depth, slope, and average bed grain diameter respectively. Adopting the Manning–Strickler resistance law yields 0:6 t Q p S0:7 D 0:9 (2.2) tc w For any given initial value of t/tc it is now possible to calculate the sensitivity of Qs to a specified change in the imposed discharge (Q) or in any of the adjustable channel properties (w, S, or D). Table 2.1 shows the percentage change in bedload capacity with a 10% change in one controlling factor at a time, for a range of typical transport stages. The sensitivity to each control is higher the closer conditions are to the threshold for motion. Grain size has more influence than any other factor in nearthreshold conditions, and substantial influence in all conditions typical of gravel-bed rivers. A change in bed GSD implies size selectivity in the entrainment, transport, and deposition of bed material. This occurs because tc varies somewhat with individual grain size in a mixture even though it depends mainly on overall surface properties: mean grain size, the structural arrangement of coarse clasts (Church et al., 1998), and sand content (Wilcock and Crowe, 2003). As flow increases above the threshold for movement the total bedload flux increases rapidly and its GSD converges on the bedsurface GSD. The bedload GSD may match that of the bed as a whole if finer sizes tend to be hidden beneath a coarse surface layer (Parker and Klingeman, 1982). Surface coarsening and associated structural changes are seen as a regulatory mechanism which reduces transport capacity to the extent necessary to match supply, with static degradational armour as the extreme case (Dietrich et al., 1989; Buffington and Montgomery, 1999). The bed GSD mediates the effect of supply on channel stability, and allows bedload transport and channel evolution to be predicted (Wilcock, 2001). From this perspective, regime theory neglects one of the potential degrees of freedom in reach self-organisation. Bed adjustment is not restricted to coarsening when supply is reduced. There are documented examples of fining after a big increase in supply (e.g., Pitlick, 1993; Montgomery et al., 1999), and downstream fining along concave long profiles can be seen as an adjustment that increases distal transport rates and thus reduces aggradation (Ferguson et al., 1996). More generally, any divergence in the total flux of mixed-size bedload can be accommodated not just by aggradation or degradation but also by change in bed GSD and therefore sizefraction availability and overall tc. The timescale for GSD change will often be Table 2.1. Percentage increase in bedload transport capacity for the indicated transport stage t/tc and the indicated percentage change in discharge (Q), width (w), slope (S) or bed grain diameter (D). See text for basis of calculations. t/tc
Q +10%
w
1.2 1.3 1.4 1.5
57 41 32 28
48 31 23 18
10%
S +10%
D
68 48 38 33
72 46 34 26
10%
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shorter than the timescale for significant change in bed elevation (Deigaard and Fredsoe, 1978; Ferguson et al., 1996). It is easier to identify this weakness in traditional regime theory than to suggest how the theory could be extended. The representative grain size cannot become a variable without adding another process constraint, and there is no obvious candidate. The alternative is to consider multiple size fractions, which necessitates a numerical approach. Width-averaged ‘sediment routing models’ that predict the coevolution of bed elevation and GSD have been applied to a range of disequilibrium situations (e.g., Talbot and Lapointe, 2002; Cui and Parker, 2005; Ferguson et al., 2006) and show encouraging agreement with field evidence. If set up with straight long profiles (but possibly unsteady discharge) they could be used to investigate regime as well as transient change. The main limitations of the current generation of models are width averaging, which may lead to underestimation of bedload transport (see Section 2.3), and the assumption of no change in width during aggradation or degradation. Allowance for these complications would require either going over to a full 2-D model (see Section 4) or parameterisation in what might be thought of as a 1.5-D model (e.g., the allowance for width change in Carroll et al., 2004).
2.3.
The significance of spatial and temporal variability
As noted in Section 2.1, traditional regime approaches to large-scale self-organisation assume uniform channel geometry and a dominant discharge, whereas natural channels are spatially non-uniform because of within-reach self-organisation and experience a spectrum of floods of different magnitude, duration, and interval. Spatial and temporal variability has major implications for in-stream ecology, and affects the realism of calculations in analytical regime theory and 1-D numerical models. Many engineered channels are straight with constant width and trapezoidal cross section. This gives uniform flow depth, and near-uniform velocity and shear stress, across and along the flat bed. A natural gravel-bed reach conveying the same discharge normally has a bar-pool-riffle morphology with a wider range of depth and more varied combinations of depth and velocity. The ecological benefits of greater diversity in physical habitat are well known, indeed they are central to modern practice in river restoration. Hydraulic diversity increases the range of ecological habitat in a reach at a given discharge and ensures that the range is maintained in flood conditions: areas that become too fast-flowing are replaced by newly inundated areas of shallower, slower flow (e.g., Mosley, 1983). Non-uniformity in flow is often accompanied by sediment sorting which further increases habitat diversity. Detailed information on the within-reach variability of ecologically relevant flow variables such as depth, velocity, and shear stress is very time-consuming to obtain using traditional point measurements. Some researchers have attempted to identify transferable statistical models for the frequency distributions of these variables (e.g., Lamouroux et al., 1995; Stewardson and McMahon, 2002) and to relate distribution parameters to discharge and reach-averaged morphological properties. It is also becoming possible to obtain distributed measurements more efficiently using new
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techniques (Section 3), or to simulate the 2-D or 3-D velocity field numerically (Section 4). Until recently the emphasis in reach-scale riverine ecology has been on fish habitat, but attention has now extended to the full range of flora and fauna. This introduces a further consideration: the less mobile the organism, the more important becomes temporal change in local physical habitat through floods, erosion, and deposition. Much of this is played out at sub-reach scale but it can affect reach properties. For example plant colonisation is constrained not only by spatial variability in bed elevation and GSD but also by the intervals between, and seasonal timing of, flow extremes which rip plants out or dry their roots. Successful colonisation feeds back to channel hydraulics through increased roughness, and to bed GSD and bank stability through fine sedimentation. Traditional regime-type characterisation of rivers in a spatially and temporally averaged way cannot begin to provide understanding of such interactions. The implications of spatial variability for regime theory and 1-D channel-change models relate to calculations of flow resistance and bedload transport. Using a grain size to parameterise flow resistance implies that resistance is primarily due to grain roughness. This ignores the possibly large contribution of form resistance in nonuniform channels. Ways round this are to inflate the resistance coefficient (but by how much?) or use a 2-D model (Section 4). Calculating a river’s total bedload flux from the width-averaged shear stress based on mean depth, when t in fact varies across the channel, tends to underestimate the true flux because transport increases non-linearly with local t. Paola (1996) and Nicholas (2000) estimated that the concentration of flow and transport in the confluences of a braided river could increase bedload flux to three times what a uniform channel would convey, and Ferguson (2003) calculated that even bigger differences are possible in highly non-uniform situations with flow not far above threshold. Such effects are, however, offset to some extent by the development of bed patchiness. Size-selective transport leads to withinreach sediment sorting, with a finer bed in locations of weaker flow such as bar tails. This can almost eliminate the effect of spatial flow variance on bedload conveyance (Ferguson, 2003), though bed patchiness does enhance the selectivity of transport along a reach (Paola and Seal, 1995). It may be possible to use measures of crosssection shape to parameterise spatial variance in t and allow for it in a 1.5-D model, but it is probably better to turn to 2-D modelling if channels are highly non-uniform.
3.
Quantifying within-reach variability
Until quite recently the only spatially distributed information about rivers that was readily available was planimetric: the water and vegetation margins shown by aerial photographs. Quantifying bed elevation required some form of surveying, usually levelling along cross sections. Levelled sections show lateral variation in depth well, and define mean bed elevation precisely enough to detect aggradation or degradation in a resurvey, but they show longitudinal variation in morphology far less well unless the sections are very closely spaced. Information on velocity has also normally been collected along cross sections, one point at a time. It is possible to obtain sparse
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distributed measurements of current speed at one or two heights, as in standard protocols for assessing physical habitat for in-stream ecology, but detailed investigation of the flow field is very laborious and few rivers remain at near-constant stage for long enough. Bed GSD and structure are directly measurable only in small areas. Obtaining gravel GSDs by bulk sieving is notoriously time consuming because large sample sizes are required for reasonable precision, so mapping spatial variation by bulk sampling is inconceivable. Pebble counting is much quicker, but attention to precision is again necessary and detailed mapping of spatial variation is a daunting task. It is fortunate, therefore, that technological developments over the last decade or so have greatly extended the possibilities for obtaining spatially distributed data about river reaches. Most of them involve remote sensing of some kind. I discuss in turn new ways to quantify river bed topography, bed material, flow field, and sediment transport. It should be noted that some of these tools have been applied to only one or a few rivers so far; they are still under development and may not be useful across the full range of gravel-bed conditions. 3.1.
Topography
Several alternatives to levelling allow the capture of more continuously distributed elevation data. On exposed gravel bars and in shallow channels, self-tracking motorised total stations allow rapid mapping of large numbers of points in a fairly random pattern for subsequent construction of a digital elevation model (DEM). This can also be done by differential GPS though with lower precision. Differencing of DEMs from successive surveys gives a fuller picture of channel change than is possible from cross sections (e.g., Brasington et al., 2003). Dense DEMs can also be constructed by digital photogrammetry using airborne or oblique terrestrial imagery (Chandler et al., 2002; Lane et al., 2003). It is possible to obtain dm-scale spatial resolution and cm-scale vertical resolution over areas of several hectares, even from non-metric imagery. When oblique imagery is used the bed topography of active channels has to be surveyed separately and merged with the photogrammetric data, but with near-vertical imagery and shallow clear water it is possible to correct for refraction errors (Westaway et al., 2001). Fig. 2.1 shows the kind of detail of channel change that can be obtained. Water depth can also be mapped from differences in radiance in multi-spectral airborne or satellite imagery (Winterbottom and Gilvear, 1997; Legleiter et al., 2004). Another recent development is the use of airborne laser surveying (LiDAR) to obtain high-resolution transects of floodplain and bar topography, even in the presence of vegetation. At the opposite extreme Butler et al. (2002) used digital photogrammetry to obtain mm-scale DEMs of bed microtopography, and Carbonneau et al. (2003) showed that even a low-cost version of this approach could deliver sub-cm precision on dry surfaces. 3.2.
Bed material
There were several attempts in the 1970s and 80s to estimate bar-surface GSDs by manual ‘photo sieving’ of close-up photographs. This saved time in the field but
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Figure 2.1. Channel change in a braided reach of the Waimakariri River, New Zealand, over a 3-month period as indicated by the difference between two DEMs based on oblique digital photogrammetry. Greyscale shows difference in elevation (in metres), with deposition positive and erosion negative. (Modified from Fig. 2.2 in Lane et al. (2003). Copyright John Wiley & Sons Limited. Reproduced with permission.)
required laborious image measurements and calculations afterwards. The advent of scanners, digital cameras, powerful personal computers, and image-analysis software has allowed the development of automated procedures (Butler et al., 2001; Sime and Ferguson, 2003; Graham et al., 2005) for GSDs in areas of 1 m2, aiding fuller characterisation of sedimentary facies and habitat patches. In principle automated grain sizing could be done with underwater photographs, though this remains to be tested. The limitation of these methods is that they are restricted to the visible surface area of grains larger than a cutoff of several mm. A very promising alternative approach uses a different kind of image processing on smaller-scale imagery obtained by low-level aerial photography. Carbonneau et al. (2004) successfully mapped median grain size along an 80-km reach from the local semivariance of digital images with a resolution of 3 cm (see Fig. 2.2 for a small extract), and work is under way to extend this to fuller information about surface GSD.
3.3.
Flow field
The development in the 1990s of small current meters using acoustic Doppler velocimetry (ADV) made it possible to measure three orthogonal components of instantaneous velocity. Quite apart from allowing much more detailed studies of turbulence, ADV current meters have been used to map flow structures in confluences and bends in more detail than before (e.g., Frothingham and Rhoads, 2003). ADV data give direct evidence on up and downwelling which previously was inferred from cross-stream components. An alternative strategy is to use ADV measurements to validate a 3-D flow model and use that to inspect the flow structure (Ferguson et al., 2003).
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Figure 2.2. Aerial photo (left, with 20-m scale bar) of a bar in the Rivie`re Sainte Marguerite, Que´bec, Canada and map (right) of median grain size (in cm) on the same bar as derived by image processing using the method of Carbonneau et al. (2004). Note correct detection of coarse/fine alternation across the bar tail, and of low vegetation.
Acoustic Doppler current profiling (aDcp) extends ADV technology to measure instantaneous velocity components simultaneously at many heights. The strong return from the bed provides the local flow depth. The near-surface flow cannot be measured, and near-bed values are unreliable because of sidelobe interference, but if enough intermediate points are sampled it is possible to get a precise estimate of the depth-averaged velocity. The deployment of aDcp from a moving boat, with GPS positioning, is becoming the method of choice for discharge measurement in large rivers, and the potential uses of aDcp are far wider than this. A shallow-water aDcp instrument can be deployed from a towed or tethered raft in a small river to capture data far faster than by ADV. This should allow flow fields to be mapped in far more detail than was previously possible. Also, since aDcp gives the velocity profile, the bed shear stress can be estimated by fitting the law of the wall to part or all of the depth (Fig. 2.3).
3.4.
Sediment transport
Bed-material transport is a key process in gravel-bed rivers because it provides the feedback from flow to morphology. It is highly variable in space and time because of its non-linear dependence on flow, and is by far the most difficult aspect of the whole fluvial system to quantify reliably in the field. Point measurement using samplers lowered onto the bed suffers from poor repeatability and a tendency to under-catch unless the sampler orifice is large compared to both transported and immobile clasts. A fairly reliable estimate of the total flux can be obtained by sampling for several minutes at each of many positions across a river, but spatial patterns cannot be mapped accurately. Pit traps and vortex-tube extractors give more reliable results at single points, and valuable insight into variation over time, but they have high installation and operating costs, are restricted to small channels, and give no information on spatial differences within a reach. Three promising alternatives exist: morphological estimation of fluxes from volumes of erosion and deposition between channel resurveys (reviewed by Ashmore
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Figure 2.3. Section across Lower Fraser River, western Canada, showing lateral variability in hydraulic properties as shown by moving-boat aDcp measurements at a mean spacing of about 1 m. Dashed grey line shows local depth. Solid line shows local vertically average velocity with open symbols for averages over successive 20-m bins. Dotted line shows local shear stress estimated from mean velocity with solid symbols for 20-m averages.
and Church, 1998); the use of tracer pebbles to estimate flux as the product of virtual velocity and active width and depth (Haschenburger and Church, 1998) and inferring local bedload velocity from the discrepancy between apparent boat velocity from aDcp bottom tracking and true boat velocity from Differential Global Positioning System (DGPS) (Rennie et al., 2002). These methods yield information at different time and space scales. The morphological method has been applied to channels of all sizes over intervals from a day to several years. It has several variants, mostly giving only a channel-wide flux and all prone to underestimation if there has been any temporal alternation of scour and fill. The results are also sensitive to survey error, but it is possible to quantify this and assess necessary point densities (e.g., Brasington et al., 2003). The tracer method is feasible only in fairly small channels and estimates mean bedload flux through a reach over a single flood event or longer period. There is some indication that estimates over different time periods are inconsistent (Ferguson and Hoey, 2002), but this may be because the best way to estimate active depth has not yet been identified. A thorough methodological investigation at a site with a good pit or vortex-tube trap would be useful, extending the work of Sear et al. (2003). The aDcp method has the greatest uncertainties in arriving at a quantitative estimate of flux, but also the greatest potential to reveal spatial and temporal differences in the intensity of bed movement. 4.
Spatially distributed modelling of gravel-bed rivers
If attention is restricted to uniform channels and flow, the implications of assumptions about process can often be deduced mathematically. This is seldom possible for
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non-uniform situations (an exception is the analysis by Repetto et al. (2002) of how bars are forced by width variation) so it is necessary to resort to numerical solutions. Fortunately the technological advances which have enabled spatially distributed monitoring also permit distributed numerical modelling, with large numbers of computational cells across as well as along a reach (a 2-D model), and perhaps also in the vertical (a 3-D model). This gives the opportunity to compare theoretically based predictions with observed river behaviour and distributed measurements, and to use models to simulate unobservable situations or what-if scenarios. Distributed models do however require more input data and user expertise. They vary in scope, process representation, grid type, and numerical solution method so almost every model is different. The literature is expanding rapidly and it is impossible to attempt more than a brief overview here; the chapters in Bates et al. (2005) contain detailed reviews of different aspects. A model may predict just the flow field, or flow together with sediment transport, or possibly also channel change. In the first two cases the channel is a fixed container represented by a grid. In morphological models the bed level, and perhaps also bed GSD, of each cell is updated at intervals; some models also simulate bank erosion, which requires remeshing of the grid.
4.1.
Flow models
The fundamental component of all models is a flow solver which computes the velocity field over the present channel configuration. There are three broad categories: 3-D computational fluid dynamics (CFD), 2-D CFD, and simplified 2-D. CFD models solve discretized versions of the 3-D Navier–Stokes equations for conservation of fluid mass and momentum, or the 2-D St. Venant equations which are the depth-averaged equivalent. Standard 3-D CFD codes treat momentum transfer by turbulence in a statistical way using any of several sub-models for the production and transport of turbulent kinetic energy. Vertical and lateral shear is explicitly modelled except in the cells touching the bed and banks where velocity is computed from the law of the wall with a specified roughness height. A rectangular computational grid is distorted into boundary-fitted coordinates (BFC) which approximate the 3-D channel geometry, and the equations are solved by finite-volume methods. This kind of model has been applied to short reaches of natural rivers by Sinha et al. (1998), Booker et al. (2001), and others. A promising alternative to BFC uses a rectangular grid with irregular topography represented by blocking cells out (Olsen and Stokseth, 1995). This permits explicit modelling of the effects of bed microtopography (Lane et al., 2004) and should eventually be computationally feasible at reach scale. In 2-D CFD, which at present is all that is possible when modelling long reaches, the St. Venant equations are solved on a BFC grid or triangular finite-element mesh. Lateral shear is represented by an eddy viscosity. Some models include a representation of how curvature-induced secondary circulation affects the primary flow. Bed roughness is parameterised, usually by Manning’s n. Leclerc et al. (1995) and Crowder and Diplas (2000) advocated such models for ecological applications, and Lisle et al. (2000) demonstrated the potential in geomorphology. Fig. 2.4 gives an
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Figure 2.4. Extract from a 2-D flow simulation of a 12-km reach of Lower Fraser River, Canada, at 60% of mean annual flood, made using the DHI MIKE21C code. Area shown is about 2.5 1.5 km (axes are labelled in UTM metres). Depth is shown by shading, vertically averaged velocity by arrows (maximum speed about 3 m s 1). Note flow divergence around bar head and recirculation in lee.
example of the kind of detail that can be simulated within a long non-uniform reach. A 2-D model that contains an allowance for secondary-circulation effects can successfully simulate the line of the fastest current even in bends, and the existence and location of recirculation. Finally, a few reach- or basin-scale morphological models differ radically by using a square or hexagonal grid and simplified flow routing rules which conserve mass but not momentum (Murray and Paola, 1994; Coulthard et al., 2002). These models do not maintain a smooth water surface and the flow field depends not just on the routing rules but also the type and resolution of the grid, in contrast to CFD where the aim is to achieve grid-independent results (Nicholas, 2005).
4.2.
Transport and morphology
A distributed flow model can drive calculations of bedload transport, and it is then straightforward to compute changes in bed level from the divergence of the sediment transport vector. In CFD-based models the driver for transport is t, calculated from velocity squared, but the simplified rule-based models use unit discharge and bed slope. The first 2-D morphological models assumed uniform sediment but a few now allow multiple sizes, as in the 1-D models mentioned in Sections 2.1 and 2.2. Some also allow for the effect of local bed slope on transport direction, which is important in multi-size calculations. A few incorporate simple algorithms for bank erosion and thus planform change, though this is currently the weakest part of these models
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(Mosselman, 1998). Simulating bedload transport requires assumptions about sediment flux into the reach, and (for multi-size calculations) the GSDs of this flux and of the initial bed in each cell. Packages of this type have been developed and extended over many years by Delft Hydraulics (Netherlands) and DHI (Denmark) for use in engineering consultancy projects, and models have also been developed by the U.S. Geological Survey (building on Nelson and Smith, 1989) and a growing number of university engineering departments. Little of the commercially directed development is reported in the periodical literature so it is not surprising that there has been some ‘reinventing the wheel’ by academic researchers (Mosselman, 2004). Recent published developments, especially as regards simulating planform change, are discussed by Lane and Ferguson (2005). There have been very few applications of 2-D bedload or morphological modelling to gravel-bed rivers so far, but there is vast potential whether for tackling practical issues of aggradation and degradation or for investigating generic behaviour such as the self-organisation of bars, bends, and braids. Fig. 2.5 gives an example from the work I am doing on gravel transport and bar growth in the lower Fraser River. The striking feature, impossible to observe using available methods or to model in 1-D, is
Figure 2.5. Extract from a 2-D bedload transport simulation for a 12-km reach of Lower Fraser River at 60% of mean annual flood. Area shown is about 3.5 2.5 km (axes are labelled in UTM metres). Flow enters at top right past a headland. Bed elevation is shown by shading and bedload transport rate by arrows.
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that high fluxes occur only locally, and on bar flanks rather than in talwegs. This accords with the observed locations and styles of bar growth.
5.
Looking ahead
Scientific understanding advances fastest through a critical interplay between observation and theory. In the context of gravel-bed rivers, the tensions and inconsistencies between traditionally separate perspectives (Section 2) point to a need to move beyond regime theory, and to learn more about within-reach variability and its implications. Powerful new techniques for spatially distributed observation (Section 3) and modelling (Section 4) should be valuable tools in tackling these agendas, but how do we know we can trust them? In this concluding discussion I consider the two research agendas first, then the methodological issues. Regime theory may be reaching its inherent limits. Eaton et al. (2004) showed there are no unique solutions even after making an optimisation assumption: just infinite combinations of three dimensionless variables. Planform is not adequately linked in, and key simplifying assumptions of the whole approach (dominant discharge, uniform channels, fixed grain size) are doubtful. Not all reaches are in regime and many practical problems relate to disequilibrium. Moving beyond the regime approach requires greater integration of work relating to different degrees of freedom in channel change: bed elevation and channel slope, bed GSD, and lateral adjustment of width and planform. 1-D sediment routing models link the first two but do not yet contain versatile parameterisations of width adjustment, and are intrinsically inadequate for modelling strongly meandering or braided reaches. Phenomenological studies are needed of how width and planform alter during incision or aggradation in a range of circumstances, to see if any generalisations can be made. 2-D morphodynamic modelling avoids the limitations of 1-D models and appears to have great potential for studying within-reach self-organisation, but requires thorough testing and sensitivity analysis before widespread adoption. Emphasis on the ecological as well as engineering health of rivers highlights the importance of spatial variability and temporal fluctuation. Probability-distribution models that extend the hydraulic geometry concept deserve further attention, focused on testing transferability between reaches and predictability of distribution parameters. I suspect distributed flow modelling is a more universally applicable approach since there is a big literature on the general validity of the approximations made and it is becoming easier to obtain detailed reach-specific test data. Open questions include whether 3-D rather than 2-D flow detail is needed for some ecological purposes, and how to include vegetation dynamics in a reach-scale flow (or morphodynamic) model. The final set of issues concerns the interplay of observation and theory, the latter increasingly in the form of models. To advocate wider use of numerical modelling is not to suggest it can replace field investigations and flume experiments. Measurements are necessary to set up a model of any particular situation, and they are traditionally the test of a model: any serious discrepancy between model predictions and real-world observations is taken to cast doubt on the process representation in
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the model, though in a complicated model it may not be obvious where the problem lies. In fact the difference between predictions and observations depends on far more than process representation (Fig. 2.6). Real-world causal mechanisms act in particular circumstances to produce outcomes, but those outcomes depend on our decision to study one system rather than another: the experimental control or site selection that excludes some processes or factors and thereby emphasises others (Richards, 1990). Moreover, the ‘observations’ we compare with predictions are a filtered and REAL WORLD ‘real’ mechanisms contingent circumstances
site selection or experimental design
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Figure 2.6. Sources of ambiguity when comparing predictions from a numerical model with observations from a river. Upper part of diagram shows real-world situation, lower part shows model. Human decisions are involved in both observation and modelling.
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blurred sample of the spatially and temporally continuous variables of interest. What we observe, at what spatial and temporal resolution, is a subjective decision constrained by available technology and resources. All measurement is imprecise, to a degree that depends on choices of technique, instrument, quality control, and data processing. Finally, model predictions are themselves a blurred representation of the consequences of the process assumptions, filtered through the grid design and numerical solution methods. Thus two attempts to model the same situation and test against measurements could come up with different predictions, observations, agreement, and conclusions. This ambiguity can be reduced by several strategies. Numerics, gridding and the representation of specific processes can be tested in simple situations with highquality measurements (e.g., flume experiments). Opportunities can be taken to validate internal variables in more physically based models (e.g., depth and velocity in morphodynamic models where the main interest is in transport and channel change), though not in rule-based models that claim only to capture key qualitative aspects of high-level behaviour. Quantitative tests of spatially distributed models can be complemented by qualitative assessment of agreement in spatial patterns. But there will always be scope for disagreement about the adequacy of a model, not just because of the ambiguities inherent in testing but also because ‘adequacy’ has to be relative to purpose and the resources available. One response to the complexity of natural rivers is to seek ever finer spatial and temporal resolution, and represent smallscale processes explicitly rather than ignoring or parameterising them, but this reductionist strategy will never completely displace simpler models which can be applied to longer reaches with less information, or to generic situations. The most important role of cutting-edge models may instead be to establish the conditions in which simplifications are acceptable, and help develop better parameterisations for simpler models. These are exciting times for reach-scale study of gravel-bed rivers, and we need to take full advantage of the opportunities afforded by technical developments to help fill the gaps in understanding that are shown by comparing regime, channel-change, bedload, and ecological perspectives. This requires an interplay of empirical and theoretical approaches. Spatially distributed modelling has as much of a role to play as spatially distributed monitoring, but both need further development and testing before they can become routine tools. We need to consider critically the reliability of both observations and predictions, and to compare models of different complexity to decide what simplifications are adequate for what purposes.
Acknowledgements I thank my colleagues Stuart Lane and Patrice Carbonneau for Figs. 2.1 and 2.2 respectively. The Fraser River data illustrated in Fig. 2.3 were obtained under Canadian NSERC grant 246057 to Mike Church; Louise Sime processed the ADCP data. The modelling results illustrated in Figs. 2.4 and 2.5 were obtained as part of UK NERC grant NER/B/S/2002/00354. The Royal Society supported my participation in the GBR6 workshop.
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References Ashmore, P., Church, M., 1998. Sediment transport and river morphology: A paradigm for study. In: Klingeman, P.C., Beschta, R.L., Komar, P.D., and Bradley, J.B. (Eds), Gravel-Bed Rivers in the Environment. Water Resource Publications, Colorado, pp. 115–148. Ashmore, P.E., 1991. How do gravel-bed rivers braid? Can. J. Earth Sci. 28, 326–341. Bates, P.D., Lane, S.N., Ferguson, R.I. (Eds), 2005. Computational fluid dynamics: Applications in environmental hydraulics. Wiley, Chichester, 531pp. Booker, D.J., Sear, D.A., Payne, A.J., 2001. Modelling three-dimensional flow structures and patterns of boundary shear stress in a natural pool-riffle sequence. Earth Surf. Process. Landf. 26, 553–576. Brasington, J., Langham, J., Rumsby, B., 2003. Methodological sensitivity of morphometric estimates of coarse fluvial sediment transport. Geomorphology 53, 299–316. Buffington, J.M., Montgomery, D.R., 1999. Effects of sediment supply on surface textures of gravel-bed rivers. Water Resour. Res. 35, 3523–3530. Butler, J.B., Lane, S.N., Chandler, J.H., 2001. Automated extraction of grain-size data from gravel surfaces using digital image processing. J. Hydraul. Res. 39, 519–529. Butler, J.B., Lane, S.N., Chandler, J.H., Porfiri, K., 2002. Through-water close range digital photogrammetry in flume and field environments. Photogramm. Rec. 17, 419–439. Carbonneau, P.E., Lane, S.N., Bergeron, N., 2003. Cost-effective non-metric close-range digital photogrammetry and its application to a study of coarse gravel river beds. Int. J. Remote Sens. 24, 2837–2854. Carbonneau, P.E., Lane, S.N., Bergeron, N., 2004. Catchment-scale mapping of surface grain size in gravel bed rivers using airborne digital imagery. Water Resour. Res. 40, art. no. W07202. Carroll, R.W.H., Warwick, J.J., James, A.I., Miller, J.R., 2004. Modeling erosion and overbank deposition during extreme flood conditions on the Carson River, Nevada. J. Hydrol. 297, 1–21. Chandler, J., Ashmore, P., Paola, C., et al., 2002. Monitoring river channel change using terrestrial oblique digital imagery and automated digital photogrammetry. Ann. Assoc. Am. Geographers 92, 631–644. Church, M., Hassan, M.A., Wolcott, J.F., 1998. Stabilizing self-organized structures in gravel-bed stream channels: Field and experimental observations. Water Resour. Res. 34, 3169–3180. Coulthard, T.J., Macklin, M.G., Kirkby, M.J., 2002. A cellular model of Holocene upland river basin and alluvial fan evolution. Earth Surf. Process. Landf. 27, 269–288. Crowder, D.W., Diplas, P., 2000. Using two-dimensional hydrodynamic models at scales of ecological importance. J. Hydrol. 230, 172–191. Cui, Y.T., Parker, G., 2005. Numerical model of sediment pulses and sediment-supply disturbances in mountain rivers. J. Hydr. Eng. ASCE 131, 646–656. Darby, S.E., et al., 1998. River width adjustment. II: Modeling (task force report). J. Hydr. Eng. ASCE 124, 903–917. Deigaard, R., Fredsoe, J., 1978. Longitudinal grain sorting by current in alluvial streams. Nord. Hydrol. 9, 7–16. Dietrich, W.E., Kirchner, J.W., Ikeda, H., Iseya, F., 1989. Sediment supply and the development of the coarse surface-layer in gravel-bedded rivers. Nature 340, 215–217. Eaton, B.C., Church, M., Millar, R.G., 2004. Rational regime model of alluvial channel morphology and response. Earth Surf. Process. Landf. 29, 511–529. Ferguson, R., Hoey, T., Wathen, S., Werritty, A., 1996. Field evidence for rapid downstream fining of river gravels through selective transport. Geology 24, 179–182. Ferguson, R.I., 2003. The missing dimension: Effects of lateral variation on 1-D calculations of fluvial bedload transport. Geomorphology 56, 1–14. Ferguson, R.I., Cudden, J.R., Hoey, T.B., Rice, S.P., 2006. River system discontinuities due to lateral inputs: Generic styles and controls. Earth Surf. Proc. Landf. 31, 1149–1166. Ferguson, R.I., Hoey, T.B., 2002. Long-term slowdown of river tracer pebbles: Generic models and implications for interpreting short-term tracer studies. Water Resour. Res. 38, art. no. 1142. Ferguson, R.I., Parsons, D.R., Lane, S.N., Hardy, R.J., 2003. Flow in meander bends with recirculation at the inner bank. Water Resour. Res. 39, art. no. 1322.
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Fonstad, M., Marcus, M.A., 2003. Self-organized criticality in riverbank systems. Ann. Assoc. Am. Geographers 93, 281–296. Frothingham, K.M., Rhoads, B.L., 2003. Three-dimensional flow structure and channel change in an asymmetrical compound meander loop, Embarras River, Illinois. Earth Surf. Process. Landf. 28, 625–644. Graham, D.J., Reid, I., Rice, S.P., 2005. Automated sizing of coarse-grained sediments: Image-processing procedures. Math. Geol. 37, 1–28. Haschenburger, J.K., Church, M., 1998. Bed material transport estimated from the virtual velocity of sediment. Earth Surf. Process. Landf. 23, 791–808. Lamouroux, N., Souchon, Y., Herouin, E., 1995. Predicting velocity frequency-distributions in stream reaches. Water Resour. Res. 31, 2367–2375. Lane, E.W., 1955. The importance of fluvial morphology in river hydraulic engineering. Proc. Am. Soc. Civil Eng. 81, 1–17. Lane, S.N., Ferguson, R.I., 2005. Modelling reach-scale fluvial flows. In: Bates, P.D., Lane, S.N., and Ferguson, R.I. (Eds), Computational Fluid Dynamics: Applications in Environmental Hydraulics. Wiley, Chichester, pp. 217–269. Lane, S.N., Hardy, R.J., Ingham, D.B., Elliott, L., 2004. Numerical modeling of flow processes over gravelly surfaces using structured grids and a numerical porosity treatment. Water Resour. Res. 40, art. no. W01302. Lane, S.N., Westaway, R.M., Hicks, D.M., 2003. Estimation of erosion and deposition volumes in a large, gravel-bed, braided river using synoptic remote sensing. Earth Surf. Process. Landf. 28, 249–271. Leclerc, M., Boudreault, A., Bechara, J.A., Corfa, G., 1995. Two-dimensional hydrodynamic modeling – a neglected tool in the instream flow incremental methodology. Trans. Am. Fish. Soc. 124, 645–662. Legleiter, C.J., Roberts, D.A., Marcus, W.A., Fonstad, M.A., 2004. Passive optical remote sensing of river channel morphology and in-stream habitat: Physical basis and feasibility. Remote Sens. Environ. 93, 493–510. Leopold, L.B., Maddock, T., 1953. The hydraulic geometry of stream channels and some physiographic implications. U.S. Geol. Surv. Prof. Paper 252, 64. Lewin, J., Macklin, M.G., Newson, M.D., 1988. Regime theory and environmental change – irreconcilable concepts? In: White, W.R. (Ed.), International Conference on River Regime. Wiley, pp. 431–445. Lie´bault, F., Pie´gay, H., 2002. Causes of 20th century channel narrowing in mountain and Piedmont rivers of southeastern France. Earth Surf. Process. Landf. 27, 425–444. Lisle, T.E., Nelson, J.M., Pitlick, J., et al., 2000. Variability of bed mobility in natural, gravel-bed channels and adjustments to sediment load at local and reach scales. Water Resour. Res. 36, 3743–3755. McLean, D.G., Church, M., 1999. Sediment transport along lower Fraser River – 2. Estimates based on the long-term gravel budget. Water Resour. Res. 35, 2549–2559. Medawar, P.B., 1967. The Art of the Soluble. Methuen. (Also incorporated in Medawar, P.B., 1982, Pluto’s Republic, Oxford University Press, 351pp.) Millar, R.G., Quick, M.C., 1998. Stable width and depth of gravel-bed rivers with cohesive banks. J. Hydraul. Eng. ASCE 124, 1005–1013. Montgomery, D.R., Panfil, M.S., Hayes, S.K., 1999. Channel-bed mobility response to extreme sediment loading at Mount Pinatubo. Geology 27, 271–274. Mosley, M.P., 1983. Response of braided rivers to changing discharge. NZ J. Hydrol. 22, 18–67. Mosselman, E., 1998. Morphological modelling of rivers with erodible banks. Hydrol. Process. 12, 1357–1370. Mosselman, E., 2004. Discussion of ‘numerical modeling of bed evolution in channel bends’ by Kassem, A.A., Chaudhry, M.H,. J. Hydraul. Eng. ASCE 130, 82. Murray, A.B., Paola, C., 1994. A cellular model of braided rivers. Nature 371, 54–57. Nelson, J.M., Smith, J.D., 1989. Evolution and stability of erodible channel beds. In: Ikeda, S. and Parker, G. (Eds), River Meandering, AGU Geophys. Monogr., pp. 321–378. Nicholas, A.P., 2000. Modelling bedload yield in braided gravel bed rivers. Geomorphology 36, 89–106.
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Nicholas, A.P., 2005. Cellular modelling in fluvial geomorphology. Earth Surf. Process. Landf. 30, 645–649. Olsen, N.R.B., Stokseth, S., 1995. Three-dimensional numerical modeling of water-flow in a river with large bed roughness. J. Hydraul. Res. 33, 571–581. Paola, C., 1996. Incoherent structure: Turbulence as a metaphor for stream braiding. In: Ashworth, P.J., Bennett, S.J., Best, J.L., and McLelland, S.J. (Eds), Coherent Flow Structures in Open Channels. Wiley, Chichester, pp. 705–723. Paola, C., Seal, R., 1995. Grain size patchiness as a cause of selective deposition and downstream fining. Water Resour. Res. 31, 1395–1407. Parker, G., 1979. Hydraulic geometry of active gravel rivers. J. Hydraulics Div. ASCE 105, 1185–1201. Parker, G., Klingeman, P.C., 1982. On why gravel bed streams are paved. Water Resour. Res. 18, 1409–1423. Pitlick, J., 1993. Response and recovery of a subalpine stream following a catastrophic flood. Geol. Soc. Am. Bull. 105, 657–670. Rennie, C.D., Millar, R.G., Church, M., 2002. Measurement of bed load velocity using an acoustic Doppler current profiler. J. Hydraul. Eng. ASCE 128, 473–483. Repetto, R., Tubino, M., Paola, C., 2002. Planimetric instability of channels with variable width. J. Fluid Mech. 457, 79–109. Rhoads, B.L., Welford, M.R., 1991. Initiation of river meandering. Prog. Phys. Geogr. 15, 127–156. Richards, K., 1990. Real geomorphology. Earth Surf. Process. Landf. 15, 195–197. Rinaldi, M., 2003. Recent channel adjustments in alluvial rivers of Tuscany, central Italy. Earth Surf. Process. Landf. 28, 587–608. Schumm, S.A., 1969. River metamorphosis. J. Hydr. Div. ASCE 95, 255–273. Sear, D.A., Lee, M.W.E., Carling, P.A., et al., 2003. An assessment of the accuracy of the spatial integration method (SIM) for estimating coarse bedload transport in gravel-bedded streams using tracers. Int. Assoc. Hydrol. Sci. Publ. 283, 164–171. Sime, L.C., Ferguson, R.I., 2003. Information on grain sizes in gravel-bed rivers by automated image analysis. J. Sediment. Res. 73, 630–636. Sinha, S.K., Sotoropoulos, F., Odgaard, A.J., 1998. Three-dimensional numerical model for flow through natural rivers. J. Hydraul. Eng. ASCE 124, 13–24. Stewardson, M.J., McMahon, T.A., 2002. A stochastic model of hydraulic variations within stream channels. Water Resour. Res. 38, art. no. 1007. Stolum, H.H., 1998. Planform geometry and dynamics of meandering rivers. Geol. Soc. Am. Bull. 110, 1485–1498. Talbot, T., Lapointe, M., 2002. Numerical modeling of gravel bed river response to meander straightening: The coupling between the evolution of bed pavement and long profile. Water Resour. Res. 38, art. no. 1074. Van der Nat, D., Tockner, K., Edwards, P.J., et al., 2003. Habitat change in braided flood plains (Tagliamento, NE Italy). Freshwater Biol. 48, 1799–1812. Ward, J.V., Tockner, K., Arscott, D.B., Claret, C., 2002. Riverine landscape diversity. Freshwater Biol. 47, 517–539. Westaway, R.M., Lane, S.N., Hicks, D.M., 2001. Remote sensing of clear-water, shallow, gravel-bed rivers using digital photogrammetry. Photogramm. Eng. Remote Sens. 67, 1271–1281. Wilcock, P.R., 2001. The flow, the bed, and the transport: Interaction in flume and field. In: Mosley. M.P. (Ed.), Gravel-bed rivers V. NZ Hydrol. Soc., Wellington, pp. 183–220. Wilcock, P.R., Crowe, J.C., 2003. Surface-based transport model for mixed-size sediment. J. Hydraul. Eng. ASCE 129, 120–128. Winterbottom, S.J., Gilvear, D.J., 1997. Quantification of channel bed morphology in gravel-bed rivers using airborne multispectral imagery and aerial photography. Regulated Rivers: Research and Management 13, 489–499. Wyzga, B., 2001. A geomorphologist’s criticism of the engineering approach to channelization of gravelbed rivers: Case study of the Raba River, Polish Carpathians. Environmental Management 28, 341–358.
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Discussion by D. Milan, G. Heritage and D. Hetherington R. Ferguson mentions several important technological advances in the acquisition of data on river bed topography. Many of the techniques (aerial LIDAR, EDM theodolites, GPS, photogrammetry) suffer coverage or resolution limitations resulting in a trade off between spatial coverage and morphologic detail captured (Fig. 2.7). This issue is particularly important when rates of spatial and temporal change are considered for fluvial systems. At a reach scale the acquisition of high-resolution topographic information is central to the effective construction of a DEM. Oblique field based laser scanning (LiDAR) now offers a significant improvement in the speed of data capture, accuracy/resolution and areal coverage of topographic data acquisition. A Rigel LMS Z210 scanning laser has been used at a number of sites in the UK and Switzerland by the authors to collect a series of independent data sets recording range distance, relative height, surface colour and reflectivity. The instrument works on the principle of ‘time of flight’ measurement using a pulsed eye-safe infrared laser source (0.9 mm wavelength) emitted in precisely defined angular directions controlled by a spinning mirror arrangement. A sensor records the time taken for light to be reflected from the incident surface. Once the scanner unit is mounted on a tripod, it is capable of scanning through 801 in the vertical and 3301 in the horizontal, stepping 0.072–0.361 depending on the resolution required and the time available for scanning. Vertical scanning rates vary between 5 and 32 scans s 1. Angular measurements are recorded to an accuracy of 0.0361 in the vertical and 0.0181 in the horizontal. Range error is 0.025 m to a radial distance of 350 m. Point densities of 10,000 m 2 have been achieved from 12 meshed scans covering and area of 2000 m2, sufficient to represent the surface at the grain scale. Five million
Figure 2.7. Spatial and temporal limitations of morphological capture techniques.
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data points may be collected in 5 min, and a vertical resolution of around 70.02 m has been achieved. The technology works best on dry river beds and exposed bar surfaces, however where the water is clear, calm, and shallow and the angle of incidence of the laser pulse is high, some penetration does occur. The speed, coverage and accuracy of the new technology clearly offers a considerable advance for topographic data acquisition in fluvial systems. Discussion by H. Lamarre and A. Roy The paper points out that the reach-scale is associated with non-uniform fluvial processes that recent technological advances may help in understanding. Although we agree that these advances have enhanced our ability to measure in detail the fluvial system, the applicability of several methods is still limited to specific environments. For instance, several techniques to measure bed topography or flow velocity are not suitable in heavily vegetated, steep, or very coarse-grained bed channels. In this context, more traditional methods are still required and, as for new technologies, they raise recurrent and crucial unresolved questions on sampling strategies. We are wondering how consideration of reach-scale properties should be used in the optimisation of the sampling designs. When measuring at the reach-scale using performing instrumentation and adequate strategies, it is possible to capture both the local scale characteristics, such as a pebble cluster or large protruding clast as well as larger features that are characteristics of the reach-scale morphology. What is the balance between the local and the reach-scale representation? Using the maximum spatial sampling density of velocity or topography that is possible to achieve given the survey time, energy, costs and limitations of the instruments, we can capture the effects of local scale characteristics which may be less significant for the reach-scale dynamics (e.g., Lamarre and Roy, 2005). If the sampling density is reduced, only larger features remain. Determining the level of detail that must be represented at the ‘reach-scale resolution’ is then essential to a useful integration of different scales of roughness and flow structures in gravel-bed rivers. Even though the optimisation of the sampling design should also include the objectives of the study and the scales of interest, what criteria should be used to determine the resolution of reach-scale surveys? References Lamarre, H., Roy, A.G., 2005. Reach-scale variability of turbulent flow characteristics in a gravel-bed river. Geomorphology 69 (1–2), 95–113.
Discussion by C.D. Rennie The author has presented a comprehensive review of the state-of-the-art in 1D and spatially distributed approaches to understanding river morphology. The paper concludes with a discussion of the interplay between monitoring and modelling of spatially distributed processes in rivers. I wholeheartedly agree that monitoring
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data points may be collected in 5 min, and a vertical resolution of around 70.02 m has been achieved. The technology works best on dry river beds and exposed bar surfaces, however where the water is clear, calm, and shallow and the angle of incidence of the laser pulse is high, some penetration does occur. The speed, coverage and accuracy of the new technology clearly offers a considerable advance for topographic data acquisition in fluvial systems. Discussion by H. Lamarre and A. Roy The paper points out that the reach-scale is associated with non-uniform fluvial processes that recent technological advances may help in understanding. Although we agree that these advances have enhanced our ability to measure in detail the fluvial system, the applicability of several methods is still limited to specific environments. For instance, several techniques to measure bed topography or flow velocity are not suitable in heavily vegetated, steep, or very coarse-grained bed channels. In this context, more traditional methods are still required and, as for new technologies, they raise recurrent and crucial unresolved questions on sampling strategies. We are wondering how consideration of reach-scale properties should be used in the optimisation of the sampling designs. When measuring at the reach-scale using performing instrumentation and adequate strategies, it is possible to capture both the local scale characteristics, such as a pebble cluster or large protruding clast as well as larger features that are characteristics of the reach-scale morphology. What is the balance between the local and the reach-scale representation? Using the maximum spatial sampling density of velocity or topography that is possible to achieve given the survey time, energy, costs and limitations of the instruments, we can capture the effects of local scale characteristics which may be less significant for the reach-scale dynamics (e.g., Lamarre and Roy, 2005). If the sampling density is reduced, only larger features remain. Determining the level of detail that must be represented at the ‘reach-scale resolution’ is then essential to a useful integration of different scales of roughness and flow structures in gravel-bed rivers. Even though the optimisation of the sampling design should also include the objectives of the study and the scales of interest, what criteria should be used to determine the resolution of reach-scale surveys? References Lamarre, H., Roy, A.G., 2005. Reach-scale variability of turbulent flow characteristics in a gravel-bed river. Geomorphology 69 (1–2), 95–113.
Discussion by C.D. Rennie The author has presented a comprehensive review of the state-of-the-art in 1D and spatially distributed approaches to understanding river morphology. The paper concludes with a discussion of the interplay between monitoring and modelling of spatially distributed processes in rivers. I wholeheartedly agree that monitoring
Gravel-bed rivers at the reach scale
55
data points may be collected in 5 min, and a vertical resolution of around 70.02 m has been achieved. The technology works best on dry river beds and exposed bar surfaces, however where the water is clear, calm, and shallow and the angle of incidence of the laser pulse is high, some penetration does occur. The speed, coverage and accuracy of the new technology clearly offers a considerable advance for topographic data acquisition in fluvial systems. Discussion by H. Lamarre and A. Roy The paper points out that the reach-scale is associated with non-uniform fluvial processes that recent technological advances may help in understanding. Although we agree that these advances have enhanced our ability to measure in detail the fluvial system, the applicability of several methods is still limited to specific environments. For instance, several techniques to measure bed topography or flow velocity are not suitable in heavily vegetated, steep, or very coarse-grained bed channels. In this context, more traditional methods are still required and, as for new technologies, they raise recurrent and crucial unresolved questions on sampling strategies. We are wondering how consideration of reach-scale properties should be used in the optimisation of the sampling designs. When measuring at the reach-scale using performing instrumentation and adequate strategies, it is possible to capture both the local scale characteristics, such as a pebble cluster or large protruding clast as well as larger features that are characteristics of the reach-scale morphology. What is the balance between the local and the reach-scale representation? Using the maximum spatial sampling density of velocity or topography that is possible to achieve given the survey time, energy, costs and limitations of the instruments, we can capture the effects of local scale characteristics which may be less significant for the reach-scale dynamics (e.g., Lamarre and Roy, 2005). If the sampling density is reduced, only larger features remain. Determining the level of detail that must be represented at the ‘reach-scale resolution’ is then essential to a useful integration of different scales of roughness and flow structures in gravel-bed rivers. Even though the optimisation of the sampling design should also include the objectives of the study and the scales of interest, what criteria should be used to determine the resolution of reach-scale surveys? References Lamarre, H., Roy, A.G., 2005. Reach-scale variability of turbulent flow characteristics in a gravel-bed river. Geomorphology 69 (1–2), 95–113.
Discussion by C.D. Rennie The author has presented a comprehensive review of the state-of-the-art in 1D and spatially distributed approaches to understanding river morphology. The paper concludes with a discussion of the interplay between monitoring and modelling of spatially distributed processes in rivers. I wholeheartedly agree that monitoring
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programs are subjectively designed, and that all observed data contain errors and represent only a portion of the actual phenomena. However, the fact remains that 2D and 3D morphodynamic models require validation with observations. Model output is becoming increasingly detailed, including mapping of the spatial distribution of bedload transport (e.g., Fig. 2.3). However, validation and calibration of morphodynamic models is usually based on comparison of observed and predicted water levels, water velocity distributions, and, perhaps, channel change. The spatial distribution of bedload transport rate, which drives the morphodynamics yet is unreliably predicted using bedload transport formulae, is not calibrated, due to the lack of available data for calibration. In order to obtain spatially distributed bedload data, which could be used to validate morphodynamic models, I have been developing the use of acoustic Doppler current profilers (aDcps) to measure bedload transport velocity (Rennie et al., 2002; Rennie and Millar, 2004; Rennie and Villard, 2004; Gaueman and Rennie, in press). As stated by the author, the technique is based on the difference in boat velocity measured by DGPS and Doppler sonar (bottom track) that is biased by bedload motion. It has already been demonstrated that spatial distributions of bedload transport can be mapped in some situations (Rennie and Millar, 2004). Calibration curves have been developed to relate the observed signal to bedload transport rate (Rennie et al., 2002), although the calibration is site specific and depends on both particle size and aDcp parameters such as operating frequency and acoustic pulse length (Rennie and Villard, 2004; Gaueman and Rennie, in press). Further research is required to determine the limitations of the technique, to specify the relation between the observed signal and actual transport rate for particular aDcps in various fluvial environments, and to develop statistical methods to employ the observed bedload spatial distributions for model calibration.
References Gaueman, D., Rennie, C.D. (in press). A comparison of two field studies of acoustic bed velocity: grain size and instrument frequency effects. In 8th Federal Interagency Sedimentation Conference. Rennie, C.D., Millar, R.G., Church, M.A., 2002. Measurement of bedload velocity using an acoustic Doppler current profiler. J. Hydraulic Eng. (ASCE) 128, 473–483. Rennie, C.D., Millar, R.G., 2004. Measurement of the spatial distribution of fluvial bedload transport velocity in both sand and gravel. Earth Surf. Process. Landf. 29 (10), 1173–1193. Rennie, C.D., Villard, P.V., 2004. Site specificity of bedload measurement using an aDcp. J. Geophys. Res. (Earth Surf.) 109 (F3), F03003, 10.1029/2003JF000106, 29 July 2004.
Discussion by G. Williams [In response to the question of Ian Reid about the ‘black hole’ of the flood event itself] The best way of ‘viewing’ a river in flood is through mobile bed physical models. You can see the nature of the sediment movement and the changing channel forms.
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programs are subjectively designed, and that all observed data contain errors and represent only a portion of the actual phenomena. However, the fact remains that 2D and 3D morphodynamic models require validation with observations. Model output is becoming increasingly detailed, including mapping of the spatial distribution of bedload transport (e.g., Fig. 2.3). However, validation and calibration of morphodynamic models is usually based on comparison of observed and predicted water levels, water velocity distributions, and, perhaps, channel change. The spatial distribution of bedload transport rate, which drives the morphodynamics yet is unreliably predicted using bedload transport formulae, is not calibrated, due to the lack of available data for calibration. In order to obtain spatially distributed bedload data, which could be used to validate morphodynamic models, I have been developing the use of acoustic Doppler current profilers (aDcps) to measure bedload transport velocity (Rennie et al., 2002; Rennie and Millar, 2004; Rennie and Villard, 2004; Gaueman and Rennie, in press). As stated by the author, the technique is based on the difference in boat velocity measured by DGPS and Doppler sonar (bottom track) that is biased by bedload motion. It has already been demonstrated that spatial distributions of bedload transport can be mapped in some situations (Rennie and Millar, 2004). Calibration curves have been developed to relate the observed signal to bedload transport rate (Rennie et al., 2002), although the calibration is site specific and depends on both particle size and aDcp parameters such as operating frequency and acoustic pulse length (Rennie and Villard, 2004; Gaueman and Rennie, in press). Further research is required to determine the limitations of the technique, to specify the relation between the observed signal and actual transport rate for particular aDcps in various fluvial environments, and to develop statistical methods to employ the observed bedload spatial distributions for model calibration.
References Gaueman, D., Rennie, C.D. (in press). A comparison of two field studies of acoustic bed velocity: grain size and instrument frequency effects. In 8th Federal Interagency Sedimentation Conference. Rennie, C.D., Millar, R.G., Church, M.A., 2002. Measurement of bedload velocity using an acoustic Doppler current profiler. J. Hydraulic Eng. (ASCE) 128, 473–483. Rennie, C.D., Millar, R.G., 2004. Measurement of the spatial distribution of fluvial bedload transport velocity in both sand and gravel. Earth Surf. Process. Landf. 29 (10), 1173–1193. Rennie, C.D., Villard, P.V., 2004. Site specificity of bedload measurement using an aDcp. J. Geophys. Res. (Earth Surf.) 109 (F3), F03003, 10.1029/2003JF000106, 29 July 2004.
Discussion by G. Williams [In response to the question of Ian Reid about the ‘black hole’ of the flood event itself] The best way of ‘viewing’ a river in flood is through mobile bed physical models. You can see the nature of the sediment movement and the changing channel forms.
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Physical models of river reaches have been used very successfully in New Zealand. Rob Ferguson did not mention them in his overview. However, we have a long way to go before numerical models will give us a good representation of the reality of river dynamics. There should still be a place for physical modelling. For coarse gravel rivers, adequate scaling is relatively easily achieved, and provided you have a large shed and pumps on hand, physical models are not that expensive.
Discussion by A. Papanicolaou The author should be complimented for addressing one of the most intriguing problems in modern sediment transport theory, viz. limitations of traditional regime theories and the need to look for an ‘outside the box’ approach by treating the bed characteristics within a reach scale as a degree of freedom characteristics. The author eloquently discusses the necessity for introducing 2-D dimensional models to describe the spatial variability within a reach scale triggered by the self organization of the bed, and the three way constant feedback process among flow, banks, and bed morphology that is especially pronounced in rivers that undergo a system-wide adjustment. Another issue that the discusser, though, believes should be further discussed amongst the members of this community is the issue of sediment supply within a reach scale. Traditionally sediment supply is provided from upstream of a stream reach by assuming that is originated from instream sediment sources. Recently, lateral sediment contributions from the banks have been accounted for by introducing the 1.5-D models (Wu et al., 2004). However, sediment sources originated from hillslopes and floodplains (the uplands) have not yet been considered (e.g., Gouthard et al., same issue). Upland sediment delivery transport, in some cases, could account for up to 80% of the total lateral sediment inputs within a stream reach (McCool et al., 2000). In an effort to generate new knowledge and improved understanding of the complex interrelationships between watershed and instream parameters and the scale integrity influences on channel morphology, an integrated watershed hydrologic/ sedimentation framework for mountainous watersheds must be considered. This framework must utilize advanced analytical techniques and physically based numerical models for simulating upland (macro level) and instream (micro level) processes in an integrated fashion (Wang, 2005). As a first attempt in this direction, Papanicolaou et al. (2003) have conducted a watershed ecosystem study in the South Fork of the Clearwater River in Idaho, USA. They identified the interdependencies between watershed and instream parameters and the clusters of parameters that primarily affect sediment supply and ultimately fish health. Papanicolaou et al. (2003) concluded the following (Fig. 2.8): (1) Instream parameters are controlled by watershed parameters. (2) Wide ranges of watershed and instream factors have cumulative effects on sediment supply of streams.
Gravel-bed rivers at the reach scale
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Physical models of river reaches have been used very successfully in New Zealand. Rob Ferguson did not mention them in his overview. However, we have a long way to go before numerical models will give us a good representation of the reality of river dynamics. There should still be a place for physical modelling. For coarse gravel rivers, adequate scaling is relatively easily achieved, and provided you have a large shed and pumps on hand, physical models are not that expensive.
Discussion by A. Papanicolaou The author should be complimented for addressing one of the most intriguing problems in modern sediment transport theory, viz. limitations of traditional regime theories and the need to look for an ‘outside the box’ approach by treating the bed characteristics within a reach scale as a degree of freedom characteristics. The author eloquently discusses the necessity for introducing 2-D dimensional models to describe the spatial variability within a reach scale triggered by the self organization of the bed, and the three way constant feedback process among flow, banks, and bed morphology that is especially pronounced in rivers that undergo a system-wide adjustment. Another issue that the discusser, though, believes should be further discussed amongst the members of this community is the issue of sediment supply within a reach scale. Traditionally sediment supply is provided from upstream of a stream reach by assuming that is originated from instream sediment sources. Recently, lateral sediment contributions from the banks have been accounted for by introducing the 1.5-D models (Wu et al., 2004). However, sediment sources originated from hillslopes and floodplains (the uplands) have not yet been considered (e.g., Gouthard et al., same issue). Upland sediment delivery transport, in some cases, could account for up to 80% of the total lateral sediment inputs within a stream reach (McCool et al., 2000). In an effort to generate new knowledge and improved understanding of the complex interrelationships between watershed and instream parameters and the scale integrity influences on channel morphology, an integrated watershed hydrologic/ sedimentation framework for mountainous watersheds must be considered. This framework must utilize advanced analytical techniques and physically based numerical models for simulating upland (macro level) and instream (micro level) processes in an integrated fashion (Wang, 2005). As a first attempt in this direction, Papanicolaou et al. (2003) have conducted a watershed ecosystem study in the South Fork of the Clearwater River in Idaho, USA. They identified the interdependencies between watershed and instream parameters and the clusters of parameters that primarily affect sediment supply and ultimately fish health. Papanicolaou et al. (2003) concluded the following (Fig. 2.8): (1) Instream parameters are controlled by watershed parameters. (2) Wide ranges of watershed and instream factors have cumulative effects on sediment supply of streams.
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Figure 2.8. The figure illustrates the instream and watershed parameters that were found to affect sediment supply and aquatic health in the South Fork of the Clearwater River (SFCR).
(3) Lack of understanding of the complex interaction between watershed parameters with instream parameters and the effects of scale on fish species has caused, in some cases, the unsuccessful implementation and failure of these management plans (National Research Council, 1996). Based on cluster and factor statistical analysis performed over 50 parameters for about 100 years of record, it was determined that anthropogenic disturbances, watershed characteristics, river hydrology, and geometry have a significant effect on sediment delivery. Specifically, for the SFCR it is shown that the governing parameters affecting sediment supply in that basin over a period of 50 years are the Mining and Debris processes, Fires and the erosion associated with them, Hillslope and other watershed physigraphical characteristics, River density, River discharge, River bank composition, and longitudinal slope. Reach scale models (e.g., 2-D or 3-D), therefore, need to account for those inputs through a coupling approach, for example, with watershed delivery models that are physically based (e.g., WEPP). Another shortcoming of the reach scale models is that they do not account for the presence of multi-modal type of distributions, especially when cohesive sediments are ubiquitous atop the river bed (Zeigler and Nisbet, 1994). In order for the reach scale to be able to truly model sand, gravel and cohesive sediment mixtures these models need to analyse either matrix-supported beds (clay and sand dominance over gravel) or clast-supported beds (gravel dominant).
References McCool, D.K., Pannkuk, C.D., Saxton, K.E., Kalita, P.K., 2000. Winter runoff and erosion on Northwestern USA cropland. Int. J. Sediment. Res. 15 (2), 149–161.
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National Research Council, 1996. Upstream Salmon Society in The Pacific Northwest. National Academy Press, Washington, DC. Papanicolaou, A., Bdour, A., Evaggelopoulos, N., Tallebeydokhti, N., 2003. Watershed and stream corridor impacts on the fish population in the South Fork of the Clearwater River, Idaho. J. Am. Water Resour. Assoc. 39 (1), 191. Wang, S.S.Y., 2005. Integrated Modeling and Hydraulic Engineering. World Water Congress 173, 420. Wu, W., Dalmo, A.V., Want, S.S.Y., 2004. One-dimensional numerical model for nonuniform sediment transport under unsteady flows in channel networks. J. Hydr. Eng. 130, 914. Zeigler, C.K., Nisbet, B.S., 1994. Fine-grained sediment transport in Pawtuxet River, Rhode Island. ASCE J. Hydraulic Eng. 120 (5), 561–576.
Reply by the author I thank the discussants for their interest and their contributions, all of which raise useful points which were omitted in my necessarily abbreviated survey of a very broad topic. Three of the discussions relate to the new data acquisition techniques which I highlighted in Section 3 of the paper. Milan et al. draw attention to something I did not mention in my outline of new approaches to quantifying morphology: the different combinations of time and space resolution with which this can be done. Their diagram shows this well, though I suspect it will be rendered out of date by future developments – just as my text was already out of date in not mentioning oblique laser scanning, which as they demonstrate extends the envelope of space–time resolution. An issue which is implicit in such developments, and which Lamarre and Roy explicitly raise, is to what extent we actually need the highest possible spatial resolution when seeking to understand reach-scale dynamics. This is an important question, and not one with a simple answer. To take their example of individual pebble clusters: it seems intuitively reasonable to neglect these as elements of the reach planform, but the effects of bed microtopography on flow resistance do need to be taken into account somehow. Usually this is done by treating individual roughness elements as sub-grid-scale features whose combined effect is parameterised through a high value of Manning’s n or the Nikuradse roughness height. But some scientists working at the frontiers of flow modelling would argue that a more rigorous approach is to model the effects of obstacle drag and wakes explicitly in a CFD model with very detailed bed geometry (e.g., Lane et al., 2004). My own feeling is that there will always be a place for parametric representations but that it would be profitable to use reductionist process models to try to constrain and improve our parameterisations. Lamarre and Roy also point out that not all of the new techniques can be used in all kinds of rivers. As they say, dense vegetation and very coarse bed material pose particular problems, and traditional techniques remain valuable in such situations. I agree, and note the implication that Milan et al.’s scale diagram shows only the potential space–time range of each technique, not what is actually possible in a given situation. However, I don’t think this alters my general point that the available toolkit is much bigger than it was a decade ago, opening up new opportunities.
Gravel-bed rivers at the reach scale
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National Research Council, 1996. Upstream Salmon Society in The Pacific Northwest. National Academy Press, Washington, DC. Papanicolaou, A., Bdour, A., Evaggelopoulos, N., Tallebeydokhti, N., 2003. Watershed and stream corridor impacts on the fish population in the South Fork of the Clearwater River, Idaho. J. Am. Water Resour. Assoc. 39 (1), 191. Wang, S.S.Y., 2005. Integrated Modeling and Hydraulic Engineering. World Water Congress 173, 420. Wu, W., Dalmo, A.V., Want, S.S.Y., 2004. One-dimensional numerical model for nonuniform sediment transport under unsteady flows in channel networks. J. Hydr. Eng. 130, 914. Zeigler, C.K., Nisbet, B.S., 1994. Fine-grained sediment transport in Pawtuxet River, Rhode Island. ASCE J. Hydraulic Eng. 120 (5), 561–576.
Reply by the author I thank the discussants for their interest and their contributions, all of which raise useful points which were omitted in my necessarily abbreviated survey of a very broad topic. Three of the discussions relate to the new data acquisition techniques which I highlighted in Section 3 of the paper. Milan et al. draw attention to something I did not mention in my outline of new approaches to quantifying morphology: the different combinations of time and space resolution with which this can be done. Their diagram shows this well, though I suspect it will be rendered out of date by future developments – just as my text was already out of date in not mentioning oblique laser scanning, which as they demonstrate extends the envelope of space–time resolution. An issue which is implicit in such developments, and which Lamarre and Roy explicitly raise, is to what extent we actually need the highest possible spatial resolution when seeking to understand reach-scale dynamics. This is an important question, and not one with a simple answer. To take their example of individual pebble clusters: it seems intuitively reasonable to neglect these as elements of the reach planform, but the effects of bed microtopography on flow resistance do need to be taken into account somehow. Usually this is done by treating individual roughness elements as sub-grid-scale features whose combined effect is parameterised through a high value of Manning’s n or the Nikuradse roughness height. But some scientists working at the frontiers of flow modelling would argue that a more rigorous approach is to model the effects of obstacle drag and wakes explicitly in a CFD model with very detailed bed geometry (e.g., Lane et al., 2004). My own feeling is that there will always be a place for parametric representations but that it would be profitable to use reductionist process models to try to constrain and improve our parameterisations. Lamarre and Roy also point out that not all of the new techniques can be used in all kinds of rivers. As they say, dense vegetation and very coarse bed material pose particular problems, and traditional techniques remain valuable in such situations. I agree, and note the implication that Milan et al.’s scale diagram shows only the potential space–time range of each technique, not what is actually possible in a given situation. However, I don’t think this alters my general point that the available toolkit is much bigger than it was a decade ago, opening up new opportunities.
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Rennie amplifies the very brief mention in my text of his novel and highly promising method for estimating local bedload transport intensity and direction from acoustic Doppler flow profiles. I agree with him that if the calibration problem can be overcome, this will give us a tremendous opportunity to constrain the least reliable part of any distributed morphodynamic model. The other two discussions relate to Section 4 on modelling. Williams asserts the ongoing value of mobile-bed physical modelling, especially in relation to observing what goes on in flood conditions. I noted in Section 2.1 of my paper that laboratory experiments have made a major contribution to understanding planform self-organisation, and I did not mean to imply that the value of physical modelling stops there. As with field and numerical approaches, though, it does have its limitations: it is hard to build up a picture of what is generic behaviour and what is specific to the particular configuration studied; dynamical scaling is not completely unproblematic (e.g., the fine tail of the prototype bed size distribution often has to be truncated); the initial bed is often looser than in nature so that transport rates are excessive (e.g., Monteith and Pender, 2005); and there is the issue of whether to feed or recirculate sediment, and if feed, at what rate and with what GSD. The question of sediment supply to a reach is the theme of Papanicolaou’s discussion, which expands on my very brief mention of this boundary condition which is often crucial in any model of bedload transport or morphodynamics. Papanicolaou draws attention to the possible significance of lateral supply from hillslopes or floodplains, as well as the instream supply to the head of the reach, and sees a need for coupling channel reach models with basin- (watershed-) scale models of sediment delivery. This is clearly essential in trying to model the complete sediment budget. How important it is for understanding channels at reach scale depends on the calibre of the lateral supply, which if fine becomes washload without much effect on the channel. Coarse lateral inputs are possible from steep tributaries, and also from bank erosion if the floodplain is mainly the product of lateral accretion and channel switching rather than vertical accretion. Indeed, in my fieldwork experience much of the bedload in braided rivers is derived from bank retreat rather than bed scour.
References Lane, S.N., Hardy, R.J., Ingham, D.B., Elliott, L., 2004. Numerical modeling of flow processes over gravelly surfaces using structured grids and a numerical porosity treatment. Water Resour. Res. 40 (1), art. no. W01302. Monteith, H., Pender, G., 2005. Flume investigations into the influence of shear stress history on a graded sediment bed. Water Resour. Res. 41 (12), art. no. W1240.
Gravel-Bed Rivers VI: From Process Understanding to River Restoration H. Habersack, H. Pie´gay, M. Rinaldi, Editors r 2008 Elsevier B.V. All rights reserved.
61
3 Hydrodynamics of gravel-bed rivers: scale issues Vladimir Nikora
Abstract The paper discusses several issues of gravel-bed river hydrodynamics where the scale of consideration is an inherent property. It focuses on two key interlinked topics: velocity spectra and hydrodynamic equations. The paper suggests that the currently used three-range spectral model for gravel-bed rivers can be further refined by adding an additional range, leading to a model that consists of four ranges of scales with different spectral behaviour. This spectral model may help in setting up scales of consideration in numerical and physical simulations as well as in better defining relevant fluid motions associated with turbulence-related phenomena such as sediment transport and flow–biota interactions. The model should be considered as a first approximation that needs further experimental support. Another discussed topic relates to the spatial averaging concept in hydraulics of gravel-bed flows that provides double-averaged (in time and in space) transport equations for fluid momentum (and higher statistical moments), passive substances, and suspended sediments. The paper provides several examples showing how the double-averaging methodology can improve description of gravel-bed flows. These include flow types and flow subdivision into specific layers, vertical distribution of the double-averaged velocity, and some consideration of fluid stresses.
1.
Introduction
The key feature that makes river flow different from other flow types is the interaction between flowing water and sedimentary bed. This interaction occurs over a wide range of scales, from the scale of a fine sediment particle to the basin scale. A small-scale subrange of this wide range of scales is formed by turbulence and turbulence-related processes. This subrange extends from sub-millimetres to a channel width and covers motion of sediment particles in individual and collective (bedforms) modes, mixing and transport of various substances (e.g., nutrients, contaminants) and flow–biota interactions. These turbulence-related phenomena E-mail address:
[email protected] ISSN: 0928-2025
DOI: 10.1016/S0928-2025(07)11113-5
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are especially important in the functioning of gravel-bed rivers and therefore constantly attract researchers’ attention, consistently forming a topic of discussion at Gravel-Bed Rivers Workshops (e.g., Livesey et al., 1998; Nelson et al., 2001; Roy and Buffin-Belanger, 2001; Wilcock, 2001). At present, turbulence research of gravel-bed rivers is based on two fundamental physical concepts: eddy/energy cascade and coherent structures. Originally these concepts have been developed independently, and it is only recently that researchers started viewing them as interlinked phenomena. These concepts, together with fundamental conservation equations for momentum, energy, and substances, represent two facets of flow dynamics and two corresponding research approaches: statistical and deterministic. The deterministic approach stems from some ‘coherency’ in turbulent motions and from hydrodynamic equations based on fundamental conservation principles, while the statistical approach recognises ‘irregular’ components in hydrodynamic fields and therefore focuses on their statistical properties. The statistical approach is based on two important procedures: (1) decomposition of hydrodynamic fields into slow (or mean) and fast (or turbulent) components; and (2) averaging or filtering of instantaneous variables and corresponding hydrodynamic equations. The first procedure is known as the Reynolds decomposition in the case of time and ensemble (i.e., probabilistic) averaging and as Gray’s (1975) decomposition in the case of spatial averaging. This procedure can be interpreted as a scale decomposition or separation of scales. The second procedure can be formulated in many different ways among which time, ensemble, and area/volume averaging are most common. This second procedure can be viewed as a scaling-up procedure that changes the scale of consideration from one level in time–space-probability domain to another level. In this respect, scale is an inherent feature of any hydrodynamic equation, which is not always recognised in Earth Sciences. The generalised hydrodynamic equations formulated in terms of statistical moments of various orders were first proposed by A.A. Friedman and L.V. Keller in the 1920s (Monin and Yaglom, 1971). As an example, the well-known Reynolds averaged Navier–Stokes equation represents an equation for the first-order moments of velocity and pressure fields. Another direction within the statistical approach is formulation of statistical turbulence theories based on physical intuition rather than on basic conservation principles expressed by hydrodynamic equations. A well known example is Kolmogorov’s turbulence theory and its associated ‘‘5/3’’ law for the inertial subrange where energy is transferred from larger scales to smaller scales without dissipation and/or additional production. Scale is an inherent feature in such theories as well. It can be argued that the currently popular terms in Earth Sciences such as scaling, scale-invariance, self-similarity, characteristic scales, and scaling behaviour largely stem from these statistical theories of turbulence (e.g., Barenblatt, 1995, 2003). The range of problems and concepts related to gravel-bed river turbulence is wide and it is impossible to address them all within a single paper. Instead, following the central theme of this Workshop, the paper will review topics where the scale issue, as described above, is a fundamental feature, proper account of which may improve current understanding of gravel-bed rivers dynamics. The velocity spectra in gravelbed rivers will be discussed first as it forms a general framework for multi-scale considerations. With this as background, a brief discussion on how time and spatial
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scales are associated with currently used hydrodynamic equations will follow. This will lead to a more detailed consideration of the double-averaging methodology dealing with hydrodynamic equations averaged in both time and space. In the author’s own research, this methodology evolved in the mid-1990s when he tried to use conventional Reynolds averaged equations to study near-bed region of gravel-bed flows and found them inconvenient because of scale inconsistency. The paper will conclude with several examples showing how the double-averaging methodology can improve description of gravel-bed flows. The examples include flow types and flow subdivision into specific layers, vertical distribution of the double-averaged velocity, and some consideration of fluid stresses. The examples support a view that this methodology opens a new perspective in gravel-bed rivers research and may help in clarifying some long-standing problems. There are many other important aspects of gravel-bed river turbulence that are not covered in this paper. Interested readers will benefit from checking a comprehensive report of Lopez and Garcia (1996) and very recent reviews of the problem given in Roy et al. (2004, and references therein) and Lamarre and Roy (2005, and references therein).
2.
Velocity spectra in gravel-bed rivers
Velocity fluctuations in gravel-bed rivers cover wide ranges of temporal and spatial scales, from milliseconds to many years and from sub-millimetres to tens of kilometres. The smallest temporal and spatial scales relate to the so-called dissipative eddies through which energy dissipation occurs due to viscosity. The largest temporal scales of velocity fluctuations relate to long-term (climatic) fluctuations of the flow rate, while the largest spatial fluctuations are forced by morphological features such as meanders or even larger structures of, for example, tectonic origin. The amplitude of velocity fluctuations typically increases with period and wavelength (i.e., with the scale). This dependence can be conveniently summarised using velocity spectra showing how the energy of fluctuations is distributed across the scales (Fig. 3.1). The spectra in Fig. 3.1 represent a result of conceptualisation of extensive turbulence and hydrometric measurements (Grinvald and Nikora, 1988). The low frequency (large periods) range in the frequency spectrum is formed by intra-annual and inter-annual hydrological variability while high-frequency (small periods) range is formed by flow turbulence (Fig. 3.1a). The connection between these two extreme ranges is not yet clear and may relate to various large-scale flow instabilities (Grinvald and Nikora, 1988), defined in Fig. 3.1a as ‘‘hydraulic phenomena’’. The low wave-number (large spatial scale) range in the wave-number spectrum is formed by morphological variability along the flow such as bars and/or meanders (Fig. 3.1b), as was mentioned above. At small spatial scales (less than flow width) velocity fluctuations are due to turbulence. If the wave-number and frequency turbulence spectra can often be linked through Taylor’s ‘frozen’ turbulence hypothesis (as can be seen in Figs. 3.1a and b, Nikora and Goring, 2000a), the relationship between large-scale ranges of the wave number and frequency spectra are not as clear. The turbulence ranges in Figs. 3.1a and b can be conceptually subdivided into macro-turbulence (between flow depth
V. Nikora
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Geomorphological variability
W/U H/U Time scale
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Velocity Frequency Spectrum
64
(ν3/ε)1/4
Figure 3.1. Schematised velocity spectra in gravel-bed rivers: (a) frequency spectrum; and (b) wavenumber spectrum (W0 and W are the river valley and river channel widths, respectively).
and flow width), meso turbulence (between dissipative scale and flow depth), and micro turbulence (dissipative eddies). There may be a variety of energy sources for flow turbulence with the key source being the energy of the mean flow, which is transferred into turbulent energy through velocity shear and through flow separation behind multi-scale roughness elements. In the velocity spectra, the first transfer occurs at the scale of the flow depth while the second transfer occurs at the scale of roughness size(s) D (Figs. 3.1a and b). The importance of a particular range in turbulence dynamics and specific boundaries of spectral ranges should depend on width to depth ratio and relative submergence. The information on turbulence spectra in gravel-bed rivers is very fragmentary and mainly covers the longitudinal velocity component u in the range of scales from approximately one tenth of depth to several depths (e.g., Grinvald and Nikora, 1988; Nezu and Nakagawa, 1993; Roy et al., 2004). It has been shown that this region usually covers the inertial subrange where velocity spectra follow Kolmogorov’s ‘‘5/3’’ law. In most such studies a three-range model of spectra has been accepted, implicitly or explicitly, which consists of: (1) the production range where spectral behaviour has not been identified specifically; (2) the inertial subrange where spectra
Hydrodynamics of gravel-bed rivers
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follow the ‘‘5/3’’ law (there is no energy production or dissipation in this subrange; Monin and Yaglom, 1975); and (3) the viscous range where spectral density decays much faster than in the inertial subrange. This conceptual model stems from Kolmogorov’s concept of developed turbulence (i.e., at sufficiently large Reynolds number; Monin and Yaglom, 1975). However, the true spectral behaviour outside the range of length scales from E0.1 to E(2 to 3) flow depths, although very important for engineering and ecological applications, is not yet clear. Below, this range of scales is revised and extended using physical and scaling arguments, and then compared with available measurements. The analysis begins with the reasonable assumption that velocity spectra Sij (k) in high Reynolds number gravel-bed flows with dynamically completely rough beds are fully determined by one velocity scale (i.e., the shear velocity u), and three characteristic length scales: (1) characteristic bed particle size (or roughness length) D, assuming that it essentially captures the effects of bed particle size distribution; (2) distance from the bed z (see Section 4.3 for a discussion of bed origin); and (3) mean flow depth H. These are the main scales for flows over both fixed and mobile beds. The bed conditions for our considerations are somewhat simplified, i.e., channel width and characteristic scales of bed-forms are excluded from our analysis. Also, the viscous range of scales is not considered. This range, although important for dissipation mechanisms (which are beyond the scope of this paper), contributes very little to the total spectral energy. With these assumptions one can have: Sij ðkÞ ¼ F ðu ; D; z; H; kÞ
(3.1)
where k is longitudinal wave number in the direction of the mean flow (k ¼ 2p/l, l is an eddy characteristic scale in the streamwise direction). After applying conventional dimensional analysis relationship (3.1) reduces to: Sij ðkÞ ¼ u2 k1 f ðkD; kz; kHÞ
(3.2)
Using (3.2) one may consider spectral behaviour of (i) the largest eddies (l4a1iH), (ii) intermediate eddies (a2i zoloa1i H), and (iii) relatively small eddies (a3i Doloa2i z) where a1i, a2i, and a3i are scaling coefficients for the ith velocity component (i ¼ 1 for the longitudinal component u, i ¼ 2 for the transverse component v, and i ¼ 3 for the vertical component w). For the largest eddies (l4a1i H4a2i z4a3i D), i.e.: H H z z kHo2pb1i o2pb2i o2pb3i or kzo2pb1i o2pb2i o2pb3i ; z D H D (3.3) 1 where bki ¼ aki incomplete self-similarity in kH (or self-similarity of the second kind after Barenblatt, 1995, 2003), and complete self-similarity in kD and kz (note that kDokzokH) are assumed. The latter means that at small kD and kz the spectrum does not depend on these variables and they can be dropped while the former means that at a small ratio H=l / kH we may present S ij ðkÞ ¼ f ðkHÞ as Sij ðkÞ / ðkHÞa . In the case of the complete similarity in kz the contributions to spectra from the largest eddies are invariant with respect to distance from the bed, which seems physically reasonable (e.g., Kirkbride and Ferguson, 1995; Nikora and Goring, 2000b; Roy et al., 2004;
V. Nikora
66 Nikora, 2005). All these reduce (3.2) to: Sij ðkÞ ¼ c1ij u2 k1 ðkHÞa
(3.4)
where c1ij is a constant. Relationship (3.4) can be further simplified using a physical argument that the largest eddies represent a link between the mean flow and turbulence, i.e., in spectra they occupy the region of turbulence energy production where eddies interact with the mean flow and between themselves. This energy exchange between large eddies suggests that their spectral contributions are invariant with wave number and so k should be dropped from (3.4). This assumption gives a ¼ 1 and simplifies relationship (3.4) to a form: z 1 (3.5) Sij ðkÞ ¼ c1ij u2 H or Sij ðkHÞ ¼ c1ij u2 or S ij ðkzÞ ¼ c1ij u2 H which is valid for kzo2pb1i ðz=HÞ (see (3.3)). For the intermediate eddies (a2i zoloa1i H), i.e.: z z 2pb1i okzo2pb2i o2pb3i (3.6) H D complete self-similarity with kD, kz, and kH is assumed that reduces (3.2) to the relationship: Sij ðkÞ ¼ c2ij u2 k1
or
S ij ðkHÞ ¼ c2ij u2 ðkHÞ1
or S ij ðkzÞ ¼ c2ij u2 ðkzÞ1
(3.7)
which is valid for 2pb1i ðz=HÞokzo2pb2i and where c2ij is a constant. Relationships (3.6) and (3.7) mean that eddies from this range of scales are independent of the characteristic scales D, z, and H and depend only on the velocity scale, i.e., u . Finally, for relatively small eddies (a3i Doloa2i z), i.e.: z z 2pb1i o2pb2i okzo2pb3i (3.8) H D incomplete self-similarity with kz and complete self-similarity with kD and kH are assumed, i.e.: Sij ðkÞ ¼ c3ij u2 k1 ðkzÞb
(3.9)
where c3ij is a constant. To define an exponent b one may use a reasonable assumption that these eddies form the inertial subrange, i.e., S ii ðkÞ / k5=3 and C uw ðkÞ / k7=3 (Monin and Yaglom, 1975) where Sii ðkÞ is the auto-spectrum for the ith velocity component (i.e, the spectrum of a single velocity component), and C uw ðkÞ is the co-spectrum, which is the real part of the cross-spectrum of longitudinal and vertical velocities. The analysis here is restricted to just this one off-diagonal component of the spectral tensor since C uw ðkÞ provides important information Ron contributions 1 from different eddies to the primary shear stress u0 w0 ; i:e:; u0 w0 ¼ o C uw ðkÞdk. This assumption gives b ¼ 2=3 for the auto-spectra and b ¼ 4=3 for the co-spectra and simplifies (3.9) to the following relationships: Sii ðkÞ ¼ c3ii u2 k5=3 z2=3 C uw ðkÞ ¼ c3uw u2 k7=3 z4=3
S ii ðkzÞ ¼ c3ii u2 ðkzÞ5=3
or or
C uw ðkzÞ ¼ c3uw u2 ðkzÞ7=3
(3.10) (3.11)
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which are valid for 2pb2i okzo2pb3i z=D. Note that the distance z from the bed in (3.8) may be interpreted as an ‘external’ Kolmogorov’s scale (Monin and Yaglom, 1975) defined by the size of ‘attached’ eddies (i.e., eddies ‘growing’ from the bed; the attached eddies hypothesis was first introduced by Townsend, 1976). This suggests that k23 z ¼ const where k23 is the low-wave-number limit for the inertial subrange, i.e., the boundary between (3.7) and (3.10). The performance of the above relationships for individual velocity components, wave-number limits for (3.5), (3.7), (3.10), and (3.11) and ‘universal’ constants c1ij , c2ij , and c3ij should be defined from experiments. The above conceptual model consists of four ranges of scales with different spectral behaviour: (I) the range of the largest eddies (l4a1i H) with Sij ðk; zÞ / k0 z0 ; (II) the range of intermediate eddies (a2i zoloa1i H) with Sij ðk; zÞ / k1 z0 ; (III) the range of relatively small eddies (a3i Doloa2i z) with S ii ðk; zÞ / k5=3 z2=3 and C uw ðk; zÞ / k7=3 z4=3 (known as the inertial subrange where no energy production or dissipation occurs); and (IV) the viscous range (not specified here). In addition to previous three-range concepts for open-channel flows (e.g., Grinvald and Nikora, 1988; Nezu and Nakagawa, 1993) this model specifies the spectral behaviour at very low wave numbers and adds an additional spectral range with S ii ðkÞ / k1 (Fig. 3.2a). If spectral ranges (I), (III), and (IV) are well known and are widely used in physical considerations, range (II) with Sij ðkÞ k1 is much less known in gravel-bed rivers research. Its physical origin is still unclear (see, e.g., Yaglom, 1993; Katul and Chu, 1998 for various concepts and associated references). A plausible physical mechanism that may explain the appearance of this spectral range is briefly reviewed below, following Nikora (1999). There are two important properties of wall turbulence (close to the bed, within the logarithmic layer which is assumed to exist) which are well tested and accepted in wall turbulence studies. A. The shear stress t is approximately constant and equal to t ¼ ru2 (u is the friction velocity, and r is fluid density). The production of the total turbulence energy P is approximately equal to the energy dissipation d that leads to P d u3 =z. These properties describe Townsend’s (1976) equilibrium wall layer with constant shear stress. B. The mean flow instability and velocity shear generate a hierarchy of eddies attached (in the sense of Townsend, 1976) to the bed so that their characteristic scales are proportional to the distance z from the bed. Using property B it can reasonably be assumed that, due to flow instability and velocity shear, the energy injection from the mean flow into turbulence occurs at each distance z from the wall, with generation of eddies with characteristic scale L z. These eddies transfer their energy at rate e to smaller eddies and may be viewed as energy cascade initiators. In other words, it is suggested here that at each z a separate Kolmogorov’s cascade is initiated which is superposed with other energy cascades initiated at other z’s. As a result of this superposition of cascades, the energy dissipation ed at a particular distance z presents a superposition of down-scale energy fluxes, e, generated at this and at larger z (contribution from cascades generated at smaller z is negligible; justification for this may be found in Townsend, 1976). Thus,
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68 a
ε(kz)~(u*3/ z )(kz) ε(kz) = εd ~ u*3/ z
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Figure 3.2. (a) Schematised velocity auto-spectra Sii ðkzÞ and energy transfer rate ðkzÞ showing: (1) the large-scale energy production range (k4H 1 ); (2) the ‘‘1’’ scaling range (H 1 okoz1 ) where energy cascades initiated at each z are superimposed and ðkÞ changes as ðkÞ k; (3) the inertial subrange (k4z1 ) which results from superposition of inertial subranges generated at each z and, therefore, ðkÞ d ; and (4) the dissipative range. (b) An example of velocity spectra at z/H ¼ 0.0095, 0.0380, and 0.4670, measurements were made with acoustic Doppler velocimeters (ADV) with the sampling frequency of 25 Hz and duration of 20 min, 1997, Balmoral Canal (flow rate ¼ 5.14 m3/s; cross-sectional mean velocity ¼ 1.05 m/s; cross-sectional mean depth ¼ 0.78 m), New Zealand [see also Nikora (2005) for more details].
the energy flux e across the scales at any z depends on the scale under consideration, i.e., on wave number k. The flux e increases with k until it reaches 2p/z and then, for k ð2p=zÞ, stabilises being equal to ed (Fig. 3.2a). In other words, at a given distance zg the energy flux ðkÞ for ko2pz1 g represents the energy dissipation ed observed at
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z ¼ 2pk1 , z4zg . Using property A (i.e., d u3 =z) and bearing in mind that L z k1 , we have ðkÞ u3 k for ð2p=HÞ k ð2p=zg Þ. The scale H is an external scale of the flow. Following this phenomenological concept and using the 2=3 4=3 7=3 one can inertial subrange relationships S ii ðkÞ d k5=3 and C uw ðkÞ d u2 k obtain (3.7), (3.10) and (3.11). Thus, the existence of the ‘‘1’’ spectral law in wallbounded turbulence is explained by the effect of superposition of Kolmogorov’s energy cascades generated at all possible distances from the wall, within an equilibrium layer. This concept is justified using only the well-known properties of wallbounded flows. The energy cascades initiated at any z may be linked to large eddies attached to the bed and scaled with z. Such eddies may be associated with coherent structures, considered for example in Roy et al. (2004). Indeed, the data presented in Nikora (2005) suggest that the clusters of bursting events are the main contributors to range I with Sij ðkÞ / u2 H while range II with S ij ðkÞ / u2 k1 is probably formed by individual bursting events. The latter may be viewed as the energy cascade initiators. The four-range model described above has been well supported by data from gravel-bed flows (e.g., Nikora and Smart, 1997; Nikora and Goring 2000b; Roy et al., 2004). As an illustration, Fig. 3.2b shows normalised spectra Sij ðkzÞ=u2 for three representative values of z (so that effects of normalisation can be clearly seen without attenuation by numerous curves) measured with Acoustic Doppler Velocimeters in a gravel-bed Balmoral Canal (New Zealand). It is evident from Fig. 3.2b that the measured spectra do support (3.7) and (3.10) for all three velocity components, although the ‘‘1’’ ranges for the transverse and vertical velocities are fairly narrow. Besides, this figure also supports scaling relationships (3.7) and (3.11) for the co-spectra. At low wave numbers all spectra tend to constant values as predicted by (3.5). The typical values for the constants c1ij, c2ij, and c3ij obtained for gravel-bed flows are c1uu 1:0, c1vv ¼ 0:13, c1ww ¼ 0:04 [see equation (3.5)], c2uu ¼ 0:90, c2vv ¼ 0:50, c2ww ¼ 0:30 [see equation (3.7)], and c3uu ¼ 0:90, c3vv ¼ 1:20, c3ww 0:9 [see equation (3.10)]. The standard measurement errors of the above values are within 5–25%. Note that the ratio c3ww =c3uu does not satisfy Kolmogorov’s theory of locally isotropic turbulence, i.e., c3ww =c3uu 1:0o4=3, which is probably due to deviation from local isotropy. The satisfactory agreement between the proposed scaling model and measurements for the intermediate flow region (not very close to either the bed or the water surface) may have immediate applications for the broad-band turbulence intensities. Indeed, the integration of the total spectra for velocity components u, v, and w gives: 2 z z si K ¼ M i N i ln ¼ 1:84 1:02 ln and (3.12) u H u2 H where si is the standard deviation of ith velocity component; K ¼ 0:5ðs2u þ s2v þ s2w Þ is the total turbulent energy; and M u ¼ 1:90, M v ¼ 1:19, M w ¼ 0:59, N u ¼ 1:32, N v ¼ 0:49, and N w ¼ 0:22 are derived from field experiments (Nikora and Goring, 2000b). Equations (3.12) show how the turbulence intensity and energy change with changing distance from the bed. Although the above conceptual model for velocity spectra in gravel-bed flows is plausible and well supported by data for particular hydraulic conditions, it should be treated as a preliminary result rather than a solution of the problem. Indeed, the
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model, while applicable for some conditions, has many limitations and does not cover many other possible scenarios encountered in the field. The future improvements should account for the effects of relative submergence, width to depth ratio, multi-scale bed forms, wake turbulence, aquatic vegetation, bed permeability, topology of coherent structures, and other factors.
3.
Scales, hydrodynamic equations, and the double-averaging methodology
Velocity fluctuations in gravel-bed rivers, highlighted in the previous sections, form a wide continuous spectrum that makes statistical approach for their description and prediction inevitable. Although ideally it would be preferable to study the whole range of scales simultaneously (i.e., resolving the smallest temporal and spatial scales involved), in practical terms it is impossible and often is not necessary. In principle, the small-scale effects can be incorporated into larger-scale dynamics by integrating corresponding hydrodynamic equations. This procedure, as already mentioned, is commonly formulated as either time or ensemble or area/volume averaging, or combination of them. This scaling-up procedure is inbuilt into currently used hydrodynamic equations. Indeed, depending on temporal and spatial resolution these equations can be broadly classified as: (1) equations with no time/ensemble and spatial averaging for (instantaneous) hydrodynamic variables (e.g., Navier–Stokes equation for momentum, NS); (2) spatially filtered hydrodynamic equations for variables with small-scale spatial averaging (e.g., Large Eddy Simulation, LES; no time averaging is involved); and (3) time-(or ensemble) averaged hydrodynamic equations with no spatial averaging, known as the Reynolds Averaged NS equations (RANS). The spatial (LES) or time (RANS) averaging of NS equations for instantaneous variables can be viewed as a scaling-up procedure that changes the scale of consideration from a point in time-space (as in NS) to a larger spatial (as in LES) or temporal (as in RANS) scales. This classification can be further extended by adding hydrodynamic equations for variables averaged in both time and space, which can be defined as the double-averaged hydrodynamic equations (DANS). The double averaging upscales the original NS in both time and space domains. The selection of the equations for hydraulic modelling is often based, implicitly or explicitly, on scale considerations, i.e., bearing in mind velocity spectra considered in the previous section. To take all advantages provided by direct numerical solution (DNS) of the Navier–Stokes equations or LES one needs access to high-performance computing facilities as well as highly resolved initial and boundary conditions, which are unlikely to be available for many real-life engineering or ecological applications. Therefore, the RANS-based modelling approach is currently the most popular in solving practical problems although methodologically it is inconsistent in accounting for drag forces acting on the rough bed. In many real-life situations the commonly used RANS equations are difficult to implement due to the highly three-dimensional small-scale structure of the mean flow and turbulence, especially in the near-bed region (e.g., Lamarre and Roy, 2005). In addition, most applications deal with spatially averaged roughness parameters that cannot be linked explicitly with local
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(point) flow properties provided by the Reynolds equations. A more straightforward approach is to use the DANS-based models, which are rigorously derived for roughbed flows and provide explicit guidance in closure development and parameterisations. DANS-based models may successfully fill a gap in modelling capabilities for gravel-bed flow problems where the RANS-based models are not suitable. In the next paragraph we introduce the double-averaging methodology, which potentially may advance current understanding of gravel-bed flow hydrodynamics as well as provide a practical modelling tool. The double-averaged equations for turbulent rough-bed flows have been first introduced and advanced by atmospheric scientists dealing with air flows within and above terrestrial canopies such as forests or bushes (Wilson and Shaw, 1977; Raupach and Shaw, 1982; Finnigan, 1985, 2000). Later the double-averaging approach has been adopted in environmental hydraulics (e.g., Gimenez-Curto and Corniero Lera, 1996; McLean et al., 1999; Lopez and Garcia, 2001; Nikora et al., 2001, 2004, 2007a, b) but its applications for modelling, experimental design, and data interpretation are still largely undeveloped. This section will briefly discuss the double-averaged momentum equation that then will be used to illustrate the advantages of this methodology. Similar equations can be also derived for conservation of mass, energy, and other velocity moments (e.g., turbulent shear stresses). In Nikora et al. (2007a) it has been shown that for a reasonably general case of static and mobile bed surfaces with roughness elements such as moving gravel particles the double-averaged (in time first and in space second) momentum equation can be written as: @h¯ui i @h¯ui i 1 @fh¯pi 1 @fhu~ i u~ j i 1 @fhu0i u0j i ¼ gi þ h¯uj i @t @xj rf @xi f @xj f @xj 1 @ @ui þ f n @xj f @xj ZZ ZZ s s 11 1 1 1 @ui þ pni dS n nj dS @xj r f V0 f V0 S int
ð3:13Þ
S int
where ui is the ith component of the velocity vector; p is pressure; gi is the i-th component of the gravity acceleration; r is fluid density; V0 is the total volume of the averaging domain (thin slab parallel to the mean bed); n is the inwardly directed unit vector normal to the bed surface (into the fluid); Sint is the extent of water–bed interface bounded by the averaging domain; and f is the rough bed ‘porosity’ also defined in Nikora et al. (2001) as the roughness geometry function; it is discussed in the next paragraph. The overbar and angle brackets in equation (3.13) denote time and spatial (volume) averaging, respectively. The superscript ‘‘s’’ denotes superficial time average (Nikora et al., 2007a) when averaging time interval includes both periods when the spatial points are intermittently occupied by fluid and when they are occupied by roughness elements (e.g., by moving gravel particles). Equation (3.13) uses Reynolds’ decomposition y ¼ y¯ þ y0 for instantaneous variables and an analogue of Gray’s (1975) decomposition for the time-averaged variables, ~ where y is a hydrodynamic variable. The wavy overbar denotes the ¯ þ y, y¯ ¼ hyi
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spatial fluctuation in the time-averaged flow variable, i.e., the difference between ~ ¼ 0), similar to ¯ and time-averaged y¯ values (y~ ¼ y¯ hyi, ¯ hyi the double-averaged hyi 0 ¯0 ¯ the conventional Reynolds decomposition of y ¼ y þ y ; y ¼ 0. The spatial averaging is often performed over a volume V0 that is a thin slab parallel to the mean (or ‘smoothed’) bed. The plane dimensions of the averaging domain should be larger than typical mean flow heterogeneities, introduced by roughness, but much smaller than the large-scale features in bed topography. For gravel-bed rivers they should be much larger than gravel particles, but much smaller than sizes of riffles or pools. Equation (3.13) has been derived in a single-step procedure from the Navier–Stokes equation for instantaneous variables using the averaging theorems linking double-averaged derivatives with derivatives of the double-averaged variables (Nikora et al., 2007a). It accounts for roughness mobility and change in roughness density with spatial coordinates and with time, which make them different from similar equations considered in terrestrial canopy aerodynamics and porous media hydrodynamics. The derivation of (3.13) accounted for both spatial porosity fs ¼ V f =V 0 and ‘time’ porosity ft ¼ T f =T, where Vf is the volume occupied by fluid within an averaging (total) volume V0; T is the total averaging time interval including periods when the spatial points are intermittently occupied by fluid and roughness elements (e.g., by moving gravel particles); and Tf is the averaging time interval equal to sum of time periods when a spatial point under consideration is occupied by fluid only. In equation (3.13) it is assumed that ft does not (spatially) correlate with the ¯ ¼ hft ihyi). ¯ For many applications this time-averaged flow parameters (i.e., hft yi assumption is reasonable and allows replacing the product fs hft i with a single symbol f ¼ fs hft i. For fixed (static) roughness elements we have ft ¼ T f =T 1 and thus f ¼ fs . For gravel-bed flows, the function fðzÞ changes upwards from the bed material porosity fs min deeply in the sediment layer to 1 at the roughness tops to zero at the air–water interface. In the case of a flat water surface, there is a discontinuity in fðzÞ when it changes from 1 to 0. In the case of a disturbed water surface (e.g., random surface waves), the change in fðzÞ from 1 to 0 is likely to be smooth, similar to the water–sediment interface. Note that in previous work (e.g., Nikora et al., 2001), the roughness geometry function was defined for area averaging and denoted by a symbol A. Here we use the symbol f to make distinction between area and volume averaging. In comparison with the conventional Reynolds-averaged Navier–Stokes equation, the proposed double-averaged momentum equation contains several additional terms which explicitly present dispersive or form-induced stresses fields, the form drag per unit hu~ i u~ j i due to spatial variations RR in time-averaged s fluid volume f pi ¼ 1=ðfV 0 Þ Sint pni dS , and viscous drag per unit fluid volume RR s f ni ¼ 1=ðfV 0 Þ Sint ðrn@ui =@xj Þnj dS . The quantities hu~ i u~ j i in equation (3.13) stem from spatial averaging, similar to u0i u0j in the Reynolds-Averaged equations which represent a result of time (ensemble) averaging of the Navier–Stokes equation for instantaneous variables. In other words, the double-averaged equations relate to the time-averaged equations in a similar way as the time-averaged equations relate to the equations for instantaneous hydrodynamic variables. Assessment of the significance of these terms in equation (3.13) for different hydrodynamic and bed roughness
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conditions is currently underway (e.g., Nikora et al., 2007b). An important additional advantage of using double-averaged hydrodynamic parameters and equations is a better coupling between the surface water flow and the sub-surface flow within the porous bed where volume-averaged variables are traditionally used (e.g., Whitaker, 1999). The next section provides a brief review of several issues of gravel-bed flow dynamics, which are discussed based on the double-averaging methodology and which illustrate its advantages.
4. 4.1.
Hydrodynamics of gravel-bed flows: double-averaging perspective Vertical structure of gravel bed flows
Based on an analysis of the double-averaged momentum equation (3.13), Nikora et al. (2001, 2007b) suggested four types of rough-bed flows (Fig. 3.3), depending on flow submergence H m =D (Hm is the maximum flow depth, i.e., the distance between water surface and roughness troughs). Here this classification is adopted, with some modifications, for gravel-bed flows. The flow type I is the flow with high relative submergence, which contains several layers and sublayers (neglecting viscous sublayers associated with gravel particles): (1) near-water-surface layer where flow structure is influenced by the free surface effects such as turbulence damping and various types of water surface instabilities, and which for a dynamic non-flat air–water interface may be further subdivided into an upper sub-layer with a smooth transition in fðzÞ from 1 (water) to 0 (air) where drag terms and hu~ i u~ j i in equation (3.13) may be important, and a lower sublayer where form-induced stresses hu~ i u~ j i may be essential (these sublayers are similar to the interfacial and form-induced sublayers at water–sediment interface described below); (2) outer or intermediate layer, where viscous effects and form-induced momentum fluxes due to water surface disturbances and bed roughness are negligible, and the spatially averaged equations are identical to the time-averaged equations; (3) the z
Mean water surface
zws Near-water-surface layer
zint
Outer (or intermediate)layer
zL
Logarithmic layer zR zc zt
Roughness Form-induced sublayer Interfacial sublayer layer Subsurface layer
dφ =0 zf dz φ(z) 0 φmin 1
Flow Type I
Flow Type IIIFlow Flow Type IV Type II
Figure 3.3. Flow types and flow subdivision into specific regions in gravel-bed flows.
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logarithmic layer (as the relative submergence is large enough to form an overlap region) that differs from the outer layer by characteristic velocity and length scales; (4) the form-induced (or dispersive) sublayer, below the logarithmic layer and just above the roughness crests, where the time-averaged flow may be influenced by individual roughness elements and thus the terms hu~ i u~ j i may become non-zero; (5) the interfacial sublayer, which occupies the flow region between roughness crests and troughs and where momentum sink due to skin friction and form drag occurs; and (6) subsurface layer below the interfacial sublayer. The interfacial and form-induced sublayers, combined together, can be defined as the roughness layer. The nearwater-surface layer can be viewed as a near-surface counterpart of the roughness layer. The other three flow types are: (II) flow with intermediate relative submergence consisting of the subsurface layer, a roughness layer, an upper flow region which does not manifest a genuine universal logarithmic velocity profile as the ratio H m =D is not large enough, and the near-water-surface layer; (III) flow with small relative submergence with a roughness layer overlapped with the near-water-surface layer; and (IV) flow over a partially inundated rough bed consisting of the interfacial sublayer overlapped with the near-water-surface layer (Fig. 3.3). These four flow types and their subdivision into specific layers are based on the presence and/or significance of the terms of equation (3.13) in a particular flow region and cover the whole range of possible flow submergence H m =D. The above flow subdivision and flow types represent a useful schematisation that may help in various problems of gravel-bed flows. For each flow type, a specific set of relationships describing ‘double-averaged’ flow properties may be developed. The next section addresses the vertical distribution of the double-averaged longitudinal velocity h¯ui, partly based on Nikora et al. (2004).
4.2.
Velocity distribution
Vertical distributions of the time-averaged velocity in gravel-bed flows can be highly variable within a reach and therefore their parameterisation and prediction may be achievable only for flows with high relative submergence and away from the bed where local effects of roughness elements are not felt. Another difficulty arises from the fact that most applications deal with spatially averaged roughness parameters that cannot be linked explicitly with local time-averaged velocities, which are variable in space. An alternative approach is to use the double-averaged velocities instead. Their vertical distribution should depend on the flow type and, furthermore, within a particular flow type it may differ in shape from layer to layer (Fig. 3.3). This section first briefly considers the least studied flow region defined in Fig. 3.3 as the interfacial sublayer, and then provides some discussion on the velocity distribution above the gravel tops. Considering the simplest case of two-dimensional, steady, uniform, spatially averaged flow over a fixed rough bed, Nikora et al. (2004) derived several models applicable to a range of flow conditions and roughness types that share some common features. Two of these models for the interfacial sublayer (linear and exponential) are directly applicable to gravel bed flows. The exponential model applies
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when the effect of the momentum flux downwards dominates over the gravity term in (3.13) that leads to the exponential velocity distribution: h¯uiðzÞ ¼ h¯uiðzc Þ exp bðz zc Þ
(3.14)
where h¯uiðzc Þ is the double-averaged velocity at the roughness crests zc; and b is a parameter. The linear model may be a good approximation for gravel beds where the function f monotonically decreases while the total drag term ðf p þ f n Þ monotonically increases towards the lower boundary of the interfacial sublayer (Nikora et al., 2001), i.e.: h¯uiðzÞ h¯uiðzc Þ ðz zc Þ ¼ u lc
(3.15)
where l c ¼ h¯uiðzc Þ=ðdh¯ui=dzÞzc ¼ dðu =h¯uizc Þ is the shear length scale characterizing flow dynamics within the roughness layer; and d is the thickness of the interfacial sublayer. In principle, relationships (3.14) and (3.15) may be applicable for the interfacial sublayer for all four types of gravel-bed flows defined above, from flows with large relative submergence to flows with partial submergence. Fig. 3.4 supports this conjecture by showing examples of vertical distributions of the double-averaged velocity obtained in laboratory experiments for flow types I, II, and III (high to small relative submergence) and covering roughness types with various densities and arrangements (Nikora et al., 2004). In real gravel-bed rivers, the double-averaged velocity profiles within the interfacial sublayer are expected to be more complicated and composed of a combination of the linear and exponential models. The distribution of the double-averaged velocity above the roughness layer for flow type I (with large relative submergence) follows the logarithmic formula (e.g., Nikora et al., 2001): h¯ui 1 zd 1 zd þ C ¼ ln for z zR ¼ ln (3.16) u k dR k z0 where k is the von Karman constant; dR is the thickness of the roughness layer; d is the displacement length (also known as a zero-plane displacement) that defines the Y=X
[(z)-(zc )]/u*
6 4 2 0 -2 -4 -6 -8 -10
Bead-covered beds Cube-covered beds Spherical-segment bed Gravel-covered beds Fixed 2-d bedforms Rock-type bed 2-d triangle bars Crushed stones
Interfacial sublayer Flow region above the interfacial sublayer
-10
-8
-6
-4
-2
0 2 (z-zc)/lc
4
6
8
10
Figure 3.4. Vertical distribution of the double-averaged velocities for various roughness types in coordinates ½h¯uiðzÞ h¯uiðzc Þ=u ¼ f ½ðz zc Þ=l c (data are fully described in Nikora et al., 2004). Deviations of the data points from Y ¼ X are consistent with the exponential distribution (3.14).
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‘hydrodynamic’ bed origin; z0 ¼ dR expðkCÞ is the hydrodynamic roughness length; and the constant C depends on the definition of dR and the roughness geometry (see Fig. 3.3 for definitions). It is useful to recall that equation (3.16) has been phenomenologically justified only for flows with large relative submergence where roughness scale D is well separated from the external flow scale such as mean flow depth H. For the genuine universal logarithmic layer (3.16) to form the required ratio H=D should well exceed 40 or even 80 (Jime´nez, 2004). However, many gravel-bed flows can often be defined as flows with intermediate submergence (flow type II), i.e., they are relatively shallow with respect to the multi-scale bed roughness (H/Do80). With no alternative rigorous theory available these low-submergence flows are nearly always studied using the logarithmic boundary layer concept, which is currently justified only for deep flows, i.e., H/D480 (Jime´nez, 2004). Nevertheless, the data available for flow type II suggest that the shape of the distribution of the doubleaveraged velocities above the roughness layer is often logarithmic (e.g., Bayazit, 1976; Dittrich and Koll, 1997; Dancey et al., 2003) and, therefore, there might be some general law behind it. Below, an explanation for logarithmic behaviour in flows of type II is suggested by modifying an overlap-based derivation of the logarithmic formula. Following the conventional dimensional analysis we can express the vertical distribution of the double-averaged velocity in the near-bed region above the roughness layer as: h¯ui zd H (3.17) ¼F ; ;g u D D i where gi are the dimensionless parameters of bed roughness (e.g., density of roughness elements); and the flow depth is defined as the difference between the mean water surface elevation and the mean bed elevation. Formula (3.17) represents the inner layer where roughness effects on the velocity field dominate. In the flow region well away from the bed, the velocity deficit h¯ui h¯uimax can be expressed as: h¯ui h¯uimax zd H ¼G ; (3.18) u H D where h¯uimax is the maximum flow velocity at z ¼ zm that often occurs at the water surface. Formula (3.18) represents the outer layer where effects of large eddies scaled with the flow depth dominate. Equations (3.17) and (3.18) differ from conventional relationships (e.g., Raupach et al., 1991) by additional variable H=D included in both functions F and G. At very large relative submergence H=D it is reasonable to assume that functions F and G do not depend on H=D. This case corresponds to conventional formulation (3.16) for flows with large relative submergence. However, at smaller values of H=D (flow type II) equations (3.17) and (3.18) state that effects of large eddies on the inner layer are not negligible with, at the same time, bed roughness effects extending into the outer layer. For this case, we can assume that there is an overlap region between the inner and outer layers where equations (3.17) and (3.18) are simultaneously valid, similar to the classical overlap approach. Then, equating the derivatives of (3.17) and (3.18) and multiplying them by (zd) we
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can obtain: 1 z d @h¯ui @F @G H H ¼ ZH ¼f ¼ ZD ¼ k u @z @Z D @Z H D D
(3.19)
where Z D ¼ ðz dÞ=D, Z H ¼ ðz dÞ=H, and the function f depends on the relative submergence H=D as it is present as a variable in both F and G. This function is expressed here as f ðH=DÞ ¼ ½kðH=DÞ1 for convenience, preserving classical formulation but interpreting k as the von Karman parameter rather than a constant. From equation (3.19) it is clear that when H=D is not large enough then the von Karman parameter k depends on H=D. Integration of equation (3.19) gives: h¯ui 1 zd H (3.20) ln þC ;g ¼ u kðH=DÞ D D i and h¯ui h¯uimax 1 zd ¼ ln u kðH=DÞ zm d
(3.21)
Equations (3.20) and (3.21) can serve, at least as a first approximation, for describing velocity distribution above roughness tops in flows with intermediate submergence (flow type II). The data available for such flows (e.g., Bayazit, 1976; Dittrich and Koll, 1997; Dancey et al., 2003) support equations (3.20) and (3.21) and show that with increase in relative submergence the von Karman parameter kðH=DÞ tends to the well-known universal constant of 0.41. Although relationships (3.20) and (3.21) are to be yet properly tested they represent a useful framework for interpreting and explaining experimental data on flows of type II. 4.3.
Bed origin and zero-plane displacement
Equations (3.16)–(3.21) contain a displacement height d that determines the origin of the logarithmic velocity profile. It is useful therefore to discuss what bed elevation should be used as the bed origin for hydrodynamic considerations. In general, at least three different ‘hydrodynamic’ bed origins may be distinguished, depending on the particular task (Nikora et al., 2002). The bed origin of type 1 corresponds to the level that should be used to measure the flow depth and the bed shear stress. It can be readily shown, using the spatial averaging approach (Nikora et al., 2001), that the spatially averaged bed elevation should be used as the bed origin in this case. The size of the spatial averaging area, which is in the plane parallel to the mean bed and which is the same for both bed topography and the hydrodynamic variables, depends on the statistical structure of bed elevations, i.e., on their probability distribution and the spectrum or correlation functions. The bed origin of type 1 is a natural choice when one considers 2D vertically averaged hydrodynamic equations (models). The definition of this bed origin does not require any details of velocity distribution as it is based purely on bulk mass conservation and spatially averaged momentum balance. Although the bed origin of this type is equally useful in 3D considerations too, there are also other options for this case. One of them is the bed origin for the logarithmic
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formula of the velocity distribution, defined here as the bed origin of type 2. Another useful bed origin, type 3, may be defined for the spatially averaged velocity distribution within the roughness layer. Two natural choices for this bed origin may be considered, i.e.: (i) the minimum elevation of the roughness troughs, and (ii) the upper boundary of the interfacial sublayer as expressed in equations (3.14) and (3.15). Both lower and upper boundaries of the interfacial sublayer may be defined in a statistical sense (e.g., 5 and 95% probability of exceedence). Bed origins of types 1, 2, and 3 do not necessarily coincide as sometimes assumed in research papers. They also do not exclude each other as they represent different flow features and, thus, all of them are useful in modelling and physical considerations. Justification for the bed origin types 1 and 3 is clear and reasonably straightforward. However, the bed origin of type 2 for the logarithmic formula is still under debate (see, e.g., Nikora et al., 2002 for review). In Nikora et al. (2002) it was suggested that the zero-plane displacement d for the logarithmic formula should be the level that large-scale turbulent eddies feel as the ‘bed’ and, thus, their dimensions linearly scale with the distance from this virtual bed. Such a definition directly follows from a slightly modified Prandtl’s mixing length phenomenology, and serves as a physical basis for determining d from velocity measurements. Nikora et al. (2002) demonstrated that for a range of roughness types the displacement height for the logarithmic formula is strongly correlated with the thickness of the interfacial sublayer and with the shear length scale l c ¼ h¯uiðzc Þ=ðdh¯ui=dzÞzc in (3.15). 4.4.
Fluid stresses in gravel-bed flows
Within the double-averaging framework, the total fluid stress in gravel-bed flows consists of three components:
1 dfh¯ui ~ n hu0 w0 i hu~ wi (3.22) tðzÞ ¼ r f dz which are expressed in equation (3.22), for simplicity, for the case of 2D flows. In most cases the viscous component in equation (3.22) can be neglected, as turbulent stresses in gravel-bed flows are normally several orders of magnitude larger. The spatially averaged turbulent stress hu0 w0 i often changes (quasi) linearly towards the bed and attains a maximum near the roughness tops. Below the roughness tops it reduces to zero due to momentum sink through viscous (skin) friction and form drag. Its distribution is reasonably well studied experimentally showing dependence on relative submergence and roughness geometry. The last component, form-induced ~ appears as a result of spatial correlation of perturbations in timestress hu~ wi, averaged velocities leading to an additional ‘canal’ of momentum flux. The change in flow submergence may lead, in principle, to the change in nature of fluid stresses. Gimenez-Curto and Corniero Lera (1996) suggested that with a decrease in flow submergence, the form-induced stress might become the dominant component of the total stress. This, in turn, may lead to a new flow regime named by the authors the ‘‘jet regime’’, in addition to the well-known laminar, turbulent hydraulically smooth, and turbulent hydraulically rough regimes (Gimenez-Curto and Corniero Lera,
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1996). However, the nature of form-induced stresses in gravel-bed flows is still un~ may not be negclear. Some preliminary experimental results suggest that hu~ wi ligible within the roughness layer and their contributions and role in the momentum balance can be important (up to 15–30% of the total fluid stress, Nikora et al., 2001; Aberle and Koll, 2004; Campbell et al., 2005).
5.
Conclusions
In this paper, several issues of gravel-bed river hydrodynamics were discussed, with the focus on two key interlinked topics: velocity spectra and hydrodynamic equations, related to each other through the scale of consideration. It is suggested that the currently used three-range spectral model for gravel-bed rivers should be further refined by adding an additional range, leading to a model that consists of four ranges of scales with different spectral behaviour. This model is considered as a first approximation that needs further experimental support. Another topic relates to the spatial averaging concept in hydraulics of gravel-bed flows that provides doubleaveraged transport equations for fluid momentum (and higher statistical moments), passive substances, and suspended sediments. The double-averaged hydrodynamic equations considered in this paper may help in developing numerical models, designing and interpreting laboratory, field, and numerical experiments.
Acknowledgements The research was partly funded by the Foundation for Research Science and Technology (C01X0307 and C01X0308), the Marsden Fund (UOA220, LCR203) administered by the New Zealand Royal Society (New Zealand), and the University of Aberdeen (Scotland). Some of studies reviewed in this paper have been completed and published in cooperation with J. Aberle, S. Coleman, A. Dittrich, D. Goring, K. Koll, I. McEwan, S. McLean, and D. Pokrajac, to whom the author is grateful. The author is also grateful for useful discussions and suggestions to J. Aberle, S. Coleman, W. Czernuszenko, J. Finnigan, D. Goring, G. Katul, K. Koll, V.C. Patel, D. Pokrajac, M. Raupach, P. Rowinski, R. Spigel, and R. Walters. R. Spigel and two anonymous reviewers provided useful comments and suggestions which were gratefully incorporated into the final manuscript.
References Aberle, J., Koll, K., 2004. Double-averaged flow field over static armor layer. In: Greco, M., Carravetta, A., and Della Morte, R. (Eds), River flow 2004, Proceedings of 2nd International Conference on Fluvial Hydraulics, June, 2004, Napoli, Italy, pp. 225–233. Barenblatt, G.I., 1995. Scaling Phenomena in Fluid Mechanics. Cambridge University Press, Cambridge. Barenblatt, G.I., 2003. Scaling. Cambridge University Press, Cambridge.
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Bayazit, M., 1976. Free surface flow in a channel of large relative roughness. J. Hydraul. Res. IAHR 14 (2), 115–126. Campbell, L., McEwan, I., Nikora, V., Pokrajac, D., Gallagher, M., 2005. Bed-load effects on hydrodynamics of rough-bed open-channel flows. J. Hydraul. Eng. ASCE 131 (7), 576–585. Dancey, C.L., Kanellopoulos, P., Diplas, P., 2003. Velocity profiles in shallow flows over fully rough boundaries. In: Nezu, I. and Kotsovinos, N. (Eds), Inland Waters: Research, Engineering and Management. XXX IAHR Congress, Greece, pp. 119–126. Dittrich, A., Koll, K., 1997. Velocity field and resistance of flow over rough surface with large and small relative submergence. Int. J. Sed. Res. 12 (3), 21–33. Finnigan, J.J., 1985. Turbulent transport in flexible plant canopies. In: Hutchinson, B.A. and Hicks, B.B. (Eds), The Forest–Atmosphere Interactions. D. Reidel Publishing Company, Dordrecht, The Netherlands, pp. 443–480. Finnigan, J.J., 2000. Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519–571. Gimenez-Curto, L.A., Corniero Lera, M.A., 1996. Oscillating turbulent flow over very rough surfaces. J. Geophys. Res. 101 (C9), 20745–20758. Gray, W.G., 1975. A derivation of the equation for multi-phase transport. Chem. Eng. Sci. 30, 229–233. Grinvald, D.I., Nikora, V.I., 1988. River Turbulence (in Russian). Hydrometeoizdat, Leningrad, Russia. Jime´nez, J., 2004. Turbulent flows over rough walls. Ann. Rev. Fluid Mech. 36, 173–196. Katul, G., Chu, C.-R., 1998. A theoretical and experimental investigation of energy containing scales in the dynamic sublayer of boundary-layer flows. Boundary-Layer Meteorol. 86, 279–312. Kirkbride, A.D., Ferguson, R.I., 1995. Turbulent flow structure in a gravel-bed river: Markov chain analysis of the fluctuating velocity profile. Earth Surf. Process. Landf. 20, 721–733. Lamarre, H., Roy, A., 2005. Reach scale variability of turbulent flow characteristics in a gravel-bed river. Geomorphology 68 (1–2), 95–113. Livesey, J.R., Bennett, S., Ashworth, P.J., Best, J.L., 1998. Flow structure, sediment transport, and bedform dynamics for a bimodal sediment mixture. In: Klingeman, P.C., Beschta, R.L., Komar, P.D., and Bradley, J.B. (Eds), Gravel-bed Rivers in the Environment. Water Resources Publications, Colorado, pp. 149–176. Lopez, F., Garcia, M., 1996. Turbulence structure in cobbled-bed open-channel flow. Hydraulic Engineering Series No 52, Department of Civil Engineering, University of Illinois at Urbana-Champaign, Illinois. Lopez, F., Garcia, M., 2001. Mean flow and turbulence structure of open-channel flow through emergent vegetation. J. Hydraul. Eng. ASCE 127 (5), 392–402. McLean, S.R., Wolfe, S.R., Nelson, J.M., 1999. Spatially averaged flow over a wavy boundary revisited. J. Geophys. Res. 104 (C7), 15743–15753. Monin, A.S., Yaglom, A.M., 1971. Statistical Fluid Mechanics: Mechanics of Turbulence. Vol. 1. MIT Press, Boston, MA. Monin, A.S., Yaglom, A.M., 1975. Statistical Fluid Mechanics: Mechanics of Turbulence. Vol. 2. MIT Press, Boston, MA. Nelson, J.M., Schmeeckle, M.W., Shreve, R.L., 2001. Turbulence and particle entrainment. In: Mosley, M.P. (Ed.), Gravel-Bed Rivers V. New Zealand Hydrological Society, Wellington, New Zealand, pp. 221–248. Nezu, I., Nakagawa, H., 1993. Turbulence in Open-Channel Flows. A.A. Balkema, Rotterdam, Brookfield, Netherlands. Nikora, V., 2005. Flow turbulence over mobile gravel bed: spectral scaling and coherent structures. Acta Geoph. 53 (4), 539–552. Nikora, V., Koll, K., McEwan, I., McLean, S., Dittrich, A., 2004. Velocity distribution in the roughness layer of rough-bed flows. J. Hydraul. Eng. ASCE 130 (7), 1036–1042. Nikora, V., Koll, K., McLean, S., Dittrich, A., Aberle, J., 2002. Zero-plane displacement for rough-bed open-channel flows. In: Bousmar, D. and Zech, Y. (Eds), Proceedings of the International Conference on Fluvial Hydraulics River Flow 2002, September 4–6, 2002, Louvain-la-Neuve, Belgium, pp. 83–92. Nikora, V., McEwan, I., McLean, S., Coleman, S., Pokrajac, D., Walters, R., 2007a. Double averaging concept for rough-bed open-channel and overland flows: theoretical background. J. Hydraul. Eng. ASCE 133 (8), 873–883.
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Nikora, V., McLean, S., Coleman, S., Pokrajac, D., McEwan, I., Campbell, L., Aberle, J., Clunie, D., Koll, K., 2007b. Double averaging concept for rough-bed open-channel and overland flows: applications. J. Hydraul. Eng. ASCE 133 (8), 884–895. Nikora, V.I., 1999. Origin of the ‘‘-1’’ spectral law in wall-bounded turbulence. Phys. Rev. Lett. 83, 734–737. Nikora, V.I., Goring, D.G., 2000a. Eddy convection velocity and Taylor’s hypothesis of ‘frozen’ turbulence in a rough-bed open-channel flow. J. Hydrosci. Hydraul. Eng. JSCE 18 (2), 75–91. Nikora, V.I., Goring, D.G., 2000b. Flow turbulence over fixed and weakly mobile gravel beds. J. Hydraul. Eng. ASCE 126 (9), 679–690. Nikora, V.I., Goring, D.G., McEwan, I., Griffiths, G., 2001. Spatially-averaged open-channel flow over a rough bed. J. Hydraul. Eng. ASCE 127 (2), 123–133. Nikora, V.I., Smart, G.M., 1997. Turbulence characteristics of New Zealand gravel-bed rivers. J. Hydraul. Eng. ASCE 123 (9), 764–773. Raupach, M.R., Antonia, R.A., Rajagopalan, S., 1991. Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44 (1), 1–25. Raupach, M.R., Shaw, R.H., 1982. Averaging procedures for flow within vegetation canopies. BoundaryLayer Meteorol. 22, 79–90. Roy, A.G., Buffin-Belanger, T., 2001. Advances in the study of turbulent flow structures in gravel-bed rivers. In: Mosley, M.P. (Ed.), Gravel-Bed Rivers V. New Zealand Hydrological Society, Wellington, New Zealand, pp. 375–404. Roy, A.G., Buffin-Belanger, T., Lamarre, H., Kirkbride, A.D., 2004. Size, shape, and dynamics of largescale turbulent flow structures in a gravel-bed river. J. Fluid Mech. 500, 1–27. Townsend, A.A., 1976. The Structure of Turbulent Shear Flow. Cambridge University Press, Cambridge. Whitaker, S., 1999. The Method of Volume Averaging. Kluwer Academic Publishers, Dordrecht. Wilcock, P.R., 2001. The flow, the bed, and the transport: interaction in flume and field. In: Mosley, M.P. (Ed.), Gravel-Bed Rivers V. New Zealand Hydrological Society, Wellington, New Zealand, pp. 183–220. Wilson, N.R., Shaw, R.H., 1977. A higher order closure model for canopy flow. J. Appl. Meteorol. 16, 1197–1205. Yaglom, A., 1993. Similarity laws for wall turbulent flows: their limitations and generalizations. In: Dracos, Th. and Tsinober, A. (Eds), New Approaches and Concepts in Turbulence. Birkhauser Verlag, Basel, pp. 7–27.
Gravel-Bed Rivers VI: From Process Understanding to River Restoration H. Habersack, H. Pie´gay, M. Rinaldi, Editors r 2008 Elsevier B.V. All rights reserved.
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4 Pressure- and velocity-measurements above and within a porous gravel bed at the threshold of stability Martin Detert, Michael Klar, Thomas Wenka and Gerhard H. Jirka
Abstract Experimental results of measurements characterising the pressure and velocity above and within a porous gravel layer are presented. The goal of this study is to give a better understanding of the flow in the hyporheic interstitial under the influence of turbulence in the main flow. Latest developments in measuring techniques were applied: miniaturised piezoelectric pressure sensors (MPPS) were used to measure turbulent pressure fluctuations inside the gravel layer. Velocity measurements were carried out by a 3D-particle tracking velocimetry system (3D-PTV) using miniaturised endoscopic stereo setups within artificial gravel pores. Additionally, in the main flow a 1D-acoustic doppler current profiler (1D-ADCP) was used. Within the main flow, alternating faster and slower fluid packets with a size scaling with the flow depth were observed. Pressure fluctuations rms( p) as well as velocity fluctuations rms(u, v, w) decrease exponentially with increasing gravel depth, mainly within the first two layers of gravel grains. 1.
Introduction
Many problems in hydraulic engineering in rivers and waterways are related to the prediction of the morphodynamical development of the bed. The efficiency of regulation works or hydraulic constructions such as groynes, weirs or embankments is strongly influenced by the stability of the river bed and the artificial geotechnical armoring layer, respectively. For example, 170,000 m3 of gravel feeding per year is needed for the Iffezheim barrage at the Rhine River near Karlsruhe to avoid erosion in the downstream river bed. The costs run up to 5 Mio. Euro each year (WSA, 2004). Over the last 100 years much research work has been done to gain insight into the background of river bed stability. Shields (1936) developed a concept of a critical shear stress t0c to describe the transition from a stable to a moving bed. This can be seen as the ‘classical’ approach in bed stability. Diverse formulae have been E-mail address:
[email protected] (M. Detert) ISSN: 0928-2025
DOI: 10.1016/S0928-2025(07)11121-4
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developed to improve this approach, e.g. Zanke (2001). Furthermore, a large number of mainly empirical approaches were published to predict erosion in nonuniform flow regions like piers, groyne heads or due to jets, etc. However, up to now no satisfactory, physically founded description has been established to answer definitely the question of bed stability. The objective of this paper is to improve the physical understanding of the hydrodynamic process above and within gravel beds. The long-term goal is to better understand erosion and sedimentation as well as exchange processes (mass, momentum) between surface and subsurface water. To study the flow within the hyporheic interstitial, miniaturised piezoelectric pressure sensors (MPPS) and 3D-particle tracking velocimetry system (3D-PTV) were applied.
2.
Background
Instantaneous shear and pressure forces acting on outer grains are the driving mechanisms for destabilisation processes of a mobile bed. Beyond their influence on the stability of a river bed, turbulent structures are also a determining factor for colmation processes and mass transfer in the transition between main flow and subsurface interstitial flow (e.g., Vollmer et al., 2002; Roy et al., 2004). To describe these mechanisms there is a need for synoptic measurements of velocity and pressure fields in the main flow as well as within the pore flow within the bed that is interacting with the main flow. Dynamic processes have a relevant influence on the flow near a rough porous bed. Eddies emerge from wakes behind roughness elements and rollup processes at free shear layers. The latter eddy-generating mechanism was first described for smooth beds by Kline et al. (1967) as the bursting phenomenon. It generated a new interest in studying the structures of boundary layer turbulence (Grass, 1971; Dittrich et al., 1996; Sechet and Guennec, 1999; Adrian et al., 2000). These coherent turbulent structures play an important role in the pressure peaks acting on the bed. Farabee and Casarella (1991) derived from literature and own wind tunnel experiments, that the relation between the pressure variance rms(p) and the bed shear stress t0 depends on the Reynolds number for the boundary layer thickness d and shear velocity u*, Re*, d ¼ u*d/V. The measured range is qffiffiffiffiffi p2 rmsðpÞ ¼ ¼ 2:5 3:5 (4.1) t0 t0 With the estimate of max(p)/rms(p) ¼ 6, found by Emmerling (1973), the maximum pressure peaks can reach up to max(p) ¼ 18 t0. Thus, loads from max(p) appear to be more than one order of magnitude larger than the critical Shields parameter t0c. In contrast to the knowledge concerning the flow over a smooth bed, the research concerning the flow over and within a rough porous bed cannot be considered complete. Twenty years after his first works, Grass et al. (1991) showed that coherent structures are also detectable on rough beds. Likewise, Smith et al. (1991) and Defina (1996) found that the lateral extension of these eddy structures merely correlates with
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the roughness height. Garcı´ a et al. (1996) depicted the effect of the coherent structures on the entrainment and transport of particles in a flow over smooth and over rough beds. Sechet and Guennec (1999) showed that the high energy containing turbulent structures govern the Reynolds stresses significantly. By means of experimental data they were able to correlate sediment transport with burst-like eddy structures near the bed. Hofland (2004) and Hofland et al. (2005) used a 2D-PIV technique and three piezometric pressure sensors on top of a rough bed of stones at the threshold to instability. They were able to correlate the movement of a single stone to a mechanism of small-scale lift fluctuations followed by a large-scale drag force. The depiction of flow on top of a rough bed from Hofland et al. (2005) is the most qualitative at present. However, as they focus on the uppermost gravel layer, no information about the interaction between open-channel and pore flow can be given. To improve the basic knowledge of this interaction, both the surface and the interstitial flow have to be surveyed.
3. 3.1.
Experiments Experimental setup
The experimental system was implemented in an open-channel flume located at the Federal Waterways Engineering and Research Institute (BAW), in Karlsruhe. The flume was L ¼ 40 m long and B ¼ 0.9 m wide. The maximum flow rate Qmax ¼ 0.275 m3/s led to low mobility conditions at the bed. In the flume (see Fig. 4.1), a sand layer of HS ¼ 0.5 m was covered by a porous gravel layer of HP ¼ 0.10 m. The effective length of the flume was L ¼ 30.10 m. The measurement area was located in the middle
(a)
Streamwise view
(b) Side view
Figure 4.1. Sketch of experimental setup with definition of the coordinate system, dimensions in [m], not to scale. (a) streamwise view with the positions of the MPPSs, (b) side view, where the positions of the three artificial gravel pores with 3D-PTV and the MPPSs are shown.
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of the flume, hence influences of inlet (fully developed boundary layer) and outlet were negligible. The medium grain diameter of the gravel was dmD ¼ 10.2 mm, with a degree of nonuniformity of Cc ¼ d60/d10 ¼ 1.25. Thus, the gravel was very uniform. The pore number was determined to be e ¼ 62.4% (loose bulk density: rbulk ¼ 1.538 g/cm3, absolute density: rabs ¼ 2.464 g/cm3). The mean grain diameter of the uniform sand was about ds ¼ 1.0 mm. The critical shear stress t0c for this material is calculated to t0c ¼ 8.8 Pa, using Shields equation with Frc* ¼ t0c/(Dr g dmD) ¼ 0.06. Fig. 4.1 illustrates the measurement setup. In particular, the setup consists of the following parts:
three endoscopic stereo probes to record image sequences of the interstitial flow inside the gravel layer with specially prepared artificial gravel pores; flow analysis by a 3D-PTV algorithm. up to ten MPPS at arbitrary locations within the gravel layer; three of the sensors attached to the artificial gravel pores.
To gain additional insight into the velocity regime, a 1D-acoustic doppler current profiler (1D-ADCP) was applied. In the following sections the measuring techniques are described in more detail.
3.2.
3D-particle tracking velocimetry (3D-PTV)
The 3D-PTV technique is a nonintrusive optical technique based on image sequence analysis. Pore flow measurements inside three single pores of the gravel layer were carried out using three miniaturised endoscopic stereo setups. The basic principle of these setups was to acquire stereoscopic image sequences of the flow field inside the pore volume by viewing it from two different directions. Two flexible fiberoptic endoscopes of 2.4 mm diameter were attached to an adapted artificial gravel pore made of grains fixed to each other (Fig. 4.2). The optical axes of the two cameras enclosed an illumination fiber pressure sensor
pore volume
holes for fixation of stereo rig
(a)
(b)
Figure 4.2. Endoscope stereo setup. (a) For velocity measurements in the gravel layer, this stereo rig is attached to an artificial gravel pore, viewing the pore volume inside. (b) Artificial gravel pore.
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angle of about 901. The size of the stereo volume was about 5 mm in all directions. For more details see Klar et al. (2002). Illumination of the pore volume was provided by an optical fiberbundle guiding the light from a halogen cold light source into the pore. The purpose of the artificial pore is to hold the endoscopes and the illumination fiber at a fixed relative position and to keep surrounding grains in the gravel layer from blocking the endoscope view. To perform flow measurements, the three artificial pores were embedded in the gravel layer at different positions (see again Fig. 4.1). A suspension of tracer particles was added to the flow upstream of the pores, and particle image sequences of the two different endoscope views were recorded simultaneously. Since the tracer particles cover this small volume very rapidly, the cameras must operate at high frame rates. Hence, two of the three artificial pores were equipped with highspeed MegapixelCMOS-cameras (Photonfocus MV-D1024). The read-out size of the cameras had been set to 184 184 pixels. Zoom optics were used to fit the endoscope image to this image size. By decreasing the image resolution in this way, a maximum frame rate of 400 Hz can be achieved. The third endoscope setup was working with standard CCD cameras running at 50 Hz. This setup could only be used in the lowermost position within the gravel layer, where the flow velocities and fluctuations are expected to be lowest. The image data of all three setups were written to RAID hard-disk arrays in real-time during the acquisition. Thus, the duration of the sequences was only limited by the RAID capacity. For a single measurement, a sequence duration of Dt ¼ 60 s has been chosen. In order to extract 3D velocity information from the image data, the stereo sequences are processed by a 3D-PTV algorithm. The result is a set of 3D Lagrangian flow trajectories of the tracer particles suspended in the water. In the 3D-PTV method, the underlying real velocity field is sampled at random points both in space and time. Velocity information is available only at those positions and time instants where tracer particles could be found and successfully tracked. If the flow is seeded homogeneously, this is not a severe limitation. Note that in PIV the distribution of tracers is also random, but the density is high and homogeneous enough to enable the determination of velocity vectors on a regular grid. In the experiments presented here, it was not possible to seed the whole water volume with tracer particles due to the very large size of the flume and the water supply system, which was also connected to several other experiments. Thus, tracers had to be added to the pore flow punctually in the vicinity of the artificial pores. With this seeding method, a homogeneous tracer distribution could not always be obtained.
3.3.
Pressure measurements by MPPS
The MPPSs were developed to measure pressure fluctuations within and on top of the gravel layer. This insitu technique turned out to be a very robust and reliable tool to determine pressure fluctuations down to dissipative scales. They offer a high adaptability within a hostile, rough environment by water resistent housing and flexible cables. The principle of the MPPS is based on the piezoresistive effect. The initial point is an element of silicium, with implanted resistances in its bending panel. Fig. 4.3
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(a)
(b)
Figure 4.3. (a) Head of MPPS outside the flume. (b) Head of MPPS fixed at y ¼ 10 mm above the gravel layer, facing upstream.
shows two photographs of the encapsulated head of the pressure pickup. The sensors were locally fixed on a grid to keep them on an accurately defined position. The differential pressure is measured in reference to atmospheric pressure, with compensation of temperature. The sensors are encapsulated with slowly hardening epoxy resin and sealed up with clear varnish to make them water resistent. The maximal dimensions of the sensors are 2 1.2 1.2 cm3, with a shape similar to a gravel grain of the larger size fraction. Due to signal conditioning by the purpose-built amplifier the guaranteed maximum measurable frequency is 100 Hz. To avoid aliasing effects, the measurements are recorded at a rate of 500 Hz. With a tolerance in accuracy of less than 1.0% full scale, the encapsulated sensors were point-calibrated at 5 V according to 3 kPa and 10 V according to 6 kPa, respectively. Hence, the absolute range of the pressure sensors is 0–6 kPa which equals 0–587.4 mmWC at 201C. The accuracy of the 12-bit AD card is limited to 587.4/212 ¼ 0.14 mmWC. However, it was possible to improve the resolution by utilisation of the dithering effect and filtering techniques to40.003 mmWC for fo20 Hz and40.012 mmWC for f420 Hz, respectively (Detert et al., 2004). Measurements were performed simultaneously by up to 10 pressure sensors over 2 min. Pressure sensors were located at vertical positions of y/dmD ¼ 1.0 (above), 0.0 (at top) and at various positions within the gravel layer. On each of the three artificial gravel pores a sensor was adapted to gain simultaneous insight in pressure and velocity, respectively. 3.4.
Velocity measurements with 1D-ADCP
An additional insight into the velocity regime of the open-channel flow was gained by an 1D-ADCP, namely a DOP 1000 (Willemetz, 1997). In pulsed Doppler ultrasound, instead of emitting continuous ultrasonic waves, an emitter periodically sends out a short ultrasonic burst and a receiver continuously collects the echo issues from targets that may be present in the path of the ultrasonic beam. By sampling the incoming echoes at the same time relative to the emission of the bursts, the shift of positions of
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scatterers are measured. Velocities are derived from the shifts in positions between the pulses. The operating principle is depicted in Fig. 4.4 for a vertical wall distance of y ¼ 150 mm and a doppler angle of y ¼ 601 against the streamwise direction, as it was installed for most of the experiments. The parameters of the 1D-ADCP have to be adjusted for each flow condition. Thus, within the measurements the resolution in space varied from 1 to 2 mm in beam direction and the resolution in time from 15 to 60 ms. The measuring technique of the 1D-ADCP allows measurement of reliable velocity profiles from yZ5 mm above the gravel layer. Closer to the gravel reflections of the ultrasonic beam lead to errors in measurement. The maximum detectable velocity in streamwise direction
150
Figure 4.4. Operating principle and geometry of the 1D-ADCP as it was installed during the experiments. The diameter of the acoustic field (main lobe) spreads from 5 mm at the transducer to the top edge of the gravel layer with a diameter of 16.7 mm containing 80%, and to 33.5 mm containing 98% of the acoustic field intensity, respectively. Dimensions in [mm], not to scale.
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resulted in max(u) ¼ 1.3 m/s. This was appropriate to the expected velocities. Profiles were measured with a duration of 1 min at various distances to the side wall in order to get time-averaged isoline velocity plots. Working with the 1D-ADCP in the measuring area was not possible because of spatial limitations. Therefore this instrument was located at x ¼ 3.3 m downstream the measuring area. By this way the other measuring techniques were not disturbed. The velocity component ux measured by the 1D-ADCP is always the component in the direction of the ultrasonic beam, x. A spacial vectorial decomposition was used to estimate the horizontal velocity component u. Starting from ux ¼ cos y ~ u þ sin y~ v
(4.2a)
! ! ! ux þ ux 0 ¼ cos yð¯u þ u0 Þ þ sin yð¯v þ v0 Þ
(4.2b)
and neglecting secondary flow effects (¯v ffi 0), the time average of equation (4.2) simplifies to u¯ ¼
1 ¼ 2:0ux cos y ux
(4.3)
However, an instantaneous analysis of flow structures can only be made along the beam axis, x. 3.5.
Measurement programme
The measurement programme was designed for variation of water depth, thickness of the gravel layer as well as flow conditions up to low mobility conditions. Table 4.1 gives the flow conditions and mean parameters of the experiments A01–A10. Within this series, the bed shear stress t0 was gradually increased to low mobility conditions. A criteria of instability is defined by t0/t0c, with t0c ¼ 8.8 Pa after Shields (1936). At t0/t0c ¼ 0.59 the transport of single grains was observed. This agrees with analytical studies of Dittrich et al. (1996) and with experimental data from Wilcock et al. (1996) for low mobility conditions and loose bed density. Table 4.2 gives the positions of the gravel sensors. In the vertical direction, y ¼ 0 is defined at 0.25 dmD below the uppermost gravel grains. Table 4.1.
Experimental conditions with a gravel layer thickness of HP ¼ 0.10 m.
Series
Unit
A01
A02
A04
A06
A08
A10
t0/t0c Q h U u* Re* ¼ u* dmD/v UADCP hADCP
[] [m3/s] [m] [m/s] [m/s] [] [m/s] [m]
0.09 56.0 0.201 0.31 0.026 260 0.31 0.200
0.18 81.8 0.203 0.45 0.040 410 0.45 0.200
0.36 120.5 0.207 0.65 0.063 640 0.67 0.199
0.48 149.8 0.219 0.76 0.078 800 0.80 0.207
0.55 173.0 0.234 0.82 0.073 740 0.86 0.224
0.59 193.4 0.249 0.86 0.085 870 0.91 0.235
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Positions of the pressure sensors for runs A01–A10.
Sensor
y (cm) (vertical)
x (cm) (longitudinal)
z (cm) (transversal)
Comment
P+10 P00a P00b P10 P20 P55 P65 P75
1.0 0.0 0.0 1.0 2.0 5.5 6.5 7.5
0.0 1.2 1.2 1.5 26.0 1.5 18.0 1.5
6.0 3.0 9.0 10.5 0.0 0.0 0.0 10.5
Above gravel, see Fig. 4.3(b) Within gravel, facing up Within gravel, facing up Within gravel, facing up At artificial gravel pore At artificial gravel pore At artificial gravel pore Within gravel, facing up
(Eq.5)
(Eq.4b)
(Eq.4a)
Figure 4.5. Velocity profiles u¯ =u and derived profiles rmsðuÞ=u , measured by 1D-ADCP. In comparison to equations (4.4) and (4.5). Run A01–A10, U ¼ 0.31–0.91 m/s, t0/t0c ¼ 0.090.59, water depth HAffi0.20 m.
4. 4.1.
Results Flow above the gravel layer
A depiction of the flow conditions above the gravel layer is given by results from the 1D-ADCP measurements. Nondimensionalised profiles of u¯ =u and profiles of mean velocity fluctuations rmsðuÞ=u gained by the 1D-ADCP are given in Fig. 4.5. Each profile results from 16 profiles evenly spread over the width of the flume, B ¼ 0.90 m, and represents a time average over approximately 1 min. The roughness height was determined by curve fitting to kS ¼ 1.68 dmD with the assumption y ¼ 0 at 0.25 dmD below the uppermost gravel grains. Unfortunately, the determination of the shear velocity, u , is subject to uncertainties. u was determined in two indirect ways. The first way was to calculate u* from the measured water surface slope. Especially at U40.70 m/s this method led to problems due to noneven water level. Therefore, u* was
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determined from roughness parameters that were identified in calibration tests before. The ultimate remaining error for u* was estimated to 75%. The velocity profiles conform to the log law for y/ho0.2 (equation (4a)) as well as to the semiempirical wake-function by Coles (1956) for the outer region y/h40.2 (equation (4b)). uðyÞ 1 y þ 8:48 (4.4a) ¼ ln u 0:4 ks y uðyÞ 1 y þ 8:48 þ 1:25 sin2 p ln ¼ u 0:4 ks 2h
(4.4b)
Problems in fitting the log profiles for U ¼ 0.45 m/s (A02) and especially for U ¼ 0.31 m/s (A01) are supposed to result from a lack of particles passing the measuring beam. The lower the flow velocity, the lower is the number of particles that reflect the ultrasonic beam. Thus, some ultrasonic bursts are possibly not reflected, what might lead to misinterpretation of the recorded signal. The projected profiles of the turbulence intensity were determined by the assumption of 2 rmsðux Þffirms(u) (see equation (4.3)). They are compared with the semiempirical formula given by Nezu and Nakagawa (1993): rmsðuÞ ¼ 2:30 e1:0y=h u
(4.5)
The order of magnitude of all profiles rmsðuÞ=u roughly complies with equation (4.5). But a closer look shows, that the measured rms(u)/u* increase less strongly near the gravel bed. There are two reasons for this deviation. First, eddies that are smaller than the measuring volume are not detectable (biasing effect). Second, near the bed the signal is deteriorated by beam reflections at the bed. Both effects result in an underestimation of the real velocity fluctuations. A proper explanation of instantaneous processes can only be given along the ultrasonic beam axis. Fig. 4.6 gives a series of measured instant profiles of velocity fluctuations ux 0 ¼ ux ux , here as an example gained from run A06. Alternating faster and slower fluid packets with a size up to half of the water depth, oh/2, are passing the 1D-ADCP beam. The total clip time of this depiction is Dt ¼ 0.791–0.422 ¼ 0.369 s. Note that ux 0 denotes the instantaneous fluctuations in line of the beam axis, x, and not in streamwise direction, x. From t ¼ 0.422–0.580 s, an older slower fluid packet I ðux 0 o0Þ disappears out of the range of the 1D-ADCP and a newer packet II with faster fluid ðux 0 o0Þ becomes significant. At time step t ¼ 0.633 s, a slower packet III starts to displace the packet II downwards. At t ¼ 0.685 s, the packet II still exists and reaches its maximal velocity max(ux 0 Þffi130 mm=s at y ¼ 40 mm. With ux (y ¼ 40 mm) ¼ 360 mm/s, this corresponds to 131% of ux . Shortly afterwards at t ¼ 0.691 s, packet III is partly displaced downward by a faster fluid packet IV. This observation agrees with the flow pattern model in the outer region of a boundary layer over smooth beds described by Adrian et al. (2000). The model specifies multiple uniform momentum zones that have a characteristic growth angle (mostly 121). These packets consist of eddies that propagate together with the packet convection speed. Unfortunately, the 1D-ADCP is not capable to resolve these ‘footprints’ of smaller
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Figure 4.6. Velocity fluctuations ux 0 ¼ ux u x in direction of the ultrasonic beam, x, measured by 1DADCP. For graphical visualisation ux 0 is projected horizontally. Run A06, UADCP ¼ 0.76 m/s, u x (y ¼ 40 mm) ¼ 360 mm/s, t0/t0c ¼ 0.48, and water depth hADCP ¼ 0.219 m.
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vortices. Within these limitations, the 1D-ADCP as an acoustic instrument consequently may help to resolve bigger flow patterns and verify multidimensional measuring techniques like 3D-PTV or PIV, respectively. However, the 1D-ADCP does not have the potential to replace the other techniques. 4.2.
Flow within the gravel layer
Fig. 4.7 presents the pressure fluctuations rms(p) measured at various positions above and within the gravel layer as well as with increasing shear stress t0. Both parameters are nondimensionalised by t0c. At t0/t0c ¼ 0.59 low mobility conditions were detected, as single stones passed the measuring area. In order to avoid mechanical deformation of the whole sensible measuring system, larger stress rates were not examined. Within a first approximation, all curves in Fig. 4.7 increase linearly with the instability criteria t0/t0c. Focussing on the two sensors P00b and P00a at the interface between gravel and open-channel flow, the inclination can be determined to a ratio of rms(p)/t0 ¼ 1.9/0.6 ¼ 3.2, which agrees with equation (4.1). Furthermore, the damping due to the gravel becomes obvious. At P10 within the gravel the rate is about 1.7/0.6 ¼ 2.8. Deeper in the gravel bed no essential difference between vertical positions can be detected. There the ratio is given mostly by 22.5. The maximum fluctuations within the main flow at y/dmD ¼ 1.0 above the gravel are 3.54 times the medium fluctuations. The pressure sensor P+10 is facing against the streamwise direction (see also Fig. 4.3b). Because of this, the measured signal is influenced by both p0 and 1/2ru0 2. 8 7 6 horizontal arrangement
rms(p) /τoc [−]
+1.0 cm 5 4
vertical arrangements
3 0 cm 2 1 −2.0 cm 0
0.1
0.2
0.3
τo / τoc [−]
0.4
0.5
−1.0 cm 0.6
Figure 4.7. Pressure fluctuations rms(p) for increasing t0, both normalised by t0c ¼ 8.8 Pa. Runs A01–A10. Positions of the sensors: see Table 4.2.
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150 +1cm
p′(t) [Pa]
100
50
-7.5cm
0
-50 -1cm -100 38
40
42
44
46
48 t [s]
50
52
54
56
58
Figure 4.8. Simultaneous time traces p0 (t) [Pa]. Run A10, U ¼ 0.86 m/s, t0/t0c ¼ 0.59, and water depth h ¼ 0.249 m. Positions of the sensors: see Table 4.2.
In Fig. 4.8, a more detailed view on the pressure fluctuations p0 (t) is presented. The given example is a time clip over Dt ¼ 5838 ¼ 20 s from run A10, i.e. at low mobility conditions. The damping of higher frequencies with increasing gravel depth becomes obvious. A correlation between the pressure signal within low frequencieso1 Hz can be identified, associated to macro-fluid structures and corresponding water level oscillations. The distances between the pressure sensors were not smaller than 20 mm, due to the size of the sensors. Therefore a correlation for higher frequencies with smaller corresponding length scales cannot be detected. Furthermore, a closer view to Fig. 4.8 shows that results p0 40 for the sensor above the gravel layer occur less frequently, but with more extremal values. Within the main flow the pressure peaks max(p) are predominantly negative and less extreme than the positive peaks. Within the gravel layer this distribution equalises. The histograms in Fig. 4.9 give a more vivid description to this fact. The probability density functions (PDF) given as example, result from measurements shown in Fig. 4.8. The distributions are characterised statistically by the skewness S(p) and the curtosis (or concavity) K(p). SðpÞ ¼
KðpÞ ¼
n 1X p 03 n i¼1 i n 1X p 04 n i¼1 i
(4.6a) ! 3
(4.6b)
The Gaussian normal distribution with S(p) ¼ 0 and K(p) ¼ 0 reads P
p0 rmsðpÞ
¼
2 1 0 pffiffiffiffiffiffi e1=2ðp =rmsðpÞ0Þ : 1 2p
(4.7)
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98 0.45
0.45
vert. arrangement y/dmD = −1.0 rms(p)= 15.9 Pa S(p) = −0.03 K(p) = 0.10
0.4
0.35
0.3
P(p′/rms(p)) [−]
P(p′/rms(p)) [−]
0.35
0.25 0.2
Eq. 7 (Gauss)
0.15
0.3 0.25 0.2
0.1
0.05
0.05
−3
(a)
−2
−1
0
1
p′/rms(p) [−]
2
3
Eq. 8 δ = 3.0 (Hofland)
0.15
0.1
0
horiz. arrangement y/dmD = +1.0 rms(p) = 70.6 Pa S(p) = 0.94 K(p) = 1.09
0.4
0
−3
4
(b)
−2
−1
0
1
2
3
4
p′/rms(p) [−]
Figure 4.9. Histograms P(p0 /rms(p)) at (a) y/dmD ¼ 1.0 in comparison to equation (4.7) and (b) y/dmD ¼ 1.0 in comparison to equation (4.8) (d ¼ 3, 0). Run A10 with Dt ¼ 120 s, U ¼ 0.86 m/s, t0/t0c ¼ 0.59, and water depth h ¼ 0.249 m.
For S(p) ¼ 0.03 and K(p) ¼ 0.10 the PDF at y/dmD ¼ 1.0 within the gravel layer follows this Gaussian shape. The distribution above the gravel at y/dmD ¼ 1.0 has a positive skewness with S(p) ¼ 0.94, and a narrow crested curtosis with K(p) ¼ 1.09. It fits very well with a distribution proposed by Hofland and Battjes (2006), referring to the quadratic approach p|u|u (equation (4.8)). It is related to the w2 distribution, i.e. the PDF of the square of a normally distributed variable. pffiffiffiffiffi 2 ðA þ mÞ s ¼ pffiffiffiffiffiffiffiffiffiffiffiffi e1=2ð jAjsignðAÞdÞ ½ for A_0 P (4.8a) s 2 2pjAj with A¼
s p0 rmsðpÞ
(4.8b)
d¼
Ub rmsðub Þ
(4.8c)
sðdÞ ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 4d2 þ 2 þ eð0:55d Þ
mðdÞ ¼ ðd2 þ 1Þ e1:63d
(4.8d) (4.8e)
The noncentrality parameter d (equation (4.8c)) has to be interpreted as the inverse of the relative turbulence intensity rms(ub)/Ub near the bed. The standard deviation s and the mean m can be calculated by fitted functions given by equations 4.8d and e. As shown in Fig. 4.9b, the shape of the PDF is predicted almost perfectly by equation (4.8) for chosen turbulence intensity of d ¼ 3.0. Thus, the pressure fluctuations measured above the gravel layer depend on u0 |u0 |. However, the normal distributed pressure
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fluctuations within the gravel layer are less dependent on the turbulent velocity fluctuations of u0 |u0 |. The dominant mechanism must be another one. The frequency-characteristic of the pressure signals is examined by the Fourier transformation. By means of the Fourier transformation, the pressure signal is transformed from the time domain into the frequency domain, as a decomposition into sine (or cosine, respectively) oscillations. The results are power spectral densities (PSD), where dominating frequency ranges and corresponding energies are revealed. Fig. 4.10 gives an exemplary PSD for low mobility conditions at t0/t0c ¼ 0.59. For the sensors P+10,P00b and P00a above and on top of the gravel layer the results disagree with the classical Kolmogorov k7/3 (f7/3) law for the turbulence cascade in openchannel flow, where k is the wave number and f the frequency (Nezu and Nakagawa, 1993). But the inclination agrees with results presented by Gotoh and Rogallo (1999), where a second inertial k5/3 range at smaller scales is described. Within the gravel
f−7/3
103
f−5/3
PSD [Pa2/Hz]
102
101
Eq. 9 Eq. 10
P+10 100 P−10
P00a P00b
others P−20 10-1 10-1
100
101
102
f [Hz] Figure 4.10. Power spectral density (PSD). Run A10, U ¼ 0.86 m/s, t0/t0c ¼ 0.59, water depth HAffi0.20 m.
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layer a significant damping between 1 and 3 Hz can be recognised. Below y/dmD ¼ 2.0 within the gravel layer there is no identifiable difference in damping pressure fluctuations higher than 3 Hz. It is hypothesised that the pressure fluctuations are dominated by the long wave fluctuating water level. The influence of an oscillating water level has been estimated as follows. A wavelength of L ¼ 0.40–2.5 m with a constant small amplitude of a ¼ 0.5 mm is assumed. By negligence of the surface tension, the wave theory of first order gives the resulting maximal bed pressure due to surface waves by rga (4.9) maxðp0 ðkÞÞ ¼ coshðkhÞ The wave number is given by k ¼ 2p/L. Within the transit from deep to shallow water, at 0.05oh/Lo0.5, the corresponding wave frequency reads 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g=k tanhðkhÞ (4.10) f ¼ L As it can be seen in Fig. 4.10, equation (4.9) combined with equation (4.10) coincides very well with the spectra calculated for the lower part of the gravel layer. Consequently, the long wave fluctuations are strongly influenced by an oscillating water level. At this moment, it can not be answered definitely whether these changes in water level are due to the experimental setup (e.g., imperfections in side wall) or due to macrofluid structures. There is a need for an intensive comparison to the velocity fields in the open-channel flow. But referring to Hofland (2002), it can be supposed that these long wave fluctuations play a minor role for the entrainment of single grains. A moving or rolling gravel grain and the driving fluid structure must have the same length scale. However, without multidimensional velocity information above the gravel layer, the correlation of time/frequency scales and length scales is difficult. The simplest way to separate the influence of an oscillating water level is to subtract the PSD gained from the lowermost sensor P75 from the other PSDs. The remaining signal is purged from water level effects. The PSDs depicted in Fig. 4.11 are simplified in this way. They are scaled by u eliminate the timescale. The PSDs are roughly congruent, independent if the hydromechanical load is corresponding to stable bed conditions at t0/t0c ¼ 0.18 (A02) and 0.36 (A04) or to low mobility conditions at t0/t0c ¼ 0.59 (A10). The characteristics of frequency and corresponding power are the same. Fig. 4.12 shows the damping rms(p)/t0 with increasing gravel depth. The pressure signal here was filtered with a high-pass f41.5 Hz to eliminate the long waves influence (see Fig. 4.12). The impact of the outer flow on the pore flow in the upper grain layer becomes clearly apparent, as rms(p) is relatively high. Moreover, all series of experiments show an exponential damping of the pressure fluctuations with an increasing gravel depth. Deeper down a relative layer depth of y/dmDo2.0, the detected fluctuations stay nearly constant, as the flow is mainly dominated by the seepage flow. Therefore, we propose a function consisting of an exponentially decaying part and a constant part to describe the fluctuations as follows sffiffiffiffiffiffiffiffiffiffiffiffiffiffi rmsðpÞ (4.11) ¼ Dp eC p y=d mD þ Bp t0
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(b)
(c) 3
Figure 4.11. Scaled power spectral densities PSD/u, roughly separated from effects of an oscillating water level. (a) t0/t0c ¼ 0.18 (run A02). (b) t0/t0c ¼ 0.36 (run A04). (c) with low mobility conditions t0/ t0c ¼ 0.59 (run A10). Derived from measuring time with Dt ¼ 120 s. Positions of the sensors see Fig. 4.10 and Table 4.2. The minimum level is defined each by the detection limit of the MPPS and corresponds to an amplitude of about 0.1 Pa.
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Figure 4.12. Damping of the pressure fluctuations rmsðpÞ=t0 within the gravel layer. Run A01–A10. The pressure fluctuations are filtered with a high-pass f41.5 Hz.
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The best fit for the filtered pressure signal results in Dp ¼ 0.92, Cp ¼ 0.86 and Bp ¼ 0.57 with a correlation coefficient of R2 ¼ 0.97. However, a more simple approach with Dp ¼ Cp ¼ 1 results in Bp ¼ 0.5 with R2 ¼ 0.92, what can also a good description of rms(p). Both fits for equation (4.11) are plotted in Fig. 4.12. To compare the pressure fluctuations to the pore flow velocity, Fig. 4.13 shows vertical profiles of the local intrinsic 3D velocity U3D and their fluctuations rms(u3D) (instead of their Cartesian components), as the flow field inside the pores is really 3D. (Typically, the u-component of the velocity trajectories is Z90% of the absolute velocity.) It becomes obvious that there is a strong scatter both in the velocity as well as in its fluctuating part. This can be explained by measurement errors as follows: the gravel layer represents a highly stochastic geometric system of channels, indirections and dead-end pores. Depending on the flow conditions and the current gravel geometry, in some experimental runs a rather homogeneous particle density was observed in the artificial pores, while in others this was not the case. As a result, the number of velocity vectors per frame is not constant. In extreme cases it may also drop to zero, i.e. there may be time periods where no velocity information is available at all since no tracer particles reached the observation volume. Two further effects are contributing to this fluctuating information density. First, it was observed that during some experimental runs dirt particles were temporarily deposited in the artificial pores. Sometimes these dirt particles completely blocked one of the endoscopes’ view or reduced the intensity of the illumination and thus the signal-to-noise ratio. The second effect is related to the limitations of the image processing. Especially under low mobility conditions, the turbulence intensity in the upper grain layers becomes very large. In these cases, the maximum pore flow velocities may reach values beyond the limits of the current endoscopic 3D-PTV. The interframe particle displacements in the image
(a)
(b)
Figure 4.13. 3D diminishing with gravel depth. Run A01–A10. P velocities within artificial pores, P (a) U 3D =u ¼ ð U i 2 Þ0:5 =u ; (b) rmsðu3D Þ=u ¼ ð rmsðui Þ2 Þ0:5 =u .
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sequences become too large and cannot be tracked any more. Again, the number of recovered velocity vectors drops and the velocity statistics get biased towards lower velocities. In spite of these inaccuracies in the 3D-PTV technique using miniaturised endoscopic stereo setups, we try to give a functional relationship that is able to describe the pore velocity. In analogy to the derivation of the log law in open-channel flow, we assume a logarithmic decrease for U3D in the transition from the main flow above the gravel layer to the flow within the uppermost gravel layers. Deeper, with increasing vertical gravel cover a constant seepage flow becomes predominant. This results in U 3D ¼ DU ln ðC u y=d mD þ BU (4.12) u Due to the scatter of the data the best fit results only in a correlation coefficient of R2 ¼ 0.38 for DU ¼ 0.08, CU ¼ 0.51 and BU ¼ 0.19, respectively. Equation (4.12) is only valid for y/dmD ¼ 1.0, were U3D equals 1=4 u , and smaller velocities deeper in the gravel layer. For the velocity fluctuations again an exponential function is assumed. It reads rmsðu3D Þ ¼ Du eC u y=d mD þ Bu u
(4.13)
The best fit for the velocity fluctuations results in Du ¼ 1.02, Cu ¼ 1.08 and Bu ¼ 0.07 with a correlation coefficient of R2 ¼ 0.97. However, a simplification with Du ¼ Cu ¼ 1 as for the declining rms(p) results in Bp ¼ 0.07 with the same R2 ¼ 0.75. Therefore, a simple, applicable scaling law for the damping of both, rms(p) and rms(u3D) within the upper porous gravel layer by ey=d mD becomes valid.
5.
Conclusions
Experimental results of pressure and velocity above and within a porous gravel layer are presented. New measuring techniques have been developed for these applications: MPPS measured turbulent pressure fluctuations inside the gravel layer. Flow measurements were carried out by a 3D-PTV using miniaturised endoscopic stereo setups within artificial gravel pores. Additionally, in the free surface flow a 1D-ADCP was used. Within the main flow, alternating faster and slower fluid packets with a size up to half of the water depth,oh/2, were observed by an 1D-ADCP. This agrees with the flow pattern model of Adrian et al. (2000) for smooth beds. Unfortunately, the ADCP-measuring technique is not capable to resolve smaller vortices to zoom into details. Pressure fluctuations rms(p) as well as velocity fluctuations rms(u, v, w) decrease exponentially with increasing gravel depth, essentially within the first two layers of gravel grains. Best-fit equations that describe this trend were given. It is supposed, that the fluctuations deeper down are dominated by a long wave oscillating mechanism. A rough filter to purge the signals from this effect was applied: within the frequency domain, the power spectral density (PSD) from the lowermost sensor
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within the gravel layer was subtracted from the other PSDs. The PSDs scale with the shear velocity u , independent if the hydromechanical load is corresponding to stable bed or to low mobility conditions.
References Adrian, R.J., Meinhart, C.D., Tomkins, C.D., 2000. Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54. Coles, D., 1956. The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1 (1), 191–226. Defina, A., 1996. Transverse spacing of low-speed streaks in a channel flow over a rough bed. In: Ashworth, P., Bennett, S., Best, J., and Mc Lelland, S. (Eds), Coherent Flow Structures in Open Channels. Wiley, England. Detert, M., Klar, M., Jehle, M., et al., 2004. Pressure fluctuations on and in subsurface gravel layer bed caused by turbulent open-channel flow. In: Greco, M., Carravetta, A., Della Morte, R. (Eds), River Flow 2004. Balkema. Dittrich, A., Nestmann, F., Ergenzinger, P., 1996. Ratio of lift and shear forces over rough surfaces. In: Ashworth, P., Bennett, S., Best, J., and Mc Lelland, S. (Eds), Coherent Flow Structures in Open Channels. Wiley, England. Emmerling, A., 1973. Die momentane Struktur des Wanddruckes einer turbulenten Grenzschichtstro¨mung. Mitteilungen aus dem Max-Planck-Institut fu¨er Stro¨mungsforschung. Farabee, T.M., Casarella, M.J., 1991. Spectral features of wall pressure fluctuations beneath turbulent boundary layers. Phys. Fluid. 3 (10). Garcı´ a, M., Nino, Y., Lo´pez, F., 1996. Laboratory observations of particle entrainment into suspension by turbulent bursting. In: Ashworth, P.J., Bennett, S.L., Best, J.L., and Mc Lelland, S.J. (Eds), Coherent Flow Structures in Open Channels. Wiley, England. Gotoh, T., Rogallo, R.S., 1999. Intermittency and scaling of pressure at small scales in forced isotropic turbulence. J. Fluid Mech. 396, 257–285. Grass, A., 1971. Structural features of turbulent flow over smooth and rough boundaries. J. Fluid Mech. 50, 233–255. Grass, A.J., Stuart, R.J., Mansour-Tehrani, M., 1991. Vortical structures and coherent motion in turbulent flow over smooth and rough boundaries. Philos. Trans. R. Soc. Lond. Hofland, B., 2002. Stability of coarse granular structures. Delft Cluster. Hofland, B., 2004. Measuring the flow structures that initiate stone movement. In: Greco, M., Carravetta, A., Della Morte, R. (Eds), River Flow 2004. Balkema. Hofland, B., Battjes, J., 2006. Probability density function of instantaneous drag forces and shear stresses on a bed. J. Hydraul. Eng. 132 (11), 1169–1175. Hofland, B., Battjes, J., Booij, R., 2005. Measurement of fluctuating pressures on coarse bed material. J. Hydraul. Eng. 131 (9), 770–781. Klar, M., Stybalkowski, P., Spies, H., and Ja¨hne, B., 2002. A miniaturised 3-D particle-tracking velocimetry system to measure the pore flow within a gravel layer. In: 11th International Symposium Applications of Laser Techniques to Fluid Mechanics. Lisbon, Portugal. Kline, S.J., Reynolds, W.C., Schraub, F.A., Runstadler, P.W., 1967. The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773. Nezu, I., Nakagawa, H., 1993. Turbulence in Open-Channel flows. Monograph Series. Balkema. Roy, A.G., Buffin-Be´langer, T., Lamarre, H., Kirkbride, A.D., 2004. Size, shape and dynamics of large scale turbulent flow structures in a gravel bed river. J. Fluid Mech. 500, 1–27. Sechet, P., Guennec, L., 1999. Bursting phenomenon and incipient motion of solid particles in bed-load transport. J. Hydraul. Res. 37 (5), 683–696. Shields, A., 1936. Anwendung der A¨hnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung. Mitteilungen der Versuchsanstalt fu¨r Wasserbau und Schiffbau, Berlin (87). Smith, C., Walker, J., Haidari, A., Sobrun, U., 1991. On the dynamics of near-wall turbulence. Philos. Trans. P. Scs. & Eng. (336), 131–175.
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Vollmer, S., Francisco, d.l.S.R., Daebel, H., Ku¨hn, G., 2002. Micro scale exchange processes between surface and subsurface water. J. Hydrol. (269). Wilcock, P., Barta, A., Shea, C., et al., 1996. Observations of flow and sediment entrainment on a large gravel bed river 32, 2897–2909. Willemetz, J., 1997. DOP1000. Signal Processing User’s Manual. WSA, 2004. Geschiebezugabe Iffezheim. Flyer. Zanke, U., 2001. Zum EinfluX der Turbulenz auf den Beginn der Sedimentbewegung. Mitteilungen des Instituts fu¨r Wasserbau und Wasserwirtschaft, Universita¨t Darmstadt (120).
Discussion by Genevie`ve A. Marquis and Andre´ G. Roy We compliment the authors for their very innovative approach to the problem. The experimental setup is meticulously designed and surely has the potential to answer some of the questions on the interactions, effects or feedbacks between flows above and within a porous gravel bed. It addresses the very difficult technical problems of measuring interstitial flow. The data presented be the authors raise several interesting issues. Here, we would like to discuss the importance of large-scale turbulent flow structures and the interaction between interstitial and above the surface flows. Firstly, the significance of the 1D-ADCP results may have been underestimated. The slower and faster packets of fluid detected and shown in Fig. 4.6 are similar to largescale turbulent structures found in flows above rough boundaries. Such structures scale with flow depth (Roy et al., 2004). The origin of these large-scale flow structures is not well known and interstitial flow may play an active role in their generation and maintenance. Looking at Fig. 4.10, it appears that there is a peak in the spectra of all pressure sensors (except the one above the bed) between 0.4 and 0.7 Hz. This range may indicate a direct relationship with large-scale turbulent structures. Second, the data showing the mechanisms of interactions between interstitial and surface flows raise interesting questions. In Figs. 4.8 and 4.12, amplitude and frequency of pressure fluctuations are diminishing with depth, the higher values being associated with the surface flow. This observation raises the bottom-up or top-down question. Are the pressure fluctuations in the interstitial flow inducted by the surface flow and is it the other way around? What is the nature of the feedback effects between the interstitial flow structure and the surface flow structure and at what scale do they operate? The shape of the pressure distributions may contain part of the answer. In Fig. 4.9, we see that the pressure distributions change from a symmetric shape within the bed to a positively skewed one above the bed. Is the mechanism responsible for this change in the shape of the distributions related to dampening of the impacts of largescale downward sweeping motions on the interstitial flow? Could the authors speculate on the role, generation or maintenance of large-scale turbulent flow structures of the surface flow in relation to the interstitial flow? References Roy, A.G., Buffin-Be´langer, T., Lamarre, H., Kirkbridge, A.D., 2004. Size, shape and dynamics of large scale turbulent flow structures in a gravel bed river. J. Fluid Mech. 500, 1–27.
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Vollmer, S., Francisco, d.l.S.R., Daebel, H., Ku¨hn, G., 2002. Micro scale exchange processes between surface and subsurface water. J. Hydrol. (269). Wilcock, P., Barta, A., Shea, C., et al., 1996. Observations of flow and sediment entrainment on a large gravel bed river 32, 2897–2909. Willemetz, J., 1997. DOP1000. Signal Processing User’s Manual. WSA, 2004. Geschiebezugabe Iffezheim. Flyer. Zanke, U., 2001. Zum EinfluX der Turbulenz auf den Beginn der Sedimentbewegung. Mitteilungen des Instituts fu¨r Wasserbau und Wasserwirtschaft, Universita¨t Darmstadt (120).
Discussion by Genevie`ve A. Marquis and Andre´ G. Roy We compliment the authors for their very innovative approach to the problem. The experimental setup is meticulously designed and surely has the potential to answer some of the questions on the interactions, effects or feedbacks between flows above and within a porous gravel bed. It addresses the very difficult technical problems of measuring interstitial flow. The data presented be the authors raise several interesting issues. Here, we would like to discuss the importance of large-scale turbulent flow structures and the interaction between interstitial and above the surface flows. Firstly, the significance of the 1D-ADCP results may have been underestimated. The slower and faster packets of fluid detected and shown in Fig. 4.6 are similar to largescale turbulent structures found in flows above rough boundaries. Such structures scale with flow depth (Roy et al., 2004). The origin of these large-scale flow structures is not well known and interstitial flow may play an active role in their generation and maintenance. Looking at Fig. 4.10, it appears that there is a peak in the spectra of all pressure sensors (except the one above the bed) between 0.4 and 0.7 Hz. This range may indicate a direct relationship with large-scale turbulent structures. Second, the data showing the mechanisms of interactions between interstitial and surface flows raise interesting questions. In Figs. 4.8 and 4.12, amplitude and frequency of pressure fluctuations are diminishing with depth, the higher values being associated with the surface flow. This observation raises the bottom-up or top-down question. Are the pressure fluctuations in the interstitial flow inducted by the surface flow and is it the other way around? What is the nature of the feedback effects between the interstitial flow structure and the surface flow structure and at what scale do they operate? The shape of the pressure distributions may contain part of the answer. In Fig. 4.9, we see that the pressure distributions change from a symmetric shape within the bed to a positively skewed one above the bed. Is the mechanism responsible for this change in the shape of the distributions related to dampening of the impacts of largescale downward sweeping motions on the interstitial flow? Could the authors speculate on the role, generation or maintenance of large-scale turbulent flow structures of the surface flow in relation to the interstitial flow? References Roy, A.G., Buffin-Be´langer, T., Lamarre, H., Kirkbridge, A.D., 2004. Size, shape and dynamics of large scale turbulent flow structures in a gravel bed river. J. Fluid Mech. 500, 1–27.
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106 Reply by the authors
y [mn]
y [mn]
The discussion authors state that the significance of the ADCP results may have been underestimated. After visualising the data in a different manner, we must admit: Yes! Fig. 4.14 gives an alternative view of the identical signal shown already in Fig. 4.6. Assuming frozen turbulence, structures that pass the ultrasonic beam can be detected as regions of high or low velocities, respectively. The time-dependent signal can be shifted to a length scale simply by multiplication with a typical transport velocity. Here, we use the bulk velocity U. The result is a streamwise length scale lx ¼ Ut instead of the time scale t. In this way, the wedge-like large-scale structures that incline in streamwise direction become more obvious. And indeed, in this example they scale with the water depth h, roughly by a factor of 0.5–4. Moreover, the discussion authors speculate that there might be a direct relationship to the peak in the pressure spectra. And again, it seems to be right: For this example, the peak value in the pressure spectra was determined to 0.5 Hz (not shown in here). Therefore, the number of the wedge-like structures within a length of time of 7.0 s must be in an order 3–4. Keeping in mind, that a time series of 7 s typically is not enough for a statistically founded statement, this fits very well with the number five fast fluid packets (colour-coded by light grey and white, respectively) we can find within the present example. Thus, the peak frequency is not only due to long wave water oscillations, but also directly related to – and induced by – the large-scale wedge-like structures. Unfortunately, the definite relation between x and lx is unclear, as a Cartesian decomposition of ux into u and v is impossible. A multidimensional measuring technique like the PIV-technique would be more adequate to study these structures in the open channel flow. The second topic in the discussion concerns the question, if the interstitial flow is mainly dominated by the surface flow or if the mechanism runs vice versa. Fig. 4.13
200 100 0 2500
200 100 0 5000
2.
2000
1500 1000 λx=U.t [mm], t=-0.2-3.3[s] 5.
4500
1.
500
0
4.
4000 3500 λx=U.t [mm], t=3.1-6.6[s] -100
3.
3000 0
2500 100
Figure 4.14. Coherent turbulent structures passing the measuring area within 7.0 s. Footprint of velocity fluctuations show ux 0 ¼ f(lx, y), measured by ADCP. lx ¼ 301–565 mm is directly according to Fig. 4.6. Flow direction from left to right.
Pressure- and velocity-measurements
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shows that the pore velocity at y/dmD ¼ 1 is U3D ¼ 0.5u*. In contrast to this, the bulk velocity in the flow over a rough bed scales typically with U ¼ 10u*. This means that most of the kinetic energy is transported in the mean flow, whereas the interstitial flow rather has a passive role. We think that the driving mechanisms are due to the surface flow, especially from the shear. The flow in the gravel bed only reflects the turbulent flow conditions in the main flow.
Gravel-Bed Rivers VI: From Process Understanding to River Restoration H. Habersack, H. Pie´gay, M. Rinaldi, Editors r 2008 Elsevier B.V. All rights reserved.
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5 Evaluating vertical velocities between the stream and the hyporheic zone from temperature data Ina Seydell, Ben E. Wawra and Ulrich C.E. Zanke
Abstract The exchange between stream and interstitial pore water is vital for the ecosystem of the hyporheic zone, since it determines oxygen supply and thermal conditions. Determining flow velocities within the sediment is extremely difficult. Sampling of temperature data in the riverbed can be used as a tracer to determine vertical flow velocities. Three different approaches to determine velocities are compared in this study. Velocities calculated using time-lag (Constanz and Thomas, 1996; Ingendahl, 1999) and temperature damping (Taniguchi, 1993) are compared with a 1D-numerical model. Simulated temperatures derived from the model are then evaluated with measured data from a field-site at the Lahn near Marburg. Results from the time-lag method differ significantly from simulated velocities. Correlation was good for modelled vertical velocities above 3 cm h1. Values calculated using temperature damping showed an excellent linear correlation with the model up to a vertical velocity of 6.6 cm h1. Temperatures determined with the 1D-numerical model are in good accordance with measured data. Zones with down-welling as well as zones of predominantly upwelling conditions could be verified as Darcy’s velocity ranged between 1 and +5 cm h1. Although velocity calculated from time-lag or temperature damping may be sufficient for some situations, these methods are restricted to situations with significant temperature amplitudes. The 1D-approach is appropriate to determine local scale (vertical) hyporheic exchange. 1.
Introduction
The hyporheic zone is the spawning habitat and refuge for a variety of species such as macroinvertebrates. It shows highest colonisation densities within the uppermost E-mail address:
[email protected] (I. Seydell) ISSN: 0928-2025
DOI: 10.1016/S0928-2025(07)11122-6
110
I. Seydell, B.E. Wawra, U.C.E. Zanke
20–40 cm of the riverbed and functions as a transition zone between the stream, the groundwater, and the semi-terrestrial flood plain with strong temporal and spatial gradients of water characteristics and high biological variability (Gibert et al., 1990; Vervier et al., 1992). Exchanges of water and solutes between the stream and its bed are vital for the ecosystem (Chapman, 1988; Ingendahl, 2001; Malcom et al., 2004). The processes were studied from the biological viewpoint since the 1960s, and from the hydrological point of view since the 1980s. In particular, the oxygen concentration depends on flow velocity and flow-path length within the sediment (Hakenkamp and Palmer, 2000). Thus, the exchange velocity and direction is of major importance. Spawning sites, for example, correlate with flow velocities within the sediment (Geist, 2000; Malcom et al., 2004). Furthermore, the mass exchange of water and solutes is not only important for hyporheic organisms, but for the groundwater fauna and the self-purification of the stream as well (Brunke, 2000). Flow-patterns in the riverbed are complex and difficult to determine. Depending on morphology and subsurface hydraulic conditions, the proportion of lateral to vertical velocity varies. As a function of this proportion, Saenger and Zanke (in print) developed a conceptual model with three hyporheic layers of exchange: active exchange, moderate exchange, and groundwater domination. The distinction between these three layers is based on the ratio between the horizontal and the vertical flow component. This model underlines the importance of the vertical exchange for the supply of hyporheic pore spaces with oxygen and nutrients. Therefore, the vertical velocity component is the fundamental parameter characterising the hyporheic exchange. In the past, a variety of methods was used to evaluate flow velocities in the riverbed, such as tracer experiments with or without the extraction of pore water (Harvey et al., 1996; Benson, 1999), dilution or erosion of material inserted into the bed (Petticrew and Kalff, 1991; Thompson and Glenn, 1994; Carling and Boole, 1996), or piezometer measurements (Saenger, 2000; Storey et al., 2003). All these methods are either time consuming and laborious, and therefore only good for short-term measurements, and may be prone to mistakes. Considering the differences between the groundwater and the stream it appears that temperature or temperature differences may be used as a natural tracer. The advantage is that continuous data collection is possible over long periods, thus providing detailed information about velocities without changing hydraulic conditions. Water temperatures in a stream show annual as well as diurnal patterns (Taniguchi, 1993; Lenk, 2000). These temperature curves continue within the riverbed and are damped with depth (Saenger, 2000). From the change of the temperature pattern with depth, down- and up-welling can be identified (Silliman and Booth, 1993; Constanz and Thomas, 1996). This can be done either by looking at the degree of damping with depth or the time-lag between temperature curves from different depths (Fig. 5.1). From this premise the following questions arise: How do we need to analyse collected temperature data to evaluate the exchange between the stream and the hyporheic pore space? Can we obtain reliable values for the vertical flow velocity?
Evaluating vertical velocities
111 dtmax
17.6
temperature (°C)
17.2 ∆Tz 16.8 ∆Tz0 16.4
dtmin
16 0
12
24
36
48
hours Figure 5.1. Example of time-lag and difference of amplitudes for temperature-damping method between two temperature curves.
Is it possible to show the correlation between riffle structure and subsurface flow with temperature data?
2.
Experimental setup and data analysis
Investigations were conducted at a riffle structure of the Lahn, near Marburg, Germany. Characteristics are given in Table 5.1. On the left hand side of the stream was a pond in which was enlarged towards the stream in September 2000. Mean surface water temperature during the study in the stream was about 12.31C. Minimal stream temperature was 1.11C and maximum was 25.81C. A maximum diurnal temperature difference of 7.41C was measured in June 2000. Mean air temperature was 10.41C. Temperatures varied between 10.8 (January 2001) and 26.31C (July 1999 and August 2001). Temperature was measured in the stream centre at two locations along the riffle (Fig. 5.2). Location C-1 was located in a down-welling zone at the upstream side of the riffle crest and location C-2 at the riffle tail. Distance between C-1 and C-2 was 49 m. We installed PRT-temperature sensors with an accuracy of 0.11C (pt-100) at the sediment surface and at depths of 20, 50, 100, and 150 cm within the sediment and continuously measured the temperature between 1999 and 2001. Data was averaged and stored every 30 min. A number of methods were utilized to determine one dimensional flow velocity from the temperature data. In the 1960s, techniques have been established to estimate
I. Seydell, B.E. Wawra, U.C.E. Zanke
112 Table 5.1.
Characteristics of the study reach at the river Lahn.
HQ1
79
m3 s1
Slope Channel width Riffle height d50 of surface layer d50 of subsurface material Sorting index Absolute porosity (determined from density) Estimated maximal effective porosity (from grain size distribution) Organic matter content for material smaller 2 mm Mean diurnal air temperature Stream water temperature
0.0015 18 0.71 70 21 4.5 25 20
– m m mm mm – % %
2 10.4 (10.8 to 26.3) 12.3 (1.1 to 25.8)
% 1C 1C
C-1
C-2
data logger
data logger
Interstiti
al pt-100 sensors
pt-100 sensors
stream
Figure 5.2. Temperature measurements with pt-100 sensors at the sediment surface and at 20, 50, 100, and 150 cm depth.
one-dimensional Darcy’s velocities from temperature curves. Cartwright (1970), calculated velocities within the sediment from continuously recorded temperature data with known thermal material properties of the sediment. The non-isothermal, one-dimensional flow within a homogenous subsurface water body was expressed by Stallmann (1965) as CM
@T @2 T @T ¼ kM 2 qC W @t @z @z
(5.1)
where CW and CM are the volumetric heat capacity of water and of the water– sediment mixture in J m3 K1, T the temperature in 1C, t the time in h, z the depth in m, kM the thermal conductivity of the water–sediment mix in W m1 K1, and q Darcy’s velocity in cm h1.
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113
The volumetric heat capacity of the water–sediment mixture is calculated as C M ¼ cs rs n þ cw rw ð1 nÞ
(5.2) 1
1
Here cS and cW are the specific heat of sediment and water in J kg K , rS and rW the density of sediment and water in kg m3, and n the total pore volume. Nowadays, numerical models of varying complexity (Storey et al., 2003) are used along with simple methods to estimate one-dimensional flow from temperature data (Pusch, 1993; Lenk, 2000). The heat capacity of the sediment–water mixture is calculated from the heat capacity of sediment and water. In this study, a 1D-model is utilized to calculate temperatures with vertical velocity components determined inversely. Two commonly used methods to calculate flow velocities from temperature data taken at different depths are tested and compared with results of the 1D numerical model. The temperature travel-time method uses the time-lag between two temperature curves to determine the travel-time of temperatures (vT). The temperature-damping approach uses damping of temperature amplitudes with depth. Both methods as well as the numerical model are based on the assumption of one-dimensional, non-isothermal flow. 2.1. 2.1.1.
Method description 1D model for comparison of methods
We applied the numerical code HydroBioGeoChem123d (hbgc123d) to build a numerical one-dimensional finite element model (Gwo et al., 1999). This code is capable of simulating coupled non-isothermal hydrologic transport of solutes and temperatures in variably saturated media. The implemented equation for heat transfer in conservative form is @T @r Y þ rðrW C W TvÞ þ r C W W T ðrW C W Y þ rbS C bS Þ @t @t rðDT rTÞ ¼ rW C W qT
ð5:3Þ
where rW is the fluid density (kg m3); Y effective moisture content (m3 m3) [ ¼ neS in which ne is the effective porosity (m3 m3), and S the degree of effective saturation of water (m3 m3)]; rbS the bulk density of the dry medium (kg m3); CW and CbS the specific heats of the groundwater and the dry medium in subsurface systems, respectively (m2 h2 K1); T the temperature (K); v the Darcy’s velocity of the groundwater(m h1); DT the thermal dispersion/diffusion/conductivity coefficient tensor (kg m h3 K1). On the right side is the source/sink term of heat that may be due to artificial injection (kg m1 h3). Transport and heat transfer equations are solved iteratively with a Lagrangian–Eulerian finite element method. We modelled the transient heat transfer with a domain representing a column (1D) of 1.5 m depth. The model consists of 751 nodes and 750 elements. Input data are the spatial distribution of nodes and elements, as well as thermal properties and moisture content of the media (Table 5.2). Boundary conditions are measured temperatures at the surface and at 1.5 m depth. The chosen velocities ranged between minus and plus
I. Seydell, B.E. Wawra, U.C.E. Zanke
114 Table 5.2.
Chosen parameters for 1D-model.
Parameter
Value
Units
rS ¼ density of sediment cS ¼ specific heat of sediment k ¼ heat conductivity of sediment Y ¼ moisture content ¼ n
2700 2.0 2.5 25
kg m3 J cm3 1C1 J s1 m1 1C1 %
20 cm h1 and are constant during each run. Output data are temporal and spatial temperature distributions. We could not determine changes in hydraulic conductivity from sediment analysis for the study reach. This means layering of the sediment could not be identified for the field site. Although anisotropy and inhomogenities have significant influence on subsurface flow pattern, their influence is visible only from velocities in the 1D-model. Therefore the sediment was simplified to be homogenous. 2.1.2.
Estimating velocities from temperature travel-time
This method assumes that the governing transport mechanism for temperature is advection while material properties like heat capacity and heat conduction may be neglected. Temperature travel-time is equal to the time-lag between two maxima or minima (dt in h) between two temperature curves from different depth (see Fig. 5.1). Travel-time divided by the travel distance (dz in m) the temperature velocity is calculated as dz (5.4) dt For this travel-time approach, the one common way to determine the time-lag found in literature is statistical cross correlation (Ingendahl, 1999; Lenk, 2000). In order to exclude trends in the dataset, temperature differences between two time steps are analysed instead of the measured temperatures. This procedure does not ensure that the lag between two minima or two maxima is determined and may produce erroneous time-lag, and thus not reliable for our dataset. To solve this problem the travel-time of temperatures was determined visually for small datasets and by a MATLAB-routine MOB (Seydell, in print) for large datasets. This program calculates the time-lag between the minima and the maxima of two temperature curves, giving the mean of those two values as time-lag. If the mean of the time-lags from minima and maxima is used, the error resulting from trends in the dataset is minimized. The travel-time analysis is limited to periods with large temperature differences between day and night as well as recognisable temperature amplitudes at all depths. Furthermore, the calculated velocity of temperature needs to be transferred into Darcy’s velocity. We compare two different approaches for this procedure. The first approach neglects material properties. Temperature is utilized as an ideal tracer without adsorption. In this case, the travel-time of temperature is equal to the vT ¼
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115
travel-time of water and Darcy’s velocity (m h1) is calculated as q ¼ vT ne
(5.5)
where vT is the temperature travel-time (h) and ne the effective porosity (). If heat capacity of water and the water sediment mixture are considered, but conductive transport is neglected as suggested by Constanz and Thomas (1996), equation (5.1) becomes q ¼ vT
CM CW
(5.6)
In this study we evaluate the error resulting from neglecting heat capacity conduction and heat capacity by comparison with the one-dimensional model. 2.1.3.
Estimating velocities from temperature damping with depth
The approach to determine velocity from temperature damping considers heat transport by advection and conduction, thus comprising relevant material properties. Based on the work of Stallmann (1965) and Cartwright (1971), Taniguchi (1993) developed a method to determine horizontal groundwater flow velocity. This method assumes one-dimensional flow and operates effectively only with sinusoidal temperature curves with pronounced amplitudes at the sediment surface. Thermal properties of the water sediment mixture are input data. Taniguchi (1993) established a dimensionless parameter b, which comprises velocity and material properties. This parameter can be obtained by fitting measured data to type curves and ranges between 2 and 2. These type curves are defined by ln(DTz/DT z0 ) versus (CM p k1 t1)0.5 (zz0) ¼ K0.5(zz0), where z0 is depth 0 at the sediment surface, z depth (m), DTz and DT z0 are the temperature amplitudes at depths z and z0 (1C), CM the specific heat (J m3 s1) of the mix, r the density of the mixture (kg m3), t the period of the sinusoidal temperature (s), and kM the thermal conductivity of the mix (W m1 1C1). Flow velocity (m s1) is calculated as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ððkM C M pÞ=tÞ q¼b CW 2.1.4.
(5.7)
Comparison of the methods
For testing and performance comparison of the travel-time and the damping methods, temperatures from a 3-day period in August 2000 were selected as boundary conditions for the numerical model. We used the output temperature curves from the model as input data for the two other methods. Velocities varied from q ¼ 20 (up-welling) to 20 cm h1 (down-welling). Finally, we compared the chosen input velocities for the model with the output velocities from the travel time and temperature-damping analysis.
I. Seydell, B.E. Wawra, U.C.E. Zanke
116 Table 5.3.
Chosen periods for simulation of typical situations at the field site.
Situation
Period
Discharge (m3 h1)
Vertical velocity for depth between 0–20
Early summer A Summer A Summer P Winter P
2.2.
20.06.–25.06.2000
0.27
26.08.–31.08.2000
1.0 to 2.0
28.09.–04.10.2000
2.5 to 4.0
01.11.–06.11.2000
1.0
C-1 C-2 C-1 C-2 C-1 C-2 C-1 C-2
+4.0 –1.0 +3.0 –1.0 0 –1.0 +1.0 –1.5
20–50 –1.5/ –1.0 0 0 0 –2.0 +0.3 –1.0
50–100 –1.5 –1.0 –1.0 0 –3.0 +1.0 +0.2 +5.0
1D model for selected periods
For the field site, four typical periods were selected to model temperatures and to determine vertical velocity components up to 1 m depth (Table 5.3). All four periods are characterized by a constant low discharge in the stream. The September period is extraordinary as a drastic change of subsurface flow direction occurred due to the filling of a nearby pond. Since we expected flow patterns to vary with depth, the onedimensional model was divided into three sub-domains to account for the change in flow conditions with depth. Each sub-domain represents a layer with three points of temperature measurement. For boundary conditions at the upper and lower end of the sub-domain we utilize measured data, whereas the temperatures in the middle of each sub-domain were modelled and then compared to the measured values. We defined the sub-domains according to the depth of the modelled temperatures within the sediment. The upper domain (sub-20) extends from 0 to 50 cm and temperatures at 20 cm were simulated, the middle domain (sub50) extended from 20 to 100 cm, and the lower domain (sub-100) from 50 to 150 cm depth. Material properties were identical to those described above and velocities were constant for each sub-domain and run. 2.3.
Quantifying model performance
To verify the model performance, a method to quantify the accuracy or the deviance between the modelled and the measured temperatures was needed. The relative performance of one model-run to another was controlled by calculating a variable ABW similar to the standard deviation, giving the mean error in 1C. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ðxmodelled xmeasured Þ2 (5.8) ABW ¼ n where xmodelled is the simulated temperature, xmeasured the measured temperature, and n the number of data points. To make this result more comparable between two series, a parameter that incorporates the range of values is needed. Since the procedure established by Nash and Sutcliffe (1970) malfunctions with periodic,
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117
respectively sinusoidal datasets a new indicator (ABWR) was calculated by dividing ABW by the range of all measured temperatures during a modelled period. ABWR ¼
ABW 100 Range of measured values
(5.9)
ABWR is the error in per cent of the range from all measured temperatures between the upper and the lower boundary.
3. 3.1.
Results Performance of the 1D-model
Behr (2002) and Kirchmaier (2003) have tested the sensitivity of vertical flow velocity to parameters characterising the sediment for ranges given in literature (Rauch, 1991; Taniguchi, 1993; Scheffer and Schachtschabel, 2002). Porosity has been varied between 0.1 and 0.3, heat capacity of the sediment between values from 1.5 to 2.5 (J m3 1C1), and heat conductivity of the saturated aquifer between 1.5 and 3.0 (W m1 1C1). Our results show that variation of these parameters show little influence, compared to the influence of even small velocities in the model. Our chosen model parameters for comparison with other methods as well as for modelling selected periods are given in Table 5.2. For the 3-day test period, modelled temperature curves show good accordance with measured data. Up to 20 cm depth, the mean deviation between modelled and measured data is about 0.31C or 3% of the measured range (Fig. 5.3a). Below 20 cm depth, the deviation decreases to about 0.11C respectively 1% of the measured range, which is in the order of the accuracy of the temperature sensors. In order to relate the mean deviance of temperature to the vertical velocity component we evaluate the relation between temperature curves and simulated velocity. The simulated velocity was varied in steps of 1 cm h1 between 10 and +20 cm h1. The change in mean temperature deviance between two subsequent model runs (ABW(runX) ABW(runX1)) shows highest variance between 4 and +4 cm h1 (see Fig. 5.3b). Outside this range, significance of ABW decreases drastically as changes of ABW with changes in velocity become very small. The relation between changes in temperature (ABW) of two model runs and changes in velocity is not a linear function. A rating curve is needed to translate the performance of temperature modelling into accuracy of velocity determination. For the investigated case we distinguished velocities between 5 and +10 cm h1 (Fig. 5.3b). Within this range the relation of ABW to velocity, respectively, the change in ABW between two subsequent model runs allows evaluation of the error in the calculated velocity. To evaluate the error induced when neglecting heat conduction in the travel-time method, we compared model runs with and without heat conduction for velocities between –10 and +20 cm h1 (see Fig. 5.3c). The results show a maximum error for small positive (downward) velocities. At 20 cm depth the maximum error occurs at 1 cm h1 with ABW ¼ 0.71C, for greater depths the maximum error is higher and occurs for larger velocities.
I. Seydell, B.E. Wawra, U.C.E. Zanke
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temperature (˚C)
17 a
16 15
measured simulated analytical
14 13 12 48
72
96
120
time (h) b
c
ABW (˚C)
1.2
0.8 20 cm 50 cm 100 cm
0.4
0 -10
0
10
-10 q (cm h-1)
0
10
20
Figure 5.3. (a) Measured, analytically calculated, and simulated temperatures at 20 cm depth for the 3-day test period. (b) Mean deviation (ABW) between simulated temperature curves for given velocities and velocity ¼ 0 cm h1. (c) Mean deviation (ABW) between simulated temperatures with and without consideration of heat conductivity k.
3.2. 3.2.1.
Comparison of methods Travel-time
The calculation of travel-time showed some obviously wrong values for the crosscorrelation approach. These errors can be excluded by visually checking the temperature curves, but then the advantage of automation is lost. Therefore, we rated this procedure as not reliable. Instead, we calculated travel-time of temperatures with the module MOB, which excludes obviously wrong time-lags, for example, negative ones, from further analysis. Due to the nature of the travel-time method, where the time-lag between temperature profiles may not be negative, up-welling (negative velocities) could not be determined. Since amplitudes were not apparent below 50 cm sediment depths, velocities were not calculated. The vertical flow velocity calculated with temperature travel-time varies, depending on the conversion of temperature travel-time into flow velocity of water (Fig. 5.4). When utilizing the travel-time of temperatures the pore velocity ranges between 0.6 and 10 cm h1. Calculated velocities were much smaller than simulated
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119
time-lag (n)
time-lag (CM / CW) 20 v (m h-1) simulated
20 v (cm h-1) simulated
damping
15 10 5 0
15 10 5 0
20 cm depth
50 cm depth -5
-5 -5
0
5
10
15
v (cm h-1) calculated
20
-5
0 5 10 15 20 v (cm h-1) calculated
Figure 5.4. Simulated velocities compared to calculated velocities from travel-time and temperature damping.
values; the error increased with velocity from 41% for a model velocity of 3 cm h1 to 66% for 20 cm h1. Including the heat capacity of water and sediment, led to calculated velocities ranged between 11 and 25 cm h1. Calculated velocities were higher than simulated values. Deviance decreased from 41% for the model velocity of 3 cm h1 to 9% for the model velocity of 20 cm h1. Both methods show that the determined velocities correlate well with simulated values as long as they were larger than +2 cm h1. 3.2.2.
Temperature damping
Velocities calculated with temperature damping ranged between 2 and +6.6 cm h1 and showed a good correlation with the numerical model (Fig. 5.4). However, the parameter b is limited to the range between 2 and +2, leading to a maximum velocity of 76.6 cm h1 for the investigated material properties and diurnal temperature amplitudes. All model velocities larger than this were calculated to be 6.6 cm h1. For velocities smaller than 2 cm h1 (up-welling) the temperature amplitudes within the sediment were rapidly damped, thus the method failed to give any result even at a depth of only 20 cm. As with the travel-time procedure, it was not possible to calculate velocities for depths greater than 50 cm, since diurnal amplitudes were too small in this area. Between model velocity of 2 and +6.6 cm h1 the values calculated from temperature damping are very close to the modelled ones, deviance varying between minus 33% for model velocities close to zero and –17% for a model velocity of 6 cm h1. 3.3.
Typical temperature regimes for selected periods at the study site
The simulation of water temperature for the selected period of 6 days each produced results that closely resembled the measured data. The period in June 2000 represents a typical early summer situation. The mean temperature of the surface water decreased from 21 to 151C with pronounced diurnal temperature amplitudes during
120
I. Seydell, B.E. Wawra, U.C.E. Zanke
the 6 day period. At location C-1 a strong down-welling with a vertical velocity component of +5 cm h1 within the uppermost 20 cm of the sediment was accompanied by a small time-lag between the falling limbs of temperature curves from the model to the measured ones (ABWR ¼ 4%). Below 20 cm depth the vertical velocity was determined to be 1.5 cm h1 and modelled temperatures closely met the measured ones (ABWR ¼ 2%). At the riffle tail (location C-2) up-welling of about 1.0 cm h1 was constant for all depths down to 1 m. For the 20 cm depth the modelled temperatures showed the largest mean deviation ABWR ¼ 4% to measured values of all modelled periods. The amplitudes within the first 2 days were much smaller in the model than measured in the field. The period in August 2000 shows a typical summer situation with a mean surface water temperature of 16.41C. Daily amplitudes ranging between 15.5 and 18.51C at the sediment surface show a slightly different pattern. Again at location C-1, a downwelling of about +3 cm h1 within the top 20 cm of sediment was accompanied by the familiar time-lag between modelled and measured temperature curves. No vertical flow was determined at 50 cm depth and a slight up-welling of about +1 cm h1 at 100 cm depth (ABWR ¼ 1%). At location C-2 an up-welling of 1 cm h1 was visible at 20 cm depth with no visible vertical flow at 50 and 100 cm within the sediment (ABWRo1%). For the periods in June and August 2000 before the enlargement of the pond, the deviation between measured and modelled temperature curves was highest at 20 cm depth. In the down-welling zone at location C-1 with pronounced amplitudes, the modelled temperatures showed a time-lag in the falling limb of the measured temperature curves between 1 and 2 h for the period during summer (Fig. 5.5, June and August). In the predominantly up-welling zone at location C-2, modelled temperature curves for the summer situations (June and August) at 20 cm depth generally showed smaller amplitudes than the measured ones. For the period in June, the simulated temperature curve meets the measured data at the daily minima. For the period in August the two curves meet at the maxima of the daily pattern. The situation in September 2000 was uncommon for the field site, as a nearby pond of the sewer treatment plant was enlarged towards the river and filled shortly before our measuring campaign. At the field site, we saw groundwater flowing through the bank into the river. At location C-1, measured surface water temperatures dropped during the last 2 days. Temperatures at 50 cm depth did not follow this trend within the given period (Fig. 5.5), thus remaining above the temperatures recorded at 20 and at 100 cm depth. From the model there is no vertical velocity apparent at 20 and 50 cm depth (ABWR ¼ 2%), however an up-welling current with a velocity of 3 cm h1 (ABWR ¼ 1%) was visible at 100 cm depth. Note that temperatures at 100 cm depth were just below those at 150 cm depth and thus just outside the expected range. In contrast, location C-2 showed up-welling between 1 cm h1 (ABWR ¼ 3%) in 20 cm depth and 2 cm h1 (ABWR ¼ 3%) in 50 cm depth and down-welling of +1 cm h1 (ABWR ¼ 1%) at 100 cm depth. For the winter scenario in November 2000, the modelled temperature related to a pattern of mainly down-welling at location C-1. Velocities ranged from +1 cm h1 at 20 cm depth to very small velocities of +0.3 cm h1 at 50 cm and +0.2 cm h1 at
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121
20 cm mod. 20
50 cm mod. 50
100 cm mod. 100
24 22 20 18 16
C-1 June 2000
C-2 June2000
C-1 August 2000
C-2 August 2000
C-1 September 2000
C-2 September 2000
C-1 November 2000
C-2 November 2000
14 18 17 temperature (˚C)
16 15 14
14 13 12 11 10 9 8 7 0
24
48
72 96 120 144 hours
0
24
48
72 96 120 144 hours
Figure 5.5. Measured and simulated temperatures at depths of 20, 50, and 100 cm within the river bed for selected periods.
100 cm depth with a deviance ABWR of less than 1% for all depths. Up-welling was apparent at location C-2 at 20 and 50 cm depth with velocities of 1.5 and 1 cm h1 respectively. At a depth of 100 cm at location C-2 the model showed a strong down-welling velocity component of 5 cm h1. Again, the deviation between modelled and measured values ABWR was less than 1% for all depths. Note that measured temperatures in 50 cm and 100 cm depth were almost identical in this case. Measurements of hydraulic heads done shortly before and after the modelled period indicated a strong lateral gradient near location C-2 at the end of October, which decreased significantly towards the end of November.
I. Seydell, B.E. Wawra, U.C.E. Zanke
122 4.
Discussion
4.1. 4.1.1.
Method rating Travel-time
The major disadvantage of this method is that the time-lag is always positive, thus negative velocities respectively up-welling cannot be identified. For model velocities above +2 cm h1 correlation between the model and calculated values was well (Fig. 5.4). When we ignored material properties the total error in the calculated values for data from the field site was larger than 50% of the calculated value (Table 5.4). A correction function of the form y ¼ a x+b was obtained for comparison with the model but it varied for different depths within the sediment. Taking heat capacity of sediment and water into account, the error was 26% at a model velocity of +4 cm h1, decreasing to 9% at a model velocity of 20 cm h1. This pattern of large relative errors for low positive velocities relies on the error resulting from neglecting heat conduction, which showed maximal errors between 0 and +5 cm h1 (see Fig. 5.3c). For a loosing reach of the Rio Grande, Constanz and Thomas (1996) found that flow calculated from travel-time with cm/CW was twice as large as flow calculated from stream flow loss. They could not determine if that finding was caused by the difficulties in estimating the stream reach surface or due to the travel-time procedure. Subsurface flow rates for depths between 30 and 300 cm calculated from temperature data were highly variable and ranged from 6 to 26 cm h1. Their velocities were obtained in a loosing reach and are consequently much higher than vertical velocities found at the Lahn field site. 4.1.2.
Temperature damping
The temperature-damping approach performs well, if material properties are known. Vertical velocity components calculated with this method showed good accordance with the model (error between 7 and 20%). Nevertheless, temperature damping calculated by Taniguchis method (1993) (as described above) showed clearly its strict limitation to very specific flow velocities and temperature conditions. In this study it was theoretically possible to calculate velocities in the range of 76.6 cm h1. Table 5.4. Correlation between simulated velocities and calculated velocities from time-lag and temperature damping. Depth (cm)
Time-lag (ne) vf ¼ 3–20 cm h1
Time-lag (CM/CW) vf ¼ 3–20 cm h1
1C-damping (Taniguchi, 1993) vf ¼ 2 to 6.6 cm h1
0–20
Y ¼ 2.23 x – 0.01 R2 ¼ 0.99 Y ¼ 2.40 x R2 ¼ 0.996
Y ¼ 0.93 x – 0.01 R2 ¼ 0.99 Y ¼ 0.9998 x R2 ¼ 0.996
Y ¼ 1.22 x – 0.001 R2 ¼ 0.99 Y ¼ 1.007 x – 0.004 R2 ¼ 0.995
20–50
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However, due to the limitation of the factor b, every velocity beyond this range was calculated to be this maximum value. Therefore, the method failed to give any result for velocities smaller than 2 cm h1, since the daily amplitude became too small to be detected within the sediment. 4.1.3.
1D-model
The performance of the temperature model was good. Mean error in temperature was 1.7%, varying between 0.5 and 4% of the measured temperature range during the test period. In cases where simulated temperatures showed a time-lag in the falling limb of the measured temperature curves (Fig. 5.5, June and August), this pattern was attributed to currents based on density differences. These differences in density caused by water temperatures at the riverbed being below the temperatures within the riverbed lead to higher downward velocities. We observed a similar effect of enhanced velocities due to a density driven flow component in laboratory experiments with coarse bed material. Thus, velocities determined from simulated temperatures underestimate down-welling when surface temperatures are below subsurface temperatures. 4.1.4.
Rating
The travel-time approach, as well as the temperature-damping method, neglects the absolute temperatures, thus ignoring the change of viscosity with temperature. For a change in temperature from 0 to 101C, dynamic viscosity and hydraulic conductivity change about 30%. For data from the investigated field site, diurnal changes in viscosity led to errors of calculated velocities of up to 15%. Seasonal differences in mean temperature of about 91C in the surface water lead to differences in calculated flow velocity of up to 27% between summer and winter. While errors and uncertainties accumulate in the travel-time method and the temperature-damping approach, the 1D-model allows for the incorporation of material properties, including their temperature dependence. Furthermore, the relation between the ABW and velocity (Fig. 5.4a) allows the determination of the accuracy of obtained velocity values. Therefore, among those considered, the 1D-model is the method best suited for determining vertical flow velocities within gravel-bed river sediments. 4.2.
Typical periods
The one-dimensional temperature model showed good performance for the study site (Table 5.5). As shown in Fig. 5.6 the determined values of velocity were all in the range of a few cm h1. They showed a pattern of down-welling at location C-1 at the upstream side of the riffle and a predominantly up-welling at the downstream side of the riffle at location C-2. From previous tracer experiments, a strong horizontal current was expected below 50 cm within the riverbed (Saenger 2002). Such flow parallel to the bed in the direction of the stream showed no significant influence on the temperature distribution with depth in the investigated situations. For an
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Table 5.5. Mean deviance ABW between simulated and measured temperatures (1C) and deviance relative to measured range ABWR (%). June
C-1 20 cm 50 cm 100 cm C-2 20 cm 50 cm 100 cm
August
September
November
ABW
ABWR
ABW
ABWR
ABW
ABWR
ABW
ABWR
0.44 0.19 0.25
4 2 2
0.32 0.09 0.11
3 1 1
0.24 0.14 0.16
2 1 1
0.13 0.06 0.08
1 0.6 0.7
0.45 0.27 0.23
4 2 2
0.25 0.05 0.17
2 0.5 1
0.29 0.23 0.06
3 2 1
0.1 0.07 0.13
0.9 0.6 1
effective porosity of 20%, the associated downward Darcy’s velocity decreased from 2 to 1 cm h1. Vertical velocities between 1 and 3.7 cm h1 were determined for a tracer experiment conducted in the field site at the Lahn in 1998 (Saenger, 2000). Values calculated from temperature data for that period showed generally good accordance with those determined from tracer experiments, except at places, where high velocities are attributed to preferential flow paths in combination with extraction of pore water (Seydell et al., in print). The vertical velocity components determined with the 1D-model in this study are in the same order of magnitude as those calculated from salt tracer experiments by Ingendahl (1999) for the Nette and Bro¨hl streams (Germany). Ingendahl observed a factor 2 increase of time-lag attributed to infiltration of fine sediment into the initially clean spawning gravel. For the present study the change in subsurface velocity was attributed to changes in subsurface flow pattern rather than infiltration of fines. In June 2000 with maximum diurnal temperature changes of 51C a clear downwelling at location C-1 and a constant up-welling at C-2 was visible. The mean error in temperature (ABWR) of simulated to measured temperature is largest during this period (4%) at 20 cm depth. This is based on a systematic deviation of temperatures during the falling limb of the diurnal variation due to temperature related density effects where surface water temperatures sank below those in the riverbed. In August, which represents a similar situation, the down-welling was less pronounced and already disappeared at 50 cm depth while the up-welling at C-2 was visible only in the upper 20 cm of the riverbed. Here smaller diurnal temperature differences of only 2.51C and higher flow in the stream lead to a reduced exchange along the riffle. The result was a smaller error in temperature and vertical velocity (Table 5.5, Fig. 5.6). For the September period, the velocity pattern within the riffle changed in quantity and quality. Although the mean temperature deviance is small, the error of velocity in relation to the calculated values is large (Fig. 5.6). Surprisingly, down-welling was visible only at location C-2 in 100 cm depth. The intense temperature damping with depth suggests a strong up-welling. The apparent up-welling was induced by a strong
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6
2
2
-2
-2
-6
-6
6 v (cm h-1)
C-1 at 20 cm
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C-1 at 50 cm
6
2
2
-2
-2
-6
-6
6
C-1 at 100 cm
6
2
2
-2
-2
-6
-6 June Aug. Sept. Nov.
C-2 at 20 cm
C-2 at 50 cm
C-2 at 100 cm
June Aug. Sept. Nov.
Figure 5.6. Simulated velocities (middle line of box) with maximum error calculated from ABW (upper and lower line of box). Positive values indicate down-welling, negative values up-welling.
lateral current from the enlarged pond. We also observed this up-welling by measuring hydraulic heads. For the period in November, when water temperatures values increased with depth, down-welling was determined at C-1 with values decreasing with depth and again at location C-2 at 100 cm depth with a value of 5 cm h1. As in September, this is explained by a strong transversal flow between 50 and 150 cm depth. Again, this lateral flow was shown by measurements of hydraulic head. Nevertheless, we need to be careful with this interpretation, since water temperature of the pond was unknown and temperatures at different depths where very close to each other in November. The simulated temperature situations illustrate the potential and the limitations of the 1D-model very well. Model performance can be quantified by the mean deviance between modelled and measured temperatures, but this deviance needs to be transformed into the accuracy of velocity estimated, respectively the error in velocity.
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If flow pattern are predominantly two dimensional and surface water temperature variation is small in stream flow direction, using a 1D-model is sufficient. 5.
Conclusion
The numerical model is an appropriate tool to evaluate vertical velocity components within the gravel bed from temperature data. For the investigated medium scale exchange between the stream and the hyporheic zone along a riffle structure, the effect of currents induced by density differences due to temperature differences is negligible. The water exchange rate between the stream and the hyporheic pore space can be determined for the zone with designated exchange between the stream and the hyporheic zone. Moreover, comparison of modelled temperature curves with measured ones allows identification of unrealistic situations as well as estimation of the achieved accuracy. Temperature measurements showed that the riffle structure influences the subsurface flow pattern although the gross hydraulic gradient showed major influence. If temperature varies with depth within the sediment, the numerical modelling of temperature curves is a powerful tool to determine exchange between the stream and the subsurface water body in a wide variety of streams and settings. If temperature data is combined with measurements of hydraulic head, more detailed information on subsurface structures and flow pattern and their variation in time can be extracted. References Behr, M., 2002. Numerische Modellierung der Stro¨mung und des Stofftransportes im hyporheischen Interstitial. Diplomarbeit, University of Technology Darmstadt, Germany. Benson, I., 1999. Using dye tracer to examine a full-scale model of a salmonid redd. Technical Report, Hydroscope Consulting Ltd. Brunke, M., 2000. Wechselwirkungen zwischen FlieXgewa¨sser und Grundwasser: Bedeutung fu¨r aquatische Biodiversita¨t, Stoffhaushalt und Lebensraumstrukturen. Wasserwirt-schaft 90, 32–37. Carling, P.S., Boole, P., 1996. An improved condumetric standpipe technique for measuring interstitial seepage velocity. Hydrobiologica 135, 3–8. Cartwright, K., 1971. Redistribution of geothermal heat by a shallow aquifer. Geol. Soc. Am. Bull. 82 (11), 3197–3200. Chapman, D.W., 1988. Critical review of variables used to define effects of fines in redds of large salmonids. Trans. Am. Fisheries Soc. 117, 1–21. Constanz, J., Thomas, C.L., 1996. The use of streambed temperature profiles to estimate the depth, duration and rate of percolation beneath arroyos. Water Resour. Res. 32 (12), 3597–3602. Geist, D.R., 2000. The interaction of groundwater and surface water within fall Chinook salmon spawning areas in the Hanford Reach of the Columbia River. Ground-water/surface-water interaction workshop. United States Environmental Protection Agency, Washington, pp. 95–98. Gibert, J., Dole-Olivier, M.J., Marmonier, P., Vervier, P., 1990. Surface waterground water ecotones. In: Naiman, R.J. and Decamps, H. (Eds), The ecology and management of aquatic terrestital ecotones. Man and the Biosphere Series, Vol. 4. UNESCO, Paris and Parthenon Publishing Group, Carnforth, UK, pp. 199–226. Gwo, J.P., D’Azevedo, E.F., Frenzel, et al., 1999. HydroBioGeoChem123D: A Coupled Model of Hydrologic Transport and Mixed Biogeochemical Kinetic/Equilibrium Reactions in Saturated-Unsaturated
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Media in One, Two, and Three Dimensions. Computer code and documentation available at http:// hbgc.esd.ornl.gov Hakenkamp, C.C., Palmer, M.A., 2000. The ecology of hyporheic meiofauna. In: Jones, J. and Mulholland, P. (Eds), Streams and ground waters. Academic Press, San Diego, pp. 307–336. Harvey, J.W., Wagner, B.J., Bencala, K.E., 1996. Evaluating the reliability of the stream tracer approach to characterize stream-subsurface water exchange. Water Resour. Res. 32, 2441–2451. Ingendahl, D., 1999. Der Reproduktionserfolg von Meerforelle (Salmo trutta L.) und Lachs (Salmo salar L.) in Korrelation zu den Milieubedingungen des hyporheischen Interstitials. Dissertation. Institut fu¨r Zoologie, Universita¨t zu Ko¨ln, Germany. Ingendahl, D., 2001. Dissolved oxygen concentration and emergence of sea trout fry from natural redds in tributaries of the River Rhine. J. Fish Biol. 58, 325–341. Kirchmaier, N., 2003. Numerische Modellierung der Temperaturen im hyporheischen Interstitial. Institut fu¨r Wasserbau und Wasserwirtschaft, University of Technology Darmstadt, Germany. Report, unpublished. Lenk, M., 2000. Hydraulische Austauschvorga¨nge zwischen FlieXgewa¨sser und Interstitial – Felduntersuchungen in einer Pool-Riffle-Sequenz an der oberen Lahn. Dissertation, Wasserbauliche Mitteilungen des Instituts fu¨r Wasserbau und Wasserwirtschaft, Heft 114, TU Darmstadt. Malcom, I.A., Soulsby, A.F., Youngson, D.M., et al., 2004. Hydrological influences on hyporheic water quality: implications for salmon egg survival. Hydrol. Process. 18, 1543–1560. Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceputal models Part1 – a discussion of principles. J. Hydrol. 10, 282–290. Petticrew, E.L., Kalff, J., 1991. Calibration of a gypsum source for freshwater flow measurements. Can. J. Fisheries Aquatic Sci. 48, 1244–1249. Pusch, M., 1993. Heterotropher Stoffumsatz und faunistische Besiedlung des hyporheischennterstitials eines Mittelgebirgsbaches (Steina, Schwarzwald). – Dissertation, Universita¨t Freiburg. Rauch, W., 1991. Ausbreitung von Temperaturanomalien im Grundwasser. Dissertation, Baufakulta¨t, Universita¨t Insbruck, Austria. Saenger, N., 2002. Estimation of flow velocity within the hyporheic zone. Verhandlungen der Internatonalen Vereinigung fu¨r theoretische und angewandte Limnologie 28 (4), 1790–1795. Saenger, N., Zanke, U.C.E. (in print). A depth-oriented view of hydraulic exchange patterns between surface water and the hyporheic zone – Analysis of field experiments at the River Lahn, Germany. Archiv fu¨r Hydrobiologie. Saenger, N., 2000. Identifikation von Austauschprozessen zwischen FlieXgewa¨sser und hyporheischer Zone. Wasserbauliche Mitteilungen, 114. Institut fu¨r Wasserbau und Wasserwirtschaft, University of Technology Darmstadt, Germany. Scheffer, F., Schachtschabel, P., 2002. Lehrbuch der Bodenkunde. Vol. 15. Spektrum Akademischer Verlag, Aufl. Heidelberg. Seydell, I., Wawra, B., Zanke, U.C.E., (in print). Patterns of permeability and clogging processes in the hyporheic zone of a gravel bed river (River Lahn, Germany). Archiv fu¨r Hydrobiologie. Silliman, S.E., Booth, D.F., 1993. Analysis of time series measurements of sediment temperature for identification of gaining versus losing portions of Juday Creek, Indiana. J. Hydrol. 146, 146–148. Stallmann, R.W., 1965. Steady one-dimensional fluid flow in semi-infinite porous medium with sinusoidal surface temperature. J. Geophys. Res. 70, 2821–2827. Storey, R.G., Howard, W.F., Williams, D.D., 2003. Factors controlling riffle-scale exchange flows and their seasonal change in a gaining stream: A three-dimensional groundwater flow model. Water Resour. Res. 39 (2), Art. No. 1034, FEB 18 2003. Taniguchi, M., 1993. Evaluation of vertical groundwater fluxes and thermal properties of aquifers based on transient temperature–depth profiles. Water Resour. Res. 29 (7), 2021–2026. Thompson, L.T., Glenn, E.P., 1994. Plaster standards to measure water motion. Limnol. Oceanogr. 39 (1), 1768–1778. Vervier, P., Gibert, J., Marmonier, P., Dole-Olivier, M.-J., 1992. A perspective on the permeability of the surface freshwater–groundwater ecotone. J. N Am. Benthol. Soc. 11 (1), 92–102.
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Discussion by Ian Reid Seydell et al. provide an interesting analysis of inferred flow within the hyporheus of a gravel bar by using thermal properties of the interstitial water as a ‘tracer’ to calibrate their model. However, the analysis appears to presume that the properties of the porous media constituting the river bed are isotropic. The stratigraphy of both ancient (e.g., Nemec and Steel, 1984) and modern (e.g., Hassan, 2005; Laronne and Shlomi, 2007) gravel-bed rivers shows us that superjacent beds with significantly different grain-size and, hence, pore-size distributions vary considerably in thickness and 3D geometry at decimetre scale. While other studies of matrices show large variations in the degree to which pores are filled and give a rationale for understanding the vertical juxtaposition of open-framework and matrix-filled interstices even within the same bed (e.g., Frostick et al., 1984; Reid and Frostick, 1985). These studies suggest that gravel-bed rivers are more likely than not to be characterized by anisotropy of hydraulic conductivity, both vertical and horizontal, and this must have significant impact on interstitial flow velocity. Questions arise, therefore, as to whether properties and dimensions of gravel-bed facies need to be taken into account when modelling hyporheic flow nets? or whether abrupt changes in hydraulic conductivity are inconsequential in affecting flows as small as those reported by Seydell et al. (up to 14 mm s1), except, presumably, where pores are tightly packed with ingressed clay grains or a clay drape is interdigitated in the microstratigraphy? References Frostick, L.E., Lucas, P.M., Reid, I., 1984. The infiltration of fine matrices into coarse-grained alluvial sediments and its implications for stratigraphical interpretation. J. Geol. Soc. London 141, 955–965. Hassan, M.A., 2005. Characteristics of gravel bars in ephemeral streams. J. Sediment. Res. 75, 203–221. Laronne, J.B., Shlomi, Y., 2007. Depositional character and preservation potential of coarse grained sediments deposited by flood events in hyper-arid braided channels in the Rift Valley, Arava, Israel. Sediment. Geol. 195(1–2), 21–37. Nemec, W., Steel, R.J., 1984. Alluvial and coastal conglomerates: their significant features and some comments on gravely mass-flow deposits. In: Koster, E.H. and Steel, R.J. (Eds), Sedimentology of gravels and conglomerates. Memoir Canadian Society Petroleum Geologists 10, 1–31. Reid, I., Frostick, L.E., 1985. Role of settling, entrainment and dispersive equivalence and of interstice trapping in placer formation. J. Geol. Soc. London 142, 739–746.
Discussion by John M. Buffington1 & Daniele Tonina2 Hyporheic exchange is principally driven by spatial variations of near-bed pressure, which can be sensitive to seasonal changes in discharge, flow depth, and watersurface profile (Tonina and Buffington, 2003, 2007). Simulations of hyporheic exchange across two-dimensional pool-riffle topography show that the strength and spatial extent of the hyporheic exchange vary with discharge (Fig. 5.7). High 1
US Forest Service, Rocky Mountain Research Station, 322 E Front St., Boise, Idaho 83702, USA. US Forest Service, Rocky Mountain Research Station, 322 E Front St., Boise, Idaho 83702, USA and Department of Earth & Planetary Science, University of California, Berkeley, California 94720, USA. 2
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Discussion by Ian Reid Seydell et al. provide an interesting analysis of inferred flow within the hyporheus of a gravel bar by using thermal properties of the interstitial water as a ‘tracer’ to calibrate their model. However, the analysis appears to presume that the properties of the porous media constituting the river bed are isotropic. The stratigraphy of both ancient (e.g., Nemec and Steel, 1984) and modern (e.g., Hassan, 2005; Laronne and Shlomi, 2007) gravel-bed rivers shows us that superjacent beds with significantly different grain-size and, hence, pore-size distributions vary considerably in thickness and 3D geometry at decimetre scale. While other studies of matrices show large variations in the degree to which pores are filled and give a rationale for understanding the vertical juxtaposition of open-framework and matrix-filled interstices even within the same bed (e.g., Frostick et al., 1984; Reid and Frostick, 1985). These studies suggest that gravel-bed rivers are more likely than not to be characterized by anisotropy of hydraulic conductivity, both vertical and horizontal, and this must have significant impact on interstitial flow velocity. Questions arise, therefore, as to whether properties and dimensions of gravel-bed facies need to be taken into account when modelling hyporheic flow nets? or whether abrupt changes in hydraulic conductivity are inconsequential in affecting flows as small as those reported by Seydell et al. (up to 14 mm s1), except, presumably, where pores are tightly packed with ingressed clay grains or a clay drape is interdigitated in the microstratigraphy? References Frostick, L.E., Lucas, P.M., Reid, I., 1984. The infiltration of fine matrices into coarse-grained alluvial sediments and its implications for stratigraphical interpretation. J. Geol. Soc. London 141, 955–965. Hassan, M.A., 2005. Characteristics of gravel bars in ephemeral streams. J. Sediment. Res. 75, 203–221. Laronne, J.B., Shlomi, Y., 2007. Depositional character and preservation potential of coarse grained sediments deposited by flood events in hyper-arid braided channels in the Rift Valley, Arava, Israel. Sediment. Geol. 195(1–2), 21–37. Nemec, W., Steel, R.J., 1984. Alluvial and coastal conglomerates: their significant features and some comments on gravely mass-flow deposits. In: Koster, E.H. and Steel, R.J. (Eds), Sedimentology of gravels and conglomerates. Memoir Canadian Society Petroleum Geologists 10, 1–31. Reid, I., Frostick, L.E., 1985. Role of settling, entrainment and dispersive equivalence and of interstice trapping in placer formation. J. Geol. Soc. London 142, 739–746.
Discussion by John M. Buffington1 & Daniele Tonina2 Hyporheic exchange is principally driven by spatial variations of near-bed pressure, which can be sensitive to seasonal changes in discharge, flow depth, and watersurface profile (Tonina and Buffington, 2003, 2007). Simulations of hyporheic exchange across two-dimensional pool-riffle topography show that the strength and spatial extent of the hyporheic exchange vary with discharge (Fig. 5.7). High 1
US Forest Service, Rocky Mountain Research Station, 322 E Front St., Boise, Idaho 83702, USA. US Forest Service, Rocky Mountain Research Station, 322 E Front St., Boise, Idaho 83702, USA and Department of Earth & Planetary Science, University of California, Berkeley, California 94720, USA. 2
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Figure 5.7. Simulated hyporheic pathlines for a synthetic two-dimensional pool-riffle topography with (a) low discharge (8% bankfull flow) and (b) high discharge (100% bankfull flow). Channel characteristics scaled from natural gravel-bed rivers in central Idaho: slope is 0.5% and the ratio of bedform amplitude to wavelength, D/l, is 0.03. Surface and subsurface flow simulated using MD_SWMS 1 (McDonald et al., 2005) and FLUENT 6.0 (FLUENT Inc.), respectively. Predicted water surface profiles are plotted separately above each panel at exaggerated vertical scales to emphasize their differences, but do not indicate flow depths over bed topography. Subsurface flow simulations use a uniform hydraulic conductivity of 0.1 cms1 (sandy gravel), with lighter-coloured hyporheic pathlines indicating faster flow.
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Figure 5.8. Simulated hyporheic pathlines for a synthetic three-dimensional pool-riffle channel with alternate bar morphology and low discharge (26% bankfull flow). Channel characteristics scaled from natural gravel-bed rivers in central Idaho: slope is 0.41% and the ratio of bedform amplitude to wavelength is 0.022 (Tonina and Buffington, 2007, experiment 1). Surface and subsurface flow simulated using FLUENT 6.0 (FLUENT Inc.), with hyporheic pathlines originating from the surface and coloured by individual trajectory. The simulation uses a groundwater slope of 0.41%, a uniform hydraulic conductivity of 5 cm s1 (Tonina and Buffington, 2007), and an alluvial depth equal to one bedform wavelength (1l). Deeper groundwater flow paths (those that do not intersect the bed surface) are not shown.
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discharges decrease the magnitude of hyporheic exchange in pool-riffle channels by smoothing the water-surface profile and decreasing the spatial variation of near-bed pressure (Fig. 5.7) (Tonina and Buffington, 2007). Furthermore, the direction of hyporheic flow (up-welling vs. down-welling) can change with discharge. For example, just downstream of the riffle crest, hyporheic flow is predicted to up-well at low discharge, but down-well at high discharge (Fig. 5.7). These changing patterns and magnitudes of hyporheic exchange together with the authors’ limited number of fixed sample sites may partially explain the seasonal variations in hyporheic flow observed at their study site (their Fig. 5.6). Furthermore, hyporheic flow paths are even more complex and strongly three dimensional in pool-riffle channels with alternate bar morphology (Fig. 5.8). Interactions between flow and bedform topography induce lateral hyporheic flow in these channels that can change with discharge and may contribute to the lateral flow observed by the authors.
References McDonald, R.R., Nelson, J.M., Bennett, J.P. 2005. Multi-dimensional surface-water modeling system user’s guide. U.S. Geological Survey Techniques and Methods, 6-B2, 136pp. (http://wwwbrr.cr.usgs. gov/projects/SW_Math_mod/OpModels/MD_SWMS/index.htm) Tonina, D., Buffington, J.M., 2003. Effects of discharge on hyporheic flow in a pool-riffle channel: Implications for aquatic habitat. EOS Trans. Am. Geophys. Union 84 (46), Fall Meeting Supplement, Abstract H52A-1154. Tonina, D., J.M. Buffington., 2007. Hyporheic exchange in gravel-bed rivers with pool-riffle morphology: Laboratory experiments and three-dimensional modeling. Water Resources Research, 43, W01421.
Reply by the authors We thank the discussants for highlighting important points. The described changes in hyporheic flow are greatly attributed to in channel flow and do not reflect necessarily seasons but different flow conditions. In the Lahn field site one interesting finding was the change from seemingly up-welling in the upper 50 cm of sediment, to downwelling at 100 cm depth during September 2000. Here the additional influence of ground water level and, in the investigated case the induced strong lateral velocity component is visible. This points out the limitation of the one-dimensional approach main aim of which is to provide an simple method for research interested in only limited information on vertical exchange between the stream and the pore water. Beyond this it is most desirable to have a 3D model as described by the Discussants with additional temperature data for a natural river bed, to determine spatial heterogeneity with greater reliability. This is currently done by the Department of Hydrogeology, UFZ Centre for Environmental Research, Leipzig-Halle, Germany.
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discharges decrease the magnitude of hyporheic exchange in pool-riffle channels by smoothing the water-surface profile and decreasing the spatial variation of near-bed pressure (Fig. 5.7) (Tonina and Buffington, 2007). Furthermore, the direction of hyporheic flow (up-welling vs. down-welling) can change with discharge. For example, just downstream of the riffle crest, hyporheic flow is predicted to up-well at low discharge, but down-well at high discharge (Fig. 5.7). These changing patterns and magnitudes of hyporheic exchange together with the authors’ limited number of fixed sample sites may partially explain the seasonal variations in hyporheic flow observed at their study site (their Fig. 5.6). Furthermore, hyporheic flow paths are even more complex and strongly three dimensional in pool-riffle channels with alternate bar morphology (Fig. 5.8). Interactions between flow and bedform topography induce lateral hyporheic flow in these channels that can change with discharge and may contribute to the lateral flow observed by the authors.
References McDonald, R.R., Nelson, J.M., Bennett, J.P. 2005. Multi-dimensional surface-water modeling system user’s guide. U.S. Geological Survey Techniques and Methods, 6-B2, 136pp. (http://wwwbrr.cr.usgs. gov/projects/SW_Math_mod/OpModels/MD_SWMS/index.htm) Tonina, D., Buffington, J.M., 2003. Effects of discharge on hyporheic flow in a pool-riffle channel: Implications for aquatic habitat. EOS Trans. Am. Geophys. Union 84 (46), Fall Meeting Supplement, Abstract H52A-1154. Tonina, D., J.M. Buffington., 2007. Hyporheic exchange in gravel-bed rivers with pool-riffle morphology: Laboratory experiments and three-dimensional modeling. Water Resources Research, 43, W01421.
Reply by the authors We thank the discussants for highlighting important points. The described changes in hyporheic flow are greatly attributed to in channel flow and do not reflect necessarily seasons but different flow conditions. In the Lahn field site one interesting finding was the change from seemingly up-welling in the upper 50 cm of sediment, to downwelling at 100 cm depth during September 2000. Here the additional influence of ground water level and, in the investigated case the induced strong lateral velocity component is visible. This points out the limitation of the one-dimensional approach main aim of which is to provide an simple method for research interested in only limited information on vertical exchange between the stream and the pore water. Beyond this it is most desirable to have a 3D model as described by the Discussants with additional temperature data for a natural river bed, to determine spatial heterogeneity with greater reliability. This is currently done by the Department of Hydrogeology, UFZ Centre for Environmental Research, Leipzig-Halle, Germany.
Gravel-Bed Rivers VI: From Process Understanding to River Restoration H. Habersack, H. Pie´gay, M. Rinaldi, Editors r 2008 Elsevier B.V. All rights reserved.
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6 Bifurcations in gravel-bed streams Marco Tubino and Walter Bertoldi
Abstract In the present paper we provide an overview on some recent experimental and theoretical works, which have been specifically designed to analyze the behaviour of bifurcations in gravel-bed streams. We first investigate the occurrence of a bifurcation starting from an initially straight channel: the interaction between bed and banks evolution determines flow bifurcation when channel width oscillations reach a maximum amplitude; the process is strongly dependent on the migration speed of bars that form in the channel. Experimental evidence on the equilibrium configurations and stability of a simple Y-shaped bifurcation, both in the case of fixed and erodible-bank channels, shows that bifurcations are likely to display unbalanced configurations, characterized by uneven partition of flow discharge and different values of free surface width of downstream branches. Moreover bed levels of downstream branches differ, in accordance with field observations on gravel-bed rivers. Theoretical predictors based on 1D schemes supplemented by suitable 2D information at the node satisfactorily replicate most of the observed features. When the channels joining at the node are free to evolve, the stability of bifurcations is controlled by the occurrence of migrating bars and by the adaptation processes of channel width and planform, as well by the morphodynamic influence of the bifurcation. The resulting evolution may also depend on the initial mechanism triggering flow bifurcation.
1.
Introduction
Braided rivers are intrinsically dynamical systems, characterized by rapid and frequent changes of bed topography and planform shape. They are typically unsteady, never reaching a static equilibrium configuration, not even in the case of a controlled laboratory model with constant water and sediment supply. They display a hierarchy of spatial and temporal scales, which range from the small scale typical of sediment transport adaptation processes and bedforms development to the intermediate-large E-mail address:
[email protected] (M. Tubino) ISSN: 0928-2025
DOI: 10.1016/S0928-2025(07)11123-8
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scales reflecting the dynamics of single branches and nodes and of the whole braided belt. Such scales are also determined by historical legacies related to sedimentological processes and to the variations of hydrological regime of flow and sediment supply (Ashmore, 1991; Hoey, 1992; Ashmore, 2001). Furthermore, in active gravel-bed networks bank cohesion and vegetation are likely to play a minor, albeit complementary, role (e.g., Gran and Paola, 2001; Gurnell et al., 2001). These evolutionary processes are strongly interconnected and the above scales range on a continuum where a clear distinction among different scales can hardly be established. Such a complexity is typically reflected in the records of sediment transport collected at the downstream-end of braided network laboratory models (Ashmore, 1988; Hoey and Sutherland, 1991; Warburton and Davies, 1994). The analysis of these evolutionary scales is a fundamental step to improve our understanding of the behaviour of river systems and of their response to natural and anthropogenic controls. This investigation gains even more relevance when considering that recent approaches to fluvial management look at a braided pattern as a suitable context to enhance different river functionalities. In fact, its intrinsic properties determine a dynamic environment with a high ecosystem diversity; furthermore, they lead to a system which displays a greater adaptability to changing flow conditions and can also mitigate the effect of extreme events (Gilvear, 1999; Klaassen et al., 2002; Van der Nat et al., 2002). In spite of the inherent complexity of braided systems, it proves to be instructive to single out the various constitutive processes and to examine their dynamics independently. The above viewpoint is adopted herein, where specific attention is devoted to the analysis of the bifurcation process, whose evolution constitutes a major ingredient responsible for the complexity of gravel-bed braided rivers (Fig. 6.1 shows an example of a bifurcation in a gravel-bed braided river). In fact, the partition of water and sediment discharge in the active channels of a braided network is mainly controlled by the occurrence of bifurcations and by their subsequent development (Leopold and Wolman, 1957; Ashmore, 1991, Bristow and Best, 1993).
Figure 6.1. Bifurcation in a gravel-bed braided river (Tagliamento River, Italy).
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Field observations of Leopold and Wolman (1957) have first highlighted the role of bifurcations as the primary cause of braiding. Further investigations have widely documented the occurrence of chute and lobe units in gravel-bed braided rivers and the close relationship between bifurcations and confluence–diffluence units, along with the control exerted on local bed topography and discharge partition in downstream branches by sediment transport processes (e.g., Southard et al., 1984; Ferguson et al., 1992). On a much larger spatial scale and in a different context, Richardson and Thorne (2001) have described the flow field in newly formed bifurcations on the sandy Jamuna River, Bangladesh. The above investigations suggest that the onset of a bifurcation can be mainly, though not invariably, related to the occurrence of chute cutoffs due to local flow acceleration. The frequent occurrence of chute cutoffs in braided streams is also reflected by the weakly meandering character of single distributaries within the network (e.g., Krigstrom, 1962; Klaassen and Masselink, 1992). This picture has been also confirmed by several investigations carried out in laboratory models of braided networks (e.g., Ashmore, 1991), though other processes have been also identified through which bifurcations may set the onset of braiding, namely central bar initiation and emergence (Ashworth, 1996), transverse bar conversion (chute and lobe), multiple bar braiding and partial avulsion (Slingerland and Smith, 2004). Further insight into the distinctive features displayed by gravel-bed bifurcations in natural contexts has been recently gained through the observations noted by Zolezzi et al. (2006) in two series of field campaigns on the Sunwapta River (Alberta, Canada) and on the Ridanna Creek (South Tyrol, Italy). The results of the detailed survey of the morphometric and hydraulic characteristics of seven selected bifurcations within the two study reaches suggest that the main recurring feature is a strong asymmetry of the morphological configuration at the node, which invariably results in an uneven partition of flow and sediment transport in downstream branches. The branch carrying the larger discharge is found to be invariably wider and deeper. Such unbalanced distribution of flow discharge is mainly driven by topographical effects: local aggradation establishes just upstream of the bifurcation point, due to flow divergence, followed by a sudden bed degradation at the inlet of the larger branch. As a result, a transverse bottom inclination characterizes the bifurcation region, whose effect may extend over a length of few channel widths upstream of the bifurcation point; furthermore, an inlet step establishes, whereby the bed level at the entrance of the smaller downstream branch sits at a higher elevation than the other branch. Field observations of Zolezzi et al. (2006) also suggest that the above asymmetry often implies that only the larger branch is morphologically active, at least at low-intermediate stages; furthermore, discharge anomaly is found to increase for decreasing values of the incoming discharge. The question then arises on whether the above asymmetry is inherently associated with the dynamic behaviour of the bifurcation or it mainly results from the combined role of non-local influences. The latter can be exerted, among others, by the migration of bars in the upstream channel, by the adjustment process to the flowing discharge of the width and curvature of channels joining at the node and by the occurrence of backwater effects. In principle, we may expect that a bifurcation remains stable when the transport capacity of downstream branches balances their
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load at the mouth; otherwise, local sedimentation and erosion occur and the system undergoes morphological changes. However, both the incoming load and the sediment carrying capacity of downstream branches depend on local flow conditions and bed topography at the node as well as on non-local effects due to external forcings. On one hand one could argue that the sudden deviation of the main flow orientation induced by a bifurcation may act as a planimetric discontinuity, like that associated with an abrupt change of channel curvature, leading to a morphodynamic influence on bed topography whose effect may be felt over a distance of several channel widths. In this respect the avenue opened by the work of Zolezzi and Seminara (2001) may provide a sound explanation of the observed behaviour of bifurcations, as it states that the influence of such a discontinuity is mainly felt upstream or downstream depending on the aspect ratio b falling above or below a resonant value br, which depends on sediment mobility and grain roughness. We note that the concept of resonance in river morphodynamics has been originally introduced by Blondeaux and Seminara (1985) (see also Seminara and Tubino, 1992), who have shown that the linear solution for flow and bed topography in meanders with a periodic distribution of channel curvature exhibits a resonant behaviour as b approaches br. For values of relevant parameters typical of single distributaries in gravel-bed braided rivers, the above resonant value is relatively small and falls within the range (5C15)1. Hence, bifurcations displaying a super-resonant behaviour can be frequently encountered in gravel-bed braided rivers, which would imply a dominant upstream influence. On the other hand, field and laboratory observations suggest that the dynamics of channels and nodes are strongly related. Channel adjustment is required by the processes of node shifting, creation or annihilation; in turn, channel migration affects the bifurcation. Furthermore, bifurcations often occur after a well-defined sequence of in-channel events which reflect the strong interaction between the planimetric and the altimetric configurations (Ashmore, 1991). The latter processes have been given a sound explanation through a large number of theoretical and experimental works (for a detailed review on the subject see Bolla Pittaluga et al., 2001), though the present knowledge is almost exclusively restricted to the case of fixed-bank channels. We also note that the available experimental data on channel bifurcations mainly provide a static description of the system, like that commonly used at a larger scale to define the overall properties of a network (link length, braiding indexes) (Ashmore, 1991). On the contrary, the assessment of the relative role of the various ingredients, which affect the stability and the evolution of the nodes would require the availability of detailed records of evolutionary processes and the consequent identification of the corresponding timescales. The lack of this information is the main reason why predicting the behaviour of a bifurcation is still a challenge for existing mathematical models, even for simple configurations (Klaassen et al., 2002; Jagers, 2003). In this respect we observe that the short time evolution of braided networks often seems to be mainly determined by the morphodynamic processes occurring in few, simultaneously active channels. Due to the generally observed asymmetry of the 1
b is the ratio between the half-width of the channel and the flow depth.
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bifurcations, these branches carry most of the water discharge, while the rest of the network is poorly affected by sediment transport (Mosley, 1983; Stojic et al., 1998). Such considerations justify, on one hand, the increasing interest for the development of simplified models, which are suitably designed to reproduce the network evolution at a ‘channel scale’ (Paola, 2001; Jagers, 2003), and, on the other hand, claim for a sounding characterization of single loops within the network. In the present paper we provide a summary of some recent experimental and theoretical works, which have been specifically designed to analyze the behaviour of a single bifurcation. We first investigate the process that leads to the establishment of a bifurcation within individual branches. Then we analyze the equilibrium configurations of a simple Y-shaped bifurcation, along with their stability, in the case of fixedbank channels. Finally, we leave the planform of the channels to be free to evolve and investigate the control exerted on the stability of the bifurcation by the occurrence of migrating bars and by the adaptation process of the channel width and planform.
2.
The onset of braiding through chute cutoff
Since the original work of Friedkin (1945) an analogous experimental procedure has been adopted by various authors to investigate the onset of braiding. An initially straight narrow channel of trapezoidal shape is cut into a cohesionless flat sloping surface and fed with a constant discharge. After some time, such a configuration invariably breaks up into a multichannel pattern, following a sequence of events resulting from the interaction between bed and channel processes. The same procedure has been recently used by Bertoldi and Tubino (2005) (hereinafter referred to as BT) to provide a detailed quantitative analysis of the processes which lead to the establishment of chute cutoffs in individual channels evolving to a bifurcated state. They have performed two series of experiments using well-sorted quartz sand distributions, with values of the mean diameter Ds of 0.5 and 1.3 mm, respectively, and two further series using bimodal mixtures (0:5C1:3 mm; 0:5C1:9 mm) with equal percentages of the two fractions. In terms of the initial values of relevant dimensionless parameters, namely the aspect ratio b and the Shields stress W, the experimental conditions of BT cover the range b0 ¼ ð3:1C6Þ and W0 ¼ ð0:07C0:16Þ, W¼
tn ; ðrs rÞgDs
b¼
b , 2D
(6.1a,b)
where b is the free surface width, D the reach averaged value of water depth, rs and r the sediment and water densities, respectively, g the acceleration due to gravity and t* the average bed shear stress (the subscript 0 denotes the initial values of parameters). BT have carefully documented the planimetric and altimetric development of the channel through series of pictures taken from a digital camera, which could be moved along the longitudinal direction, and frequent surveys of bed topography, performed through a laser scanning device. In such a way they have measured the bed and channel configuration at different stages, from the initial state characterized
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by the development of alternate bars in a nearly straight channel, the subsequent development of a weakly meandering channel displaying large width oscillations, until the final occurrence of flow bifurcations through chute cutoffs. The above observations concern a highly simplified bifurcating system, where the unsteady character of water and sediment inputs and the reworking effects resulting from the interaction between different branches are not considered; however, they provide a physical basis to set suitable rules which can be used in predictive models of channel changes in braided rivers (Jagers, 2003). Experimental results of BT suggest that the bed pattern of individual channels is highly reworked during the above evolutionary sequence, though some distinctive characteristics of the initial morphodynamical processes persist even in the final stage. In particular, the planimetric non-uniformities of the channel (curvature and width variations), whose intensity gradually increases, strongly affect bed topography and promote the transition from migrating free responses, which mostly exhibit an alternate bar structure, to a quasi-steady configuration where central bar structures (or more complex transverse structures) eventually dominate. This clearly results from the Fourier spectra of bed topography, as shown in Fig. 6.2a where the amplitude of the leading components of bed topography measured at the initial stage (open symbols) is compared with that measured immediately before flow bifurcation (closed symbols) for the whole set of experiments performed by BT. On the other hand, the longitudinal spacing of bifurcation points is found to be essentially controlled by the length of bars that form in the initial stage of the process and lead to a sequence of erosional bumps along both banks. In fact, both the length of bars and that of bank oscillations remain almost fixed during further evolution of the channel. This fact has been also confirmed by further laboratory observations performed in channels developing within a laboratory model of a braided network (Bertoldi et al., 2005). Due to the strong interrelation between the altimetric and the planimetric pattern, the length of the bars which form in newly developing channels is set by the initial formative process, and it is then unable to conform to further channel widening. This may be seen as an indication of the fact that the length scale of morphological processes loses its dependence on the actual channel width, which, on the contrary, would be implied by the results of bed stability theories for fixed-bank channels (e.g., Colombini et al., 1987). Further in general, the experimental results of BT suggest that linear theories, which have led to the establishment of theoretical predictors of river planform based on bar formation criteria (e.g., Fredsoe, 1978; Kuroki and Kishi, 1985) can hardly be applied to predict the transverse mode selection which sets the onset of braiding in gravel-bed bifurcating channels, since alternate bar can undergo a finite amplitude development which is strongly conditioned by non-linear effects resulting from the forcing effect of planform shape. Experimental observations of BT also indicate that the control exerted by the latter forcing on the subsequent channel dynamics is crucially dependent on the ratio between the migration speed of bars and the bank erosion rate, such that a quite different scenario can be observed depending on local flow conditions. At relatively high values of sediment mobility, bar migration is sufficiently fast to prevent the occurrence of intense localized bank erosion; this, in turn, inhibits the amplification
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amplitude of modes 2 + 3
a)
b)
0.5
0.35
max 0.3
initial stage incipient bifurcation
0.4
0.25
0.3
0.2 0.2
0.15
0.1
0.1
0 0
0.1
0.2
0.3
0.4
0.5
amplitude of mode 1
c) erosion rate [m/s]
0.05 0.06
0.07
d)
1
umax
downstream migration lateral migration
0.08 Shields stress
0.09
0.1
0.04 c
1
0.8
0.1
0.03
0.6 0.02 0.4
0.01
0.2 0.001 0.06
0.07
0.08
0.09
0.10
0.11
Shields stress
e) angle of bifurcation [˚]
uniform sediments graded sediments fast runs
0.07
0.08
0.09
0 0.11
0.10
Shields stress
f)
70
0.3 0.25
uniform sediments 60
0 0.06
0.01
umax migration speed
graded sediments
0.2
50
0.15
40
0.1
30
0.05 0
20 10
15
20 aspect ratio
25
30
5
10
15
20 25 30 aspect ratio
35
40
Figure 6.2. Experimental results of Bertoldi and Tubino (2005): (a) the amplitude of alternate bars (mode 1) and of central and multiple bars (mode 2 and 3) at the initial stage and at the bifurcation; (b) peak values of the dimensionless amplitude of bank oscillations dmax , scaled with half channel width, as a function of Shields stress (crosses denote those runs where bars were not observed to cease their migration); (c) downstream and lateral migration of the channel as a function of Shields stress for the experimental runs B; (d) the migration speed of bars, c, and the local excess of longitudinal velocity at the bank, umax , scaled by the mean flow velocity, as predicted by linear stability analysis of free bars (Colombini et al., 1987) for the experimental runs B; (e) bifurcation angles; (f) the dimensionless amplitude of bank oscillations d, scaled with half channel width, is plotted as a function of the aspect ratio.
of channel curvature and of width variations, whose intensity remains small and is then unable to reduce significantly bar migration. At lower values of Shields stress channel planform develops on a timescale comparable with that of bar migration, which implies that the amplitude of bank oscillations may reach larger values, as shown in Fig. 6.2b. Under these conditions, both channel curvature and width variations significantly slow down bar migration speed, such that bars can no longer move relative to the channel. In this respect the observed phenomena conform to the results of previous laboratory and theoretical investigations on fixed-bank channels with variable curvature (Kinoshita and Miwa, 1974; Tubino and Seminara, 1990) and variable width (Repetto and Tubino, 1999; Repetto et al., 2002).
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We note that both the migration speed and the bank erosion rate are essentially related to bar dynamics, since in laterally unconstrained channels the rate of local erosion is mainly controlled by the topographical expression of migrating bars. Hence, the observed dependence on Shields parameter of the evolutionary process of bifurcating channels, which is summarized in Fig. 6.2c for one series of BT’s experiments, can be given as an explanation on the basis of theoretical results for alternate bars (e.g., Seminara and Tubino, 1989). In fact, such results suggest that bar migration becomes faster as Shields stress increases, while the maximum value of the excess velocity at the banks due to the presence of bars, which provides a suitable measure of the rate of bank retreat, remains almost constant (see Fig. 6.2d). It is worth noticing that, though the resulting process exhibits a quite different behaviour, a clear threshold can hardly be defined in terms of the relevant dimensionless parameters, since Figs. 6.2b, c, d indicate that a smooth transition occurs from one behaviour to the other within a fairly narrow range of values of Shields parameter, say smaller than 0.1. This sensitive dependence of channel dynamics on the local value of Shields stress may turn out to pose a quite restrictive condition for the applicability of numerical models to predict the evolution of braided networks. We also note that, according to BT’s experiments with graded sediments and previous experimental and theoretical works (Lisle et al., 1991; Lanzoni and Tubino, 1999), sorting effects are likely to enhance the suppressing action of planform shape on bar migration and invariably lead to the formation of central wedge deposits of coarse particles acting as precursors of the bifurcation. Measured angles of streamlines of the two branches at bifurcation for both uniform and graded sediment experiments of BT are reported in Fig. 6.2e. Similar values of bifurcation angles have been observed by Zolezzi et al. (2006) and have been also reported by Federici and Paola (2003), who investigated the occurrence of bifurcations within a flume consisting of a straight constant-width channel, with fixed walls, followed by a linearly diverging reach, ending in a much wider constant width channel. Further information concerning the onset of the bifurcation has been obtained from the analysis of bank profiles. As pointed out before, the formation of bars leads to the establishment of a regular sequence of erosional bumps, whose amplitude increases as the planimetric forcing and channel widening inhibit further migration of bars. BT have found that the Fourier spectrum of bank profiles of channels evolving to a bifurcated state is always dominated by a component whose length coincides with that of bars and whose amplitude increases in time, until a maximum value is invariably reached at the onset of the bifurcation. In fact, once a bifurcating flow establishes, it induces the erosion of bank regions that were previously undisturbed, which implies a reduction of the amplitude of bank oscillations, as shown in Fig. 6.2f. The occurrence of this maximum may provide a suitable criterion to set the onset of the bifurcation in terms of the aspect ratio and the Shields stress of the incoming flow.
3.
Laboratory investigation on the equilibrium configurations of a bifurcation
We now turn to the relevant problem of defining the equilibrium configurations of a bifurcation. The subject poses a number of questions that must be addressed. As
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pointed out in ‘‘Introduction’’, channel bifurcations in gravel-bed braided rivers are almost invariably asymmetrical. Is this asymmetry related to the final configuration towards which the system is driven in its evolution? How long does the system take to attain an equilibrium state? Are these states stable or do channel bifurcations invariably evolve until one of the downstream branches eventually closes? Which is the influence exerted on the above configurations and on their stability by bed and channel processes resulting from the continuous rearrangement of the network? Furthermore, a bifurcation may occur as the result of a recently opened small branch, through chute cutoff or avulsion processes, or may initially consist of two channels receiving nearly balanced discharges as in anastomosed systems. Does the equilibrium configuration depend on the initial state of the system? Answering the above questions preliminarily requires the collection of detailed experimental data along with the availability of a sound model able to reproduce the complex flow structure which establishes at the bifurcation. Such a complexity has been recently highlighted by the numerical results of de Heer and Mosselman (2004), who tried to reproduce the experimental observations performed by Bulle (1926) in alluvial diversions with fixed side-walls. The above results seem to indicate that the peculiar 3D structure of the flow field at the node may be responsible for a strongly unbalanced sediment partition in downstream branches, though the above effect is presumably much less intense in gravel-bed bifurcations which generally display relatively small flow depths. In order to gain a deeper insight into the dynamical behaviour of a bifurcation we first consider the results of experiments which have been recently performed with reference to a simple configuration consisting of a symmetrical Y-shaped bifurcation, with fixed walls, in which a main channel divides into two downstream distributaries. The experiments have been mainly devoted to measure water and sediment partition in the downstream branches, for different hydraulic conditions of the incoming flow, and to provide a detailed characterization of final bed topography attained by the system at equilibrium. The experimental runs have been carried out in the ‘p flume’, a large experimental facility (25 m long and 3.14 m wide) located in the Hydraulic Laboratory of Trento University, which has been originally designed for scale models of braided networks. The flume has been filled with well-sorted, sieved quartz sand, with mean diameter of 0.63 mm; a symmetrical bifurcation has been built inside the flume, joining three channels with fixed walls, rectangular cross section and movable bed. The widths of the upstream channel (a) and of downstream branches (b and c) have been set equal to 0.36 and 0.24 m, respectively, following the indication of rational regime theories which predict a non-linear relationship between the flow discharge and the channel width, implying a ratio nearly equal to 1.3 between the total width of downstream channels and the upstream width, for a symmetrical configuration (Ashmore, 2001). The bifurcation angle has been set to 301, with downstream branches diverging symmetrically from the direction of the upstream flow. Further details on the experimental setting and procedures can be found elsewhere (Bertoldi et al., 2005; Bertoldi and Tubino, 2006). In order to determine the equilibrium configuration of the bifurcation and to assess the influence of bars developing in the upstream branch, two different sets of
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experiments have been performed. In each set different hydraulic conditions have been tested changing the incoming water discharge Qa and keeping the same initial value of the longitudinal bed slope. The sediment input has been regulated according to the transport capacity of the incoming uniform flow estimated through Parker (1990) formula. In the first set of runs, the slope has been set to the value of 0.3%: in this case, due to the relatively low values of the aspect ratio ba, the formation of free bars in the upstream channel was inhibited. In the second series the slope has been set to 0.7%: in all runs the formation of migrating alternate bars has been invariably observed in the upstream branch, since ba always exceeded the threshold value predicted by bar theories (Colombini et al., 1987). In few runs bars also developed in downstream branches; however, their effect on bifurcation has been always found to be negligible. The experimental conditions and the values of the relevant dimensionless parameters of the incoming flow, namely the aspect ratio ba and the Shields stress Wa, are reported in Table 6.1, where S is the mean longitudinal slope at the end of the run and Da is the mean flow depth measured in channel a. In the same table, we also summarize the measured equilibrium values of the discharge ratio of downstream branches rQ ¼ Qc =Qb , where the subscript ‘b’ always denotes the main downstream channel. Experimental findings indicate that, in the absence of backwater effects, the response of the system is mainly determined by flow and sediment transport conditions
Table 6.1. Experimental conditions and measured values of discharge ratio and inlet step at equilibrium in Y-shaped bifurcations with fixed walls. Run
S
Q (l/s)
Da (m)
ba
Wa
rQ
DZ
F3-18 F3-20 F3-21 F3-23 F3-25 F3-29 F3-37 F3-45 F3-61 F7-06 F7-07 F7-08 F7-09 F7-10 F7-12 F7-13 F7-15 F7-17 F7-20 F7-24
0.0031 0.0026 0.0027 0.0031 0.0026 0.0031 0.0033 0.0037 0.0029 0.0065 0.0066 0.0077 0.0078 0.0067 0.0070 0.0076 0.0076 0.0068 0.0078 0.0072
1.8 2 2.1 2.3 2.5 2.9 3.7 4.5 6.1 0.6 0.7 0.8 0.9 1 1.2 1.3 1.5 1.7 2 2.4
0.0167 0.0189 0.0191 0.0194 0.0215 0.0223 0.0254 0.0277 0.0363 0.0068 0.0075 0.0077 0.0083 0.0093 0.0102 0.0105 0.0113 0.0126 0.0134 0.0153
10.77 9.55 9.45 9.26 8.38 8.08 7.09 6.50 4.95 26.30 23.91 23.30 21.66 19.38 17.71 17.21 15.88 14.28 13.45 11.73
0.0459 0.0425 0.0453 0.0524 0.0487 0.0599 0.0721 0.0873 0.0855 0.092 0.084 0.082 0.076 0.0574 0.0655 0.0734 0.0787 0.0784 0.0943 0.0985
0.294 0.466 0.56 0.730 0.65 0.8 0.91 0.99 0.97 0 0 0 0.25 0.05 0.45 0.5 0.5 0.45 1 1
0.694 0.594 0.514 0.365 0.312 0.153 0.043 0.022 0.019 1.307 1.370 1.726 1.318 1.228 0.821 0.773 0.397 0.722 0.485 0.198
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in the upstream channel and follows two distinct behaviours. At relatively high values of Wa the bifurcation remains stable, keeping a balanced partition of water and sediment discharge in downstream branches (or returning to a balanced state once perturbed with an extra amount of sediment feed in one branch). At lower values of Wa, in spite of the symmetrical character of the bifurcation, the system evolves towards an unbalanced configuration, where different flow and sediment discharges are conveyed in downstream branches, such that rQ attains equilibrium values invariably lower than 1. Examples of the temporal evolution of both balanced and unbalanced bifurcations are given in Fig. 6.3a. In the latter case the system undergoes strong morphological changes, such that the final bed configuration is characterized by a distinctive asymmetry, which is found to replicate the main features displayed by natural bifurcations. In particular, local aggradation occurs at the node, while the average bed level reached by downstream branches is significantly different, as shown in Fig. 6.3b, the main downstream channel being invariably located at a lower level. Hence, a transverse inlet step establishes at the node, whose amplitude DZ, scaled with the flow depth Da, is also reported in Table 6.1 (such parameter has been computed as the difference between the values of bed elevation at the inlet of distributaries obtained through linear interpolation of their longitudinal bed profiles). The uneven partition of flow discharge at the node is sustained by the bed configuration of the upstream channel, where a transverse deformation gradually establishes, in the form of a steady alternate bar, over a length of few channel widths upstream of the bifurcation. Such depositional bar, whose intensity depends on local flow conditions, drives the flow and the sediment transport towards the main branch; its occurrence reflects the upstream morphological influence exerted by the sudden deviation of the main flow orientation induced by the bifurcation. Measured equilibrium values of the discharge ratio rQ and of the inlet step DZ are reported in Figs. 6.3c and d in terms of the Shields stress and of the aspect ratio of the upstream flow, respectively, for the whole set of experiments. It is worth noticing that, for a given channel slope, increasing values of Wa correspond to decreasing values of ba. Hence, the stronger is the degree of asymmetry of bed configuration, that is the larger is DZ, the smaller is the discharge ratio rQ, which implies a highly unbalanced bifurcation. The above results highlight the strong link between the discharge distribution and the bed topography at the bifurcation point, which is implied by the almost linear relationship between rQ and DZ. For those runs in which alternate bars did not occur such relationship takes the following simple form: DZ ¼ 1 rQ
(6.2)
Experimental results show that a Y-shaped bifurcation is driven towards more unbalanced equilibrium configurations as the Shields stress decreases. At low values of sediment mobility the system becomes unable to keep active both downstream branches, such that one branch closes and rQ vanishes. Under these conditions the measured difference of bed level at the inlet of downstream branches is comparable with the average depth of the incoming flow. It is worth noting that the above results conform to those recently obtained by Federici and Paola (2003), who investigated
M. Tubino, W. Bertoldi a)
b)
1.2
0 -0.2 -0.4 -0.6 -0.8 -1 -1.2 -1.4 -1.6 -1.8 -2
bed elevation [cm]
discharge ratio rQ
144
1 0.8 0.6 0.4 0.2 0 00.00
run F3-21 run F3-45 04.00
c)
08.00 12.00 time[hours]
16.00
0
20.00
d)
0.6 0.4
50 100 150 200 250 longitudinal coordinate [cm]
1 0.8 0.6 0.4
0.2
0.2 0 0.04
e) 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0.00
0.06 0.08 Shields stress
0.1
0.12
a
0
5
f)
10 15 aspect ratio a
20
25
20.00
0.00
discharge ratio rQ
7
2.00
4.00 time [hours]
6.00
6 5 4 3 2 1 0 0.00
8.00
4.00
8.00 12.00 16.00 time [hours]
h) 1.4
g) 1
1.2 inlet step ∆η
discharge ratio rQ
S = 0.3% S = 0.7%
0.8 0.6 0.4 0.2
1 0.8 0.6 0.4 S = 0.3% S = 0.7%
0.2 0
0 -1
300
S = 0.3% S = 0.7%
1.2
0.8
0 0.02
discharge ratio rQ
1.4
S = 0.3% S = 0.7% inlet step ∆
discharge ratio rQ
1.2 1
right channel left channel
0
1 2 (a-R)/R
3
4
-1
0
1 2 (a-R)/R
3
4
Figure 6.3. Experiments in Y-shaped bifurcations with fixed banks: (a) time evolution of the discharge ratio rQ measured in the balanced run F3-45 and in the unbalanced run F3-21; (b) longitudinal bed profiles of the downstream branches (run F3-21); (c) and (d) time evolution of the discharge ratio measured in two runs in which alternate bars have been observed (runs F7-24 and F7-08); (e) discharge ratio and (f) inlet step at equilibrium as a function of the Shields stress and the aspect ratio of the upstream channel; (g) discharge ratio and (h) inlet step at equilibrium as a function of the distance from resonant conditions.
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the stability of bifurcations occurring in a diverging channel, fed by an upstream channel with constant width and fixed walls. They observed that the bifurcation was stable and fairly symmetrical for relatively large values of the Shields parameter of the incoming flow; at lower values, say smaller than 0.15, bifurcations were unstable since the flow switched repeatedly and randomly from one branch to the other. Figs. 6.3c and d also suggest that the development of free alternate bars in the upstream channel, as observed in the second series of experiments, does not seem to change the above scenario, at least qualitatively (the corresponding equilibrium values of rQ and DZ are reported as closed triangles). However, we have found that bar occurrence enhances the tendency of the system towards the establishment of unbalanced configurations, since in this set of experiments we have invariably measured smaller values of the discharge ratio, and consequently larger values of the inlet step, for similar values of the dimensionless parameters of the incoming flow. Furthermore, a more complex and irregular evolutionary process has been detected, such that the system has never achieved a steady configuration, unless in the case of strongly unbalanced bifurcations. Examples of the measured variations of the discharge ratio in the experiments characterized by the presence of migrating bars are reported in Figs. 6.3e and f both for a stable and an unstable bifurcation. In the former case, the discharge distribution remains almost balanced: the effect of migrating bars is reflected by the fluctuations of rQ around the equilibrium value. In the latter case, which corresponds to smaller values of Shields stress, the presence of migrating alternate bars causes, since the beginning of the experiment, a sudden instability of the bifurcation, which leads to a strongly unbalanced configuration. Due to the morphodynamic influence exerted by the bifurcation, a steady bed deformation establishes in the incoming channel, whose amplitude is comparable with that of migrating bars, which in turn affects bar migration. However, bedforms migration is still able to destabilize the system such that the flow switches from one channel to the other. The above behaviour highlights the crucial role played by the mutual interaction between steady and migrating bed responses on the stability of the bifurcation. It also suggests the opportunity to revisit the experimental findings in the light of the concept of morphodynamic influence, as it has been stated theoretically by Zolezzi and Seminara (2001) and more recently confirmed experimentally by Zolezzi et al. (2005). The experimental runs summarized in Table 6.1 correspond to both sub-resonant and super-resonant conditions. If we report the measured values of rQ and DZ in terms of the relative distance from the resonant conditions ðb bR Þ=bR , as in Figs. 6.3g and h, we find that experimental data fall approximately on the same curve: sub-resonant conditions typically correspond to balanced equilibrium configurations, while in super-resonant conditions the bifurcation evolves towards unbalanced configurations. Furthermore, increasing the distance from the resonant value bR, the degree of asymmetry of the bifurcation becomes larger. Such results can be given a relatively simple physical explanation. In super-resonant conditions the morphodynamic influence of the bifurcation is mainly felt upstream, which implies that, as the main flow changes its orientation at the node, a transverse bed deformation occurs in the upstream branch, which in turn determines an unbalanced
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flow partition. In sub-resonant conditions the influence of the node can be only reflected by downstream topography. Hence, the bifurcation can keep stable. These results, which need to be confirmed by further experimental evidence, seems to suggest the possibility of interpreting the response of a bifurcation to the variations of the incoming flow in terms of a single parameter which measures the distance of local flow conditions from the resonant range.
4.
The theoretical model of Bolla Pittaluga et al. (2003)
Theoretical models which have been proposed so far to investigate the stability of channel bifurcations essentially differ for the different structure of the nodal point conditions accounting for the sediment exchange at the node (Slingerland and Smith, 2004). A proper formulation of such conditions has been found to be the crucial ingredient, which is required to replicate the observed characteristics of natural bifurcations. For gravel-bed bifurcations a relatively simple model has been recently proposed by Bolla Pittaluga et al. (2003) (hereinafter referred to as BRT) within the context of a 1D approach. The model considers the same configuration analyzed in the previous section, namely a Y-shaped bifurcation with fixed banks; however, the possible development of migrating bars in the incoming channel is not accounted for. BRT’s approach follows closely the procedure originally introduced by Wang et al. (1995), according to which the equilibrium configurations of a Y-shaped bifurcation are determined through the solution of five nodal point conditions, which must be imposed at the node in a 1D model, along with two stage discharge relationships for the downstream branches. Using the same notation adopted in the previous section, the above conditions read: Qa ¼ Q b þ Q c ; Hi ¼ Ha Q i ¼ bi C i D i
(6.3)
ði ¼ b; cÞ; pffiffiffiffiffiffiffiffiffiffiffiffi gRi Si
(6.4a,b) ði ¼ b; cÞ.
(6.5a,b)
They impose the balance of water discharge Q and the constancy of water level H at the node, along with uniform flow conditions in downstream branches, where C is Chezy resistance coefficient and R the hydraulic radius. Wang et al. (1995) have used an empirical condition to model the partition of sediment discharge at the node, along with a condition similar to (6.3) expressing the sediment discharge balance. An alternative approach has been proposed by BRT, which is able to account for topographically driven effects on flow and sediment transport which occur just upstream of the bifurcation. They have employed a ‘‘quasi two-dimensional approach’’ close to the bifurcation, whereby the last reach of the upstream channel, over a length of few channel widths, aba , has been divided in two adjacent cells, both fed with a sediment discharge proportional to their upstream width and each feeding a downstream branch. Applying Exner (1925) equation to both cells they have derived the following nodal point conditions for sediment
Bifurcations in gravel-bed streams
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transport: 1 ba dZi qi qa ðba =ðbb þ bc ÞÞ qy þ ¼0 ð1 pÞ 1 þ bb þ bc dt bi 2 aba
ði ¼ b; cÞ,
(6.6a,b)
where t is time, p the sediment porosity, Z the bed elevation, q the sediment discharge per unit width; furthermore, qy the transverse exchange of sediments between the two cells due to lateral flow exchange and gravitational effects, which has been evaluated through a suitable generalization of the relationship used to describe bedload transport over a gently sloping bed in quasi-unidirectional flow (e.g., Ikeda et al., 1981). We note that qy depends both on the discharge ratio rQ and on the inlet step DZ. Hence, this term embodies the fundamental mechanism retained in BRT model: whenever one of the downstream branches receives less water or its average bed level is higher than the level of the other branch, the resulting excess of bedload is diverted to the other branch. Due to the inclusion of this effect, the model of BRT is able to capture the main distinctive features of gravel-bed bifurcations. In particular, according to model results, the behaviour of the bifurcation is found to depend upon the values of relevant parameters describing the incoming flow, namely Wa, ba and Sa. In agreement with experimental findings for a symmetrical bifurcation (bb ¼ bc ), stable equilibrium solutions in which the two downstream branches are fed with the same water and sediment discharges are only possible for relatively large values of the Shields parameter Wa; for smaller values of Wa, say smaller than 0:1C0:15, a further equilibrium solution appears (along with its reciprocal), which is found to be invariably stable and implies a strong imbalance of discharge partition in downstream branches. The threshold curves below which the balanced solution is no longer stable, as obtained by BRT, are plotted on the plane (Wa, ba) in Fig. 6.4a, for different values of the upstream slope Sa. As shown in Fig. 6.4b the agreement between theoretical predictions and experimental findings is fairly good, particularly for the set of experiments in which bars didn’t form (in Fig. 6.4b values of the discharge ratio rQ larger than 0.9 have been considered as implying balanced bifurcations). The theoretical model also reproduces the observed asymmetry of bed configuration at the node, though with an accuracy compatible with its simple 1D character. In fact, unbalanced solutions are found to be invariably characterized by different values of the flow depth in downstream branches; through equation (6.4) this implies that the local bed levels differ at the node such that an inlet step forms. Furthermore, the model replicates the observed tendency towards the establishment of strongly unbalanced configurations for smaller values of Wa (or larger values of ba), and predicts the corresponding increase of the amplitude of the inlet step. Stability diagrams for a Y-shaped symmetrical bifurcation are reported in Figs. 6.4c and d. They are given in terms of the equilibrium values of the discharge ratio rQ ¼ Qc =Qb and of the amplitude of inlet step DZ. Stable solutions are denoted by solid lines, while dashed lines indicate unstable solutions. We note that unlike Fig. 6.9 of BRT, for which Meyer-Peter and Muller’s transport relationship was employed, Figs. 6.4c and d have been obtained using Parker (1990)’s bedload transport relationship, which behaves smoothly as the Shields stress tends to zero.
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0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
0.12
BALANCED SOLUTION UNSTABLE
0.08 0.06 0.04 0.02
0
5
10
15
20
0
25
aspect ratio a
5
10
15
20
25
30
aspect ratio a
d)
10 discharge ratio rQ
unbalanced runs balanced runs
0
c)
1
inlet step ∆
0.5
1
0
-0.5
0.1
-1 0
5
e)
10 aspect ratio a
15
20
0
5
f)
100
10 aspect ratio a
15
20
1
10
100
1.2 0.8
10
inlet step ∆
discharge ratio rQ
Bolla Pittaluga et al. (2003)
0.1
a
S = 0.005 S = 0.01 BALANCED S = 0.025 SOLUTION STABLE
Shields stress
Shields stress
a
a)
1 0.1
0.4 0 -0.4 -0.8
0.01 0.01
0.1
1 slope ratio rS
10
100
-1.2 0.01
0.1
slope ratio rS
Figure 6.4. Theoretical results of Bolla Pittaluga et al. (2003): (a) equilibrium configurations of a symmetrical Y-shaped bifurcation (the threshold line separates the region where the balanced configuration is the only stable solution from the region where two further unbalanced solutions occur); (b) comparison between the experimental results of Bertoldi and Tubino (2006) and the theoretical predictions; (c) discharge ratio and (d) inlet step as a function of the aspect ratio of the upstream channel (W ¼ 0:1; S ¼ 0:007); (e) discharge ratio and (f) inlet step as a function of the slope ratio of the distributaries (b ¼ 15; W ¼ 0:1; S ¼ 0:007).
It is worth noting that the governing mathematical problem, set in terms of the equations (6.3)–(6.6), displays a further degree of freedom, in that the stability of the bifurcation is also affected by the downstream boundary conditions through the dependence on downstream slopes included in (6.5). In particular, the stability diagrams reported in Figs. 6.4c and d refer to equilibrium solutions for which the values of downstream slopes coincide, namely rS ¼ S c =S b ¼ 1: otherwise, balanced solutions cannot occur. In the work of BRT this effect has been included through the dependence of the solution on the ratio of the lengths of downstream channels (see Fig. 6.7 of BRT). Implicit in their procedure is the assumption that the downstream conditions set a unique value of the water surface elevation for both branches, which
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may represent the case of a closed loop where channels rejoin at a downstream node as well as that of two branches delivering into a pond. In this respect, the model of BRT follows the classical viewpoint of long-term morphodynamic analysis. In fact, following the lead of Wang et al. (1995), BRT assume that the time evolution of the channel loop can be described as a sequence of uniform flow conditions, such that sediment continuity is applied to downstream branches in global form, accounting for the sediment discharge entering each channel through the upstream mouth and leaving it from the outlet section. One can readily argue that the above approach implies that the stability of the system is investigated on a relatively long timescale, namely that required for the morphological bed response of channels joining at the node to adapt to flow discharge and to the effect of downstream boundary conditions. However, due to the relatively small values of Shields parameter typical of gravel-bed channels, the timescale required for the morphodynamic influence of downstream boundary conditions to be felt may be quite large when compared with the timescale over which significant morphological changes occur at the node, like those which lead to node shifting or annihilation. An alternative approach has been recently proposed by Miori et al. (2006) (see also Hirose et al., 2003), whereby a local analysis has been introduced which neglects the effect of downstream boundary conditions and assumes that the flow in downstream branches is in equilibrium with the local bed slope, according to a suitable stage–discharge relationship. The above approach is obviously unable to account for backwater effects, which may be induced, at high flows, by the physical constraint imposed by the geometry of slopes flanking the braided reach or by the presence of a regulating weir at the outlet, as in the case of Ridanna Creek (Zolezzi et al., 2006). However, a local analysis seems more suitable to describe the inherent response and the stability of bifurcations subject to relatively rapid changes, as it occurs in gravelbed braided rivers. It is worth noting that the adoption of the latter viewpoint does not affect the resulting pattern of equilibrium configurations and their stability; however, it leads to a different definition of the timescale of the evolutionary process, which loses it dependence on the length of downstream channels. Hence, the above distinction may turn out to be relevant for the assessment of the relative role on the stability of the bifurcation of further processes, like channel width adjustment or bar migration, each of them characterized by a distinctive timescale. The dependency on the slope ratio rS ¼ S c =Sb of the equilibrium values of the discharge ratio and of the amplitude of inlet step, as predicted by the theoretical model, is shown in Figs. 6.4e and f. It appears that for values of rS falling within a convenient range around rS ¼ 1 three configurations are possible, where the flow discharge is always unevenly apportioned between branches, unless rS ¼ 1. Furthermore the solution corresponding to the less unbalanced configuration (dashed lines in Figs. 6.4e and f) is always unstable. Hence, within this range of values of rS the bifurcation invariably evolves towards a highly unbalanced configuration and the flow switch to a given branch is not conditioned by the local values of channel slope. For values of the slope ratio rS falling outside the above region, the systems only
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admits of one solution, which is strongly unbalanced and conveys the flow in the channel characterized by the larger slope.
5.
Channel bifurcations with erodible banks
Setting the banks of the channels to be fixed, as we have done in the preceding sections, is equivalent to consider that the timescale of planimetrical changes is much larger than the timescale of bed evolution. This is a quite common assumption for single-thread meandering channels, where bank erosion is mainly controlled by sediment cohesion and vegetation. In gravel-bed braided rivers, however, the timescales of bank and bed erosion may be comparable and single channels can be often considered, up to a certain extent, as laterally unconstrained (Murray and Paola, 1994). Field evidence suggests that during formative events the overall structure of the braided network undergoes major changes. It is then reasonable to expect that, as the bifurcation evolves, the channels joining at the node can adjust their width to the flowing discharge. Whether or not channel width adaptation can proceed such as to accomplish a regime relationship with the actual flow conditions crucially depends on the timescale of the process, as compared with the typical timescale of the bifurcation evolution. We also note that, if we leave the channel width to be free to change, a further element of asymmetry is introduced in the process. In fact a gravel-bed channel widens when its discharge increases. On the contrary, the counterpart process of channel narrowing does not occur in response to a discharge fall, at least on a relatively short timescale. The above considerations have motivated two further series of experiments that have been carried out in the ‘p flume’. In the first set of experiments (‘‘M’’-type) we have removed the fixed banks of downstream branches, leaving the upstream channel at the original width of 0.36 cm. In the second set (‘‘L’’-type) the channels joining at the node have been traced directly on the sand-plain, leaving the whole system to be free to evolve. Hence, while in the former series the incoming conditions were fixed and the observed evolution has been mainly induced by the variation of the shape, orientation and position of the node, as well as by downstream channels widening, in the latter series the incoming conditions changed during each run and the evolutionary processes of the bifurcation have been also influenced by the slow planimetric evolution of the weakly meandering upstream branch. Experimental conditions are summarized in Table 6.2. We may note that in all cases the system evolved towards unbalanced configurations. However, measured data do not display a regular trend as in the case of fixed-bank channels. This reflects the highly dynamical character of these runs, whose evolution has been markedly conditioned by the interaction of various bed and channel processes, which often prevented the achievement of stable equilibrium configurations (measured data reported in the table correspond to quasi-equilibrium conditions which lasted for a sufficiently long time span). Notwithstanding such complexity, the above experiments provide a consistent picture of some distinctive features of the evolutionary process of a bifurcation. The
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Table 6.2. Experimental conditions and measured values of discharge ratio and inlet step at quasi-equilibrium in bifurcations with erodible banks. Run
S
Q (l/s)
Da (m)
ba
Wa
rQ
DZ
M3-19 M3-21 M3-23 M3-25 M3-28 M3-33 L7-08 L7-10 L7-12 L7-15
0.0027 0.0032 0.003 0.0029 0.0028 0.0033 0.0063 0.0062 0.0066 0.006
1.9 2.1 2.3 2.5 2.8 3.3 0.8 1 1.2 1.5
0.0179 0.0182 0.0195 0.0209 0.0225 0.0236 0.0155 0.0141 0.0151 0.0162
10.1 9.9 9.2 8.6 8 7.6 11.1 14.4 15.9 16.8
0.0431 0.0511 0.0516 0.0522 0.0549 0.0678 0.0771 0.0707 0.0803 0.0802
0.14 0.22 0.02 0.2 0.04 0.14 0.7 0.6 0.4 0.55
0.546 0.464 0.819 0.529 0.725 0.554 0.296 0.128 0.378 0.164
experimental findings suggest that the time behaviour of the discharge ratio rQ observed in most of the runs can be approximated through an exponentially decreasing function towards the equilibrium value, as shown in Fig. 6.5a. Hence, from these data a suitable timescale can be determined, through a best-fit procedure, which may be taken as a representative scale of the dynamical response of the bifurcation. In order to filter out the dependence of the above scale on bedload intensity, which measures the speed of any morphological process obeying to Exner (1925) equation, we have scaled the time variable using the morphological timescale bD t ¼ qffiffiffiffiffiffiffiffiffiffiffiffi , gDD3s F
(6.7)
where D is the sediment relative density and F the bedload intensity. Interpolated values of the dimensionless timescale T are plotted in Fig. 6.5b in terms of the parameter ðba bR Þ=bR , which measures the relative distance from the resonant conditions in the upstream channel. Data refer both to ‘‘F’’-type experiments (fixed banks) and to ‘‘M’’-type experiments. In the latter runs we have invariably observed a slower evolution, as a consequence of the adjustment process of the width of downstream branches. Hence, as shown in Fig. 6.5b the resulting timescale T is larger. Experimental findings also suggest that, in terms of the scaled time variable, the evolutionary process is much faster under super-resonant conditions, when the equilibrium configuration is more unbalanced, while T increases sharply as we cross the resonant range. We note that T provides a measure of the ratio between the timescale of the bifurcation and the morphological scale (6.7) and does not represent the actual speed of the process. Within the super-resonant range typical values of T are much smaller than 1, which implies that the bifurcation evolves on a relatively fast timescale. All the experiments performed with erodible banks have displayed a quite similar behaviour. A distinctive sequence of phases has been identified, which reflected the influence exerted by various morphological processes acting on different timescales. Such behaviour can be reconstructed on the basis of the results reported
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b)
discharge ratio rQ
1.2
0.8 0.6 0.4 0.2 0 0
c)
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 dimensionless time t*
discharge asymmetry AQ
1 0.8 0.6 0.4 0.2 0 0.00 -0.2 -0.4 -0.6
2.00
4.00
6.00
period of rQ oscillations [min]
time scale T
1
1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 -0.4
Fruns Mruns
-0.2
d)
0
0.2 0.4 (a-R)/R
0.6
0.8
1
80 70 60 50 40 30 20 10 0 0
time [hours]
10
20 30 40 50 60 70 period of bar migration [min]
80
migration speed [m/s]
e) 0.0018 0.0016 0.0014 0.0012 0.001 0.0008 0.0006 0.0004 0.0002 0 0.00
0.15
0.30
0.45
1.00
1.15
1.30
time [hours]
Figure 6.5. (a) The time evolution of the discharge ratio measured in run M3-19 and the corresponding exponential curve; (b) the dimensionless timescale T as a function of the relative distance from resonant conditions; (c) time evolution of discharge asymmetry measured in the experimental run L7-10; (d) relationship between the period of oscillation of the discharge ratio and the period of bar migration; (e) damping of bar migration speed observed in run L7-10.
in Figs. 6.5c, d, e. An example of the observed time evolution of discharge asymmetry AQ ¼
Qb Qc Qb þ Qc
(6.8)
is given in Fig. 6.5c. In the first phase AQ fluctuates due to the development of bars in the incoming channel, which eventually reach the inlet of downstream branches such that flow switches its direction; at this stage the period of oscillation is fixed by the migration speed of bars, as shown in Fig. 6.5d. In the meantime the node shifts downstream, due to the high erosion rate of incoming flow, the angle between downstream branches increases, reaching a maximum value ranging 60–701, and a steady bed pattern gradually establishes just upstream of the node. Furthermore, the channels joining at the node widen and modify their planimetric configuration, assuming a weakly meandering pattern.
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These processes affect in turn the development of bars, and lead to a marked and rapid decrease of their speed, as shown in Fig. 6.5e, while their length remains almost fixed in spite of channel widening, like in BT experiments. Furthermore, they lead to the establishment of a dominant channel and discharge asymmetry AQ rapidly increases until it reaches a peak value. This also drives the incoming bars towards the main downstream branch. However, as two consecutive bars enter in the same channel, the flow suddenly switches to the other branch. The subsequent evolution of the bifurcation is mainly determined by the planimetric evolution of the channels joining at the node. A further switch of the configuration is determined on a longer timescale by the planimetric shift of the weakly meandering upstream branch, though small-scale fluctuations due to migrating bedforms are still detectable. The bifurcation angle decreases and eventually reaches a value falling in the range 45–601, as observed in other laboratory experiments (see Section 2). The above observations provide a picture which is far from being conclusive and would need to be integrated with further detailed measurements on the behaviour of bifurcations within a network, such as to account for the effect brought by the interaction between the various objects constituting the network and by the preceding development of the network itself. However, experimental findings unequivocally suggest that balanced bifurcations can hardly be expected. Furthermore, they show that the evolution of the node is strongly related both to width changes and to channel shift. A recent attempt to include the former effect in the model of BRT is due to Miori et al. (2006) (hereinafter referred to as MRT). In the analysis of BRT the channel widths are fixed and are prescribed as input data. In order to account for channel width adaptation a suitable relationship is needed to relate the channel width to the hydraulic characteristics. However, as pointed out by Chew and Ashmore (2001), empirical formulas based on data collected in single-thread channels often fail in describing the longitudinal width changes of braided reaches. Water discharge indeed dominates empirical regime relations, while field data collected on a braided reach of the Sunwapta River suggest that the effect of grain size plays an important role on channel width adjustment. The above limit is partially removed by rational regime formulas which, however, still predict rather unprecise values of the observed channel width, despite accounting for the effect of grain size. In their analysis MRT have adopted both a rational regime formula and an empirical relationship, namely: b ¼ 5:28QS 1:26 D3=2 s b ¼ 0:087O0:599 D0:445 s
ðGriffiths; 1981 Þ ðAshmore; 2001Þ
(6.9)
(6.10)
where O ¼ gSQ is the stream power and g the water specific weight. We note that (6.10) is an empirical formula specifically designed for gravel-bed channels, which has been proposed by Ashmore (2001) on the basis of a statistical regression on field data.
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a)
b)
0.05
0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0
Shields stress ϑ
Shields stress
Two novelties are introduced with respect to BRT in the analysis of the equilibrium configurations of a Y-shaped bifurcation. A first novelty is brought in the dimensionless representation of the incoming flow, as the adoption of (6.9) or (6.10) imposes a given relationship among the dimensionless parameters of the upstream flow Wa, Sa and ba, as plotted in Figs. 6.6a and b. In particular we note that the empirical formula (6.10) implies a slight increase of Shields stress as the aspect ratio increases, which is also implied by any rational regime formula, analogous to (6.9), which although displays a much weaker dependence. Furthermore, for any given set of dimensionless parameters characterizing the incoming flow, the governing system (6.3)–(6.6) must be supplemented with two further relationships of the form (6.9) or (6.10) to account for width adjustment of downstream branches to the local flow conditions. MRT have found that in both cases, whatever value of the aspect ratio is used, the Y-shaped configuration
0.04
0.03
S = 0.003 S = 0.007 S = 0.015
0.02 0
5
c)
10 15 aspect ratio
20
25
0
10 15 aspect ratio
20
25
10 width ratio rb
discharge ratio rQ
5
d)
100 10 1 0.1
1
0.1
0.01 0
5
e)
10 15 aspect ratio a
20
25
0
5
0
1
f)
1
1
0.8
0.8
width ratio rb
discharge ratio rQ
S = 0.003 S = 0.007 S = 0.015
0.6 0.4 0.2 0
10 15 aspect ratio a
20
25
2 3 4 dimensonless time t /
5
0.6 0.4 0.2 0
0
1
2 3 4 dimensonless time t /
5
Figure 6.6. Theoretical results of Miori et al. (2006): the relationship between Shields parameter and aspect ratio, for different values of channel slope, as obtained through Griffiths (1981) formula (a) and Ashmore (2001) relationship (b); the equilibrium values of rQ (c) and of DZ (d) reached by the system starting from a symmetrical initial condition, as a function of ba (Sa ¼ 0:007); the time evolution of the discharge ratio rQ (e) and of the width ratio rb (f) starting from different initial conditions (Sa ¼ 0.007).
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invariably admits of unbalanced equilibrium solutions. This is shown in Fig. 6.6c where we report the equilibrium states of the bifurcation, in terms of the equilibrium values of discharge ratio rQ, as obtained using the empirical relationship (6.10) and the transport formula proposed by Parker (1990), for rS ¼ Sc =S b ¼ 1. We note that the resulting inability of the system to maintain a balanced configuration when banks are erodible conforms to the results of experimental observations. The model of MRT also provides an estimate of the equilibrium width of downstream channels: as shown in Fig. 6.6d, for typical values of the aspect ratio of the incoming flow, the main downstream channel at equilibrium may be 2–4 times wider than the smaller channel. In order to investigate the stability of such equilibrium configurations MRT have adopted a local approach. As discussed before, this implies that the time evolution of the system is no longer dependent on the length of downstream branches, as in BRT. As a consequence, the speed of the process is governed by the nodal conditions (6.6a, b) and, through the remaining set of nodal equations, is related to the local characteristics of the bifurcation. Furthermore, in order to account for the different response of the channel width to discharge rise and fall, MRT have introduced a simplified approach such that channel widening has been computed through the empirical formula of (6.10), while channel narrowing has been precluded. This simple mechanism turns out to be quite important to disclose a further property of the system. In fact, MRT analysis reveals that, in addition to the previously discussed equilibrium configuration, which essentially requires that both downstream channels conform their width to a regime formula, further equilibrium states may exist which depend on the initial state. In fact, according to the model of MRT the bifurcation cannot reach a final configuration in which one branch is narrower than its initial value. It is worth noting that the initial condition, which can be arbitrarily imposed in the model, essentially embodies the effect of different inception mechanisms. Hence, the main consequence of the results of MRT is that the equilibrium configurations are found to depend on the mechanism through which the bifurcation is formed. Results of MRT are summarized in Figs. 6.6e and f, where we plot the time evolution of the discharge ratio rQ ¼ Qc =Qb and of width ratio rb ¼ bc =bb of a Y-shaped bifurcation for different initial values of the width ratio rb of downstream branches. The equilibrium value of the above ratios corresponding to regime conditions of both downstream branches are reported with dotted lines. Fig. 6.6f suggests that the geometry of the bifurcation, namely the ratio between the widths of the downstream distributaries, is quite sensitive to the initial conditions, such that the possible equilibrium states covers almost the whole range of values. On the contrary, Fig. 6.6e shows that the range of equilibrium values of rQ is quite narrow. Furthermore, when the initial value of rb is larger than the corresponding equilibrium value under regime conditions, the final configuration attained by the system is strongly reminiscent of the initial state. This may be the case of distributive bifurcations, where the initial channels display almost comparable widths. On the other hand, a bifurcation originating from the incision of an initially narrow branch leaving the main channel is driven towards an equilibrium
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configuration which does not differ appreciably from that occurring when both downstream branches satisfy a regime relationship. In fact, in this case the bifurcation is initially characterized by a strong imbalance, which implies that the subsequent evolution of the bifurcation is dominated by widening of the smaller channel, while the width of the main branch remains almost fixed.
6.
Concluding remarks
Recent theoretical and experimental investigations on gravel-bed rivers bifurcations provide a deeper insight into one of the dynamical processes that mainly controls the complexity of braided networks. The recurring asymmetrical configurations observed in the field are reproduced both by laboratory models and by simplified theoretical models, which indicate an intrinsic tendency towards unbalanced configurations mainly due to local effects. This picture does not change significantly due to external controls, as those exerted by bar occurrence and by channel shift. It is also shown how equilibrium in cohesionless bifurcations with erodible banks is strongly sensitive to the initial configuration: such dependence is quite relevant for natural streams subject to irregular duration and intensity of the forming events. The above results, far from being exhaustive, may significantly enhance the chances of success in predicting channel pattern evolution of braided streams, provided they can be transformed in simplified rules to be incorporated into predictive numerical models (e.g., Paola 2001, Jagers 2003). Research on this topic would benefit from a deeper investigation of the interplay between the intrinsic timescale of bifurcation and those related to migrating bars and determined by the duration of formative events. Finally, a more complete understanding of bifurcation dynamics within a braided network will require further insight into the complex interaction of local processes with channel and node shifting occurring at various locations in the braided river.
Acknowledgments This work has been developed within the framework of the ‘Centro di Eccellenza Universitario per la Difesa Idrogeologica dell’Ambiente Montano – CUDAM’, the projects ‘Morfodinamica delle reti fluviali – COFIN2001’ and ‘La risposta morfodinamica di sistemi fluviali a variazioni di parametri ambientali – COFIN 2003’, co-funded by the Italian Ministry of University and Scientific Research (MIUR) and the University of Trento, and the project ‘Rischio Idraulico e Morfodinamica Fluviale’ financed by the Fondazione Cassa di Risparmio di Verona, Vicenza, Belluno e Ancona. The authors gratefully acknowledge Guido Zolezzi for carefully reading the paper and Stefano Miori for the plots. The authors are deeply thankful to all the people who joined and participated in the laboratory activities and data processing, in particular to Stefania Baldo, Alessio Pasetto and Luca Zanoni.
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Hoey, T., 1992. Temporal variations in bedload transport rates and sediment storage in gravel-bed rivers. Prog. Phys. Geogr. 16 (3), 319–338. Hoey, T., Sutherland, A., 1991. Channel morphology and bedload pulses in braided rivers: a laboratory study. Earth Surf. Process. Landf. 16, 447–462. Ikeda, S., Parker, G., Sawai, K., 1981. Bend theory of river meanders. Part 1: Linear development. J. Fluid Mech. 112, 363–377. Jagers, H., 2003. Modelling planform changes of braided rivers. Ph.D. Thesis, University of Twente, The Netherlands. Kinoshita, R., Miwa, H., 1974. River channel formation which prevents downstream translation of transverse bar. Shinsabo (in Japanese) 94, 12–17. Klaassen, G., Douben, K., van der Waal, M., 2002 (4–6 September). Novel approaches in river engineering. In: Proceedings of RiverFlow 2002. Lovain la Neuve, Belgium, pp. 27–43. Klaassen, G., Masselink, G., 1992. Planform changes of a braided river with fine sand as bed and bank material. In: Proceedings of 5th International Symposium on River Sedimentation, Vol. I, Karlsruhe, Germany, pp: 459–471. Krigstrom, A., 1962. Geomorphological studies of sandar plains and their braided rivers in iceland. Geogr. Ann. 44, 328–365. Kuroki, M., Kishi, T., 1985. Regime criteria on bars and braids. Report, Hokkaido University, Japan, Vol. 14, pp. 283–300. Lanzoni, S., Tubino, M., 1999. Grain sorting and bar instability. J. Fluid Mech. 393, 149–174. Leopold, L.B., Wolman, G., 1957. River channel patterns: braided, meandering and straight. United States Geological Survey Professional Paper 282B, pp. 39–85. Lisle, T., Ikeda, H., Iseya, F., 1991. Formation of stationary alternate bars in a steep channel with mixed size sediment: a flume experiment. Earth Surf. Process. Landf. 16, 463–469. Miori, S., Repetto, R., Tubino, M., 2006. A one-dimensional model of bifurcations in gravel bed channels with erodible banks. Water Resour. Res. 42 (11), W11413. Mosley, M., 1983. Response of braided rivers to changing discharge. J. Hydrol. NZ 22, 18–67. Murray, B., Paola, C., 1994. A cellular model of braided rivers. Nature 371, 54–57. Paola, C., 2001. Modelling stream braiding over a range of scales. In: Mosley, M.P. (Ed.), Gravel-Bed Rivers V. New Zealand Hydrologic Society, Wellington, pp. 11–46. Parker, G., 1990. Surface-based bedload transport relation for gravel rivers. J. Hydraul. Res. 28, 417–436. Repetto, R., Tubino, M., 1999. Transition from migrating alternate bars to steady central bars in channels with variable width. In: Proceedings of International Symposium on River, Coastal and Estuarine Morphodynamics, Genova, Italy, 6–10 September. Repetto, R., Tubino, M., Paola, C., 2002. Planimetric instability of channels with variable width. J. Fluid Mech. 457, 79–109. Richardson, W., Thorne, C., 2001. Multiple thread flow and channel bifurcation in a braided river: Brahmaputra-Jamuna River, Bangladesh. Geomorphology 38, 185–196. Seminara, G., Tubino, M., 1989. Alternate bars and meandering: Free, forced and mixed interactions. In: Ikeda, S. and Parker, G. (Eds), River Meandering. Water Resources Monographies, 12, pp. 267–320. Seminara, G., Tubino, M., 1992. Weakly nonlinear theory of regular meanders. J. Fluid Mech. 244, 257–288. Slingerland, R., Smith, N., 2004. River avulsions and their deposits. Ann. Rev. Earth Planet Sci. 32, 257–285. Southard, J., Smith, N., Kuhnle, R., 1984. Chutes and lobes: Newly identified elements of braiding in shallow gravelly streams. In: Koster, E.H. and Steel, R.J. (Eds), Sedimentology of Gravels and Conglomerates. Can. Soc. Petr. Geol. Mem. 10, pp. 51–59. Stojic, M., Chandler, J., Ashmore, P., Luce, J., 1998. The assessment of sediment transport rates by automated digital photogrammetry. Photogramm. Eng. Rem. Sens. 64 (5), 387–395. Tubino, M., Seminara, G., 1990. Free-forced interactions in developing meanders and suppression of free bars. J. Fluid Mech. 214, 131–159. Van der Nat, D., Schmidt, A., Tockner, K., Edwards, P., Ward, J., 2002. Inundation dynamics in braided floodplains: Tagliamento river, northeast Italy. Ecosystem 5, 636–647.
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Wang, B., Fokking, R., De Vries, M., Langerak, A., 1995. Stability of river bifurcations in 1D morphodynamics models. J. Hydraul. Res. 33 (6), 739–750. Warburton, J., Davies, T., 1994. Variability of bedload transport and channel morphology in a braided river hydraulic model. Earth Surf. Process. Landf. 19, 403–421. Zolezzi, G., Bertoldi, W., Tubino, M., 2006. Morphological analysis and prediction of channel bifurcations. In: Sambrook-Smith, G.H., Best, J.L., Bristow, C.S., and Petts, G.E. (Eds), Braided Rivers: Process, Deposits, Ecology and Management. IAS Special Publication 36, Blackwell, Oxford, UK, pp. 233–256. Zolezzi, G., Guala, M., Termini, D., Seminara, G., 2005. Experimental observation of upstream overdeepening. J. Fluid Mech. 531, 191–219. Zolezzi, G., Seminara, G., 2001. Downstream and upstream influence in river meandering. Part 1. General theory and application of overdeepening. J. Fluid Mech. 438, 183–211.
Discussion by Rob Ferguson You have shown very elegantly that it is possible to consider the stability of bifurcations by a simple analytical approach, and to include the effects of differences in bed level between the two channels. Your assumption that all the flow is within the channels seems very reasonable for avulsions and for mature bifurcations in braided rivers, but what about incipient bifurcation around a newly formed mid-channel bar in a braided river? In this case some of the flow will be over the bar. Could this alter the stability of the bifurcation, and could it be included in your analytical approach?
Reply by the authors The analytical model presented here is obviously unable to describe the effect of over-bank flow because it is essentially a 1D model based on the assumption that all the flow is within the channels. Hence, the model may not be suitable to describe the dynamics of a bifurcation forming through the deposition of a mid-channel bar, as well as the analogous inception process discussed in Section 2 due to the interaction between bars and bank erosion. However, in gravel-bed braided rivers the flow is typically shallow and sediments transport mainly occurs where the flow field is relatively intense, even under formative conditions. Hence, in active bifurcations morphological processes are mainly restricted to the deeper areas inside the branches and over-bank flow is likely to play a minor role, at least at intermediate high stages. This may be also due to bed material sorting effects that typically produce an armoured layer. Recent observations performed on Tagliamento river support the above conjecture in that mayor changes in bed topography have been measured where a channelled flow was clearly identifiable. Therefore, we do not expect the overall stability of a bifurcation to be strongly affected by over-bank flow. In this respect we may note that our theoretical model is also able to reproduce, at least qualitatively, experimental findings with
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Wang, B., Fokking, R., De Vries, M., Langerak, A., 1995. Stability of river bifurcations in 1D morphodynamics models. J. Hydraul. Res. 33 (6), 739–750. Warburton, J., Davies, T., 1994. Variability of bedload transport and channel morphology in a braided river hydraulic model. Earth Surf. Process. Landf. 19, 403–421. Zolezzi, G., Bertoldi, W., Tubino, M., 2006. Morphological analysis and prediction of channel bifurcations. In: Sambrook-Smith, G.H., Best, J.L., Bristow, C.S., and Petts, G.E. (Eds), Braided Rivers: Process, Deposits, Ecology and Management. IAS Special Publication 36, Blackwell, Oxford, UK, pp. 233–256. Zolezzi, G., Guala, M., Termini, D., Seminara, G., 2005. Experimental observation of upstream overdeepening. J. Fluid Mech. 531, 191–219. Zolezzi, G., Seminara, G., 2001. Downstream and upstream influence in river meandering. Part 1. General theory and application of overdeepening. J. Fluid Mech. 438, 183–211.
Discussion by Rob Ferguson You have shown very elegantly that it is possible to consider the stability of bifurcations by a simple analytical approach, and to include the effects of differences in bed level between the two channels. Your assumption that all the flow is within the channels seems very reasonable for avulsions and for mature bifurcations in braided rivers, but what about incipient bifurcation around a newly formed mid-channel bar in a braided river? In this case some of the flow will be over the bar. Could this alter the stability of the bifurcation, and could it be included in your analytical approach?
Reply by the authors The analytical model presented here is obviously unable to describe the effect of over-bank flow because it is essentially a 1D model based on the assumption that all the flow is within the channels. Hence, the model may not be suitable to describe the dynamics of a bifurcation forming through the deposition of a mid-channel bar, as well as the analogous inception process discussed in Section 2 due to the interaction between bars and bank erosion. However, in gravel-bed braided rivers the flow is typically shallow and sediments transport mainly occurs where the flow field is relatively intense, even under formative conditions. Hence, in active bifurcations morphological processes are mainly restricted to the deeper areas inside the branches and over-bank flow is likely to play a minor role, at least at intermediate high stages. This may be also due to bed material sorting effects that typically produce an armoured layer. Recent observations performed on Tagliamento river support the above conjecture in that mayor changes in bed topography have been measured where a channelled flow was clearly identifiable. Therefore, we do not expect the overall stability of a bifurcation to be strongly affected by over-bank flow. In this respect we may note that our theoretical model is also able to reproduce, at least qualitatively, experimental findings with
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Wang, B., Fokking, R., De Vries, M., Langerak, A., 1995. Stability of river bifurcations in 1D morphodynamics models. J. Hydraul. Res. 33 (6), 739–750. Warburton, J., Davies, T., 1994. Variability of bedload transport and channel morphology in a braided river hydraulic model. Earth Surf. Process. Landf. 19, 403–421. Zolezzi, G., Bertoldi, W., Tubino, M., 2006. Morphological analysis and prediction of channel bifurcations. In: Sambrook-Smith, G.H., Best, J.L., Bristow, C.S., and Petts, G.E. (Eds), Braided Rivers: Process, Deposits, Ecology and Management. IAS Special Publication 36, Blackwell, Oxford, UK, pp. 233–256. Zolezzi, G., Guala, M., Termini, D., Seminara, G., 2005. Experimental observation of upstream overdeepening. J. Fluid Mech. 531, 191–219. Zolezzi, G., Seminara, G., 2001. Downstream and upstream influence in river meandering. Part 1. General theory and application of overdeepening. J. Fluid Mech. 438, 183–211.
Discussion by Rob Ferguson You have shown very elegantly that it is possible to consider the stability of bifurcations by a simple analytical approach, and to include the effects of differences in bed level between the two channels. Your assumption that all the flow is within the channels seems very reasonable for avulsions and for mature bifurcations in braided rivers, but what about incipient bifurcation around a newly formed mid-channel bar in a braided river? In this case some of the flow will be over the bar. Could this alter the stability of the bifurcation, and could it be included in your analytical approach?
Reply by the authors The analytical model presented here is obviously unable to describe the effect of over-bank flow because it is essentially a 1D model based on the assumption that all the flow is within the channels. Hence, the model may not be suitable to describe the dynamics of a bifurcation forming through the deposition of a mid-channel bar, as well as the analogous inception process discussed in Section 2 due to the interaction between bars and bank erosion. However, in gravel-bed braided rivers the flow is typically shallow and sediments transport mainly occurs where the flow field is relatively intense, even under formative conditions. Hence, in active bifurcations morphological processes are mainly restricted to the deeper areas inside the branches and over-bank flow is likely to play a minor role, at least at intermediate high stages. This may be also due to bed material sorting effects that typically produce an armoured layer. Recent observations performed on Tagliamento river support the above conjecture in that mayor changes in bed topography have been measured where a channelled flow was clearly identifiable. Therefore, we do not expect the overall stability of a bifurcation to be strongly affected by over-bank flow. In this respect we may note that our theoretical model is also able to reproduce, at least qualitatively, experimental findings with
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non-channelled bifurcating flows. In particular, theoretical results highlight the role of Shields stress of incoming flow as the crucial parameter affecting flow partition at the bifurcation, in agreement with Federici and Paola (2003) observations. Furthermore, the stable symmetrical configurations that have been invariably observed by Ashworth (1996) are in fairly good agreement with the sub-critical character of his experimental runs.
Gravel-Bed Rivers VI: From Process Understanding to River Restoration H. Habersack, H. Pie´gay, M. Rinaldi, Editors r 2008 Elsevier B.V. All rights reserved.
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7 The importance of floods for bed topography and bed sediment composition: numerical modelling of Rhine bifurcation at Pannerden Erik Mosselman and Kees Sloff
Abstract The morphological response of the Dutch Rhine branches to interventions depends sensitively on the morphological development of the bifurcations. Computations in the 1990s revealed that proper modelling of this morphological development requires the inclusion of physical mechanisms for grain sorting. Therefore we apply a twodimensional (2D) morphological Delft3D model with graded sediment to the Rhine bifurcation at Pannerden (‘‘Pannerdensche Kop’’). We find that such a computation, unlike computations with uniform sediment, hardly produces any changes in bed topography at a discharge of 2400 m3/s. Only a less frequent flood discharge of 6000 m3/s is found to produce topography changes. Apparently, the highest floods need to be included when modelling the combined evolution of bed topography and bed sediment composition. We explain this from the time scales for bed topography development and the development of bed sediment composition. If the composition pattern develops fast with respect to bed topography, the sediment is rearranged immediately in a way that eliminates the gradients in sediment transport capacity, after which the bed topography remains unchanged. We show theoretically that the ratio of transport layer thickness to flow depth is the key parameter that determines the ratio of these time scales. The findings also suggest that existing theories tend to underestimate the thickness of the transport layer, with the important implication that computational results may give the false idea of a stable bed topography in cases where the real topography is not stable at all. 1.
Introduction
The river Rhine divides into three branches in the Netherlands (Fig. 7.1). The morphological stability of these branches depends on how sediment transport is distributed over the branches at the Pannerdensche Kop and IJsselkop bifurcations. E-mail addresses:
[email protected] (E. Mosselman),
[email protected] (K. Sloff) ISSN: 0928-2025
DOI: 10.1016/S0928-2025(07)11124-X
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Figure 7.1. Location of Pannerdensche Kop bifurcation of river Rhine, the Netherlands.
If the distribution of sediment transport is perturbed, branches short of sediment will erode and branches overfed with sediment will experience sedimentation. This eventually changes the discharges of the branches, thus having important implications for flooding risks, navigation depths and regional water supply. Wang et al. (1995) demonstrate that the dependence of downstream branches on the distribution of sediment transport at bifurcations can be very sensitive. Currently the two Rhine bifurcations are more or less stable, despite a small trend of diminishing discharges in the Waal branch. However, extensive interventions are being prepared to comply with a new policy for safety against flooding. This policy seeks to provide more space to the river rather than to continually raise the embankments in response to climate change scenarios and improved risk assessments. Interventions to create more room include the removal of bottlenecks, the lowering of floodplains, the modification of groynes and the excavation of secondary channels. They will affect sediment transport and morphology, including the distribution of sediment transport at the bifurcations. The impacts can be assessed using a numerical morphological model. In the 1980s, application of a two-dimensional (2D) morphological model to the Pannerdensche Kop bifurcation was seen as a great success, because the bed topography computed by the model agreed better with prototype measurements than the bed topography obtained in a mobile-bed physical model (Fig. 7.2). Those computations had been carried out by assuming, for each of the branches separately, spatially constant sediment properties and a spatially constant Che´zy coefficient for hydraulic resistance. Samples of river bed material indicated, however, that sediment granulometry varies spatially due to grain sorting. The computations were therefore
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Figure 7.2. Morphological modelling of Pannerdensche Kop bifurcation in the 1980s, with bed topography from field measurements (top), scale model (centre) and 2D numerical model (bottom).
repeated at the end of the 1990s using spatially varying grain sizes, albeit without physics-based process descriptions for changes in bed sediment composition. Surprisingly, it appeared no longer possible to reproduce the bed topography correctly. The topography was found to be affected significantly by both spatial grain size variations and spatial variations in hydraulic roughness (Mosselman et al., 1999,
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2003). The success of computations using spatially constant sediment properties and a spatially constant Che´zy coefficient was ascribed to the fact that the effect of spatial grain size variations is more or less counterbalanced by the effect of spatial roughness variations. However, there are no reasons to assume that this counterbalancing is exact or that it occurs under other conditions as well. Proper modelling was therefore considered possible only if physical mechanisms for grain sorting and alluvial roughness would be included in the model. Given the importance of grain sorting, we apply a 2D morphological model with formulations of physical mechanisms for the transport of graded sediment to the Pannerdensche Kop bifurcation, where the main branch of the Rhine, called ‘‘BovenRijn’’, divides into the Waal to the left and the Pannerdensch Kanaal to the right (Fig. 7.1). The riverbed in this area consists of coarse sands and fine gravels. We investigate the performance of the model at average and flood discharges. Remarkably, the bed topography hardly changes under the average discharge despite substantial sediment transport in the computation. Only a high, less frequent flood discharge is found to produce changes in bed topography, thus questioning the common opinion that a representative annual discharge hydrograph or even a single bed-forming discharge close to bankfull provides sufficient information on the hydrodynamic conditions that cause long-term morphological change. We explain this from the time scales for bed topography development and development of bed sediment composition. If the sediment composition pattern develops fast with respect to the development of bed topography, it is the sediment composition that responds immediately to the initial conditions in a way that eliminates the gradients in sediment transport capacity, after which the bed topography remains unchanged. We show theoretically that this occurs when the thickness of the active or transport layer on the bed is much smaller than the flow depth. A combined evolution of bed topography and bed sediment composition is only possible if the two time scales have the same order of magnitude, i.e., if the active-layer thickness has the same order of magnitude as about one fifth of the flow depth. As this occurs during the larger, less frequent floods, it demonstrates the importance of floods for bed topography and bed sediment composition in the Dutch Rhine branches at Pannerden. We argue, however, that the explanation based on floods may not be sufficient. It is also possible that textbook values for active-layer thickness underestimate the true values that should be adopted in the model.
2. 2.1.
Numerical model Two-dimensional river morphodynamics
The Delft3D modules for 2D river morphodynamics are based on depth-averaged, steady-flow equations, a volumetric sediment balance and formulae relating magnitude and direction of sediment transport to local flow field and bed topography. The first 2D model of this kind was developed by Van Bendegom (1947), but its application without the modern computer devices of the present was very laborious.
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Subsequent work on helical flow in river bends (e.g., Kalkwijk and De Vriend, 1980) and forces on sediment grains on a transversely sloping bed (e.g., Engelund, 1974; Odgaard, 1981) resulted in the model of Struiksma (1985), Struiksma et al. (1985) and Olesen (1987). Similar models were developed by Shimizu and Itakura (1985) and Nelson and Smith (1989). The earlier flow and bed topography model by Kennedy et al. (1984) does not fall into this class of models since it does not use the sediment balance. Instead, it uses an axisymmetrical relationship to link the bed topography directly to the local flow field. Struiksma et al. (1985) also developed important insights for proper calibration and verification of numerical morphological models. They found that the bed topography in bends of flumes and rivers can be understood as a superimposition of a uniform transversely sloping bed and a pattern of non-migrating alternate bars that attenuates in the tail of the bend. Reproduction of the attenuated alternate bars in the tail of the bend is the main indicator that the model can properly reproduce bed topographies in rivers with arbitrary geometries. However, a model that fails to reproduce these attenuated bars can still produce individual cross-sections that agree well with observations. A major pitfall is hence that 2- and 3-D morphological models are calibrated and verified against individual cross-sections only, without considering the spatial patterns of bars and pools. Historically, the Delft3D modules for 2D river morphodynamics can be seen as direct descendants of the models by Van Bendegom (1947), Struiksma (1985) and Struiksma et al. (1985), but with additional features, such as the transport of graded sediment. Moreover, the integration of these models into a larger software system has led to several modifications in the hydrodynamic modules. To assure that such modifications do not deteriorate the performance of the model, each new version of Delft3D is validated on the basis of a test bank containing 70 cases of laboratory experiments and exact analytical solutions, including specific cases of river morphodynamics. Lesser et al. (2004) present the full hydrodynamic equations of Delft3D. These equations are quasi-3D in the sense that the vertical momentum equation has been reduced to the hydrostatic pressure equation by assuming that vertical flow accelerations are negligible compared to gravity. The 3D model thus consists of several 2D layers that are coupled through the hydrostatic pressure equation and a continuity equation for mass conservation. This allows an approach in which the horizontal sizes of the computational grid are much larger than the vertical sizes. This suits the modelling of natural water bodies such as rivers, because in these systems the horizontal extent of the computational domain is usually much larger than the water depth. We use a single layer in our morphological computations, which means that we use 2D hydrodynamic equations despite the availability of quasi-3D equations in the software. We do this because morphological computations require a new computation of the flow field after each time step of bed evolution, leading to long computation times. Fast computation of the flow field greatly improves the overall performance of the model. The essential 3D feature of helical flow is included in the 2D equations by means of a parameterization. Helical flow arises in curved flows and produces a difference between the near-bed flow direction and the depth-averaged
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flow direction. In rivers with predominantly bedload, the near-bed flow direction is equal to the direction of sediment transport over a flat bed. The equilibrium intensity of the helical flow, I e , is calculated by Ie ¼
hu R
(7.1)
where h denotes flow depth, u is the depth-averaged flow velocity and R is the radius of streamline curvature defined by 1 1 @ur ¼ R us @s
(7.2)
where us is the flow velocity component along the streamline, ur the flow velocity component perpendicular to the streamline and s a local coordinate along the streamline. An advection–diffusion equation describes how the actual helical flow intensity, I, adapts to the equilibrium helical flow intensity, Ie. The angle, at , between the near-bed flow direction and the depth-averaged flow direction is calculated from the actual helical flow direction by pffiffiffi g I 2 tan at ¼ 2 1 (7.3) 2kC u k where k is the Von Karman constant (k ¼ 0:4), g is the acceleration due to gravity (g ¼ 9.8 m/s2) and C is the Che´zy coefficient for hydraulic roughness. Sediment transport is described by semi-empirical transport formulae and a depthaveraged sediment balance. The latter reads ð1 Þ
@zb @qsx @qsy þ þ ¼0 @t @x @y
(7.4)
in which qsx and qsy are volumetric sediment transport components per unit width (excluding pores) in the x- and y-direction, respectively, t is time, x and y are horizontal space co-ordinates, zb denotes bed level and e is the porosity of the bed. The porosity factor translates the net volume of sediment grains into the bulk volume which corresponds to the volumetric changes of bed topography due to erosion and sedimentation. Usually e ¼ 0.4 is assumed (e.g., Jansen et al., 1979). Similar balance equations can be written for individual size fractions of a mixture of graded sediment. This is elaborated in the next section. The transport formula for graded sediment is presented in the next section as well. Besides helical flow, transverse bed slopes also cause a difference between the directions of bedload and depth-averaged flow. This effect is modelled by tan as ¼
sin at ð1=f Þð@zb =@yÞ cos at ð1=f Þð@zb =@xÞ
(7.5)
where as is the angle between the sediment transport direction and the depthaveraged flow direction, and f is a dimensionless parameter. The next section presents the relation for f in case of graded sediment.
The importance of floods for bed topography and bed sediment composition 2.2.
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Graded sediment
Graded sediments are accounted for through (i) division of the sediment mixture into separate fractions, (ii) transport formulae and mass conservation equations for each of the separate fractions, (iii) hiding-and-exposure corrections for the critical shear stress of each of the fractions, (iv) an active layer or transport layer affected by erosion and sedimentation (Hirano, 1972) and (v) a bookkeeping system for substratum that has become inactive due to sedimentation. The relative occurrence of a sediment size fraction i in the active layer is indicated by pi;a , and in the substratum by pi;0 . By definition X X pi;a ¼ 1 and pi;0 ¼ 1 (7.6) i
i
The mass conservation equation or sediment balance for each fraction reads ( pi;a sedimentation @pi;a d @z0 @qsxi @qsyi þ pi ðz0 Þ þ þ ¼ 0 pi ðz0 Þ ¼ ð1 Þ pi;0 erosion @t @t @x @y (7.7) in which z0 is the upper level of the substratum, pi ðz0 Þ is the relative occurrence of a sediment size fraction i at this level (taken equal to pi;a during sedimentation and equal to pi;0 during erosion), d is the thickness of the active layer, and qsxi and qsyi are volumetric bedload transport components per unit width for fraction i in the x- and y-direction, respectively. The actual bed level is given by zb ¼ z 0 þ d
(7.8)
The sediment transport rate per fraction is described using a standard transport formula. Here the formula of Meyer-Peter and Mu¨ller (1948) is taken as a starting point. For graded sediment, this formula is written as !3=2 3=2 qffiffiffiffiffiffiffiffiffiffiffiffi C t b 0:047xi qsi ¼ Acal gDD3i rw gDDi C 90
(7.9)
where qsi is the total bedload transport rate per unit width for fraction i, Acal is a calibration factor (equal to 8 in Meyer-Peter and Mu¨ller’s original formula), D is the relative density of the sediment under water, defined by D ¼ (rsrw)/rw, rw and rs are mass densities of water and sediment, respectively, Di is the grain size of fraction i, C90 is a Che´zy coefficient for grain roughness, tb is the magnitude of the bed shear stress and xi is the hiding-and-exposure correction. The grain roughness is based on a Nikuradse roughness of 3D90 instead of Meyer-Peter and Mu¨ller’s original D90: 12h (7.10) C 90 ¼ 18 log 3D90 where D90 denotes the grain size exceeded by 10090 ¼ 10% of the sediment mixture.
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The hiding-and-exposure correction is modelled according to the Egiazaroff (1965) formulation, adjusted by Ashida and Michiue (1972, 1973) Dm xi ¼ 0:85 Di 2 32 log 19 5 xi ¼ 4 log 19 DDmi
for
Di o0:47 Dm
for
Di 0:47 Dm
(7.11)
where Dm denotes the average grain size of the sediment mixture. Equation (7.5) for the effect of transverse bed slopes is applied to calculate the direction of sediment transport for each size fraction separately. The corresponding parameters, fi, are calculated by Bsh C sh Dsh tb Di Dm fi ¼ Ash (7.12) rw gDDi h Di in which Ash , Bsh , C sh and Dsh are calibration parameters. However, as very little is known about the proper formulation for graded sediments, the distinction between different values for different size fractions is switched off by setting Csh ¼ 0 and Dsh ¼ 0. The usual value for Bsh is 0.5. The implementation of the graded-sediment equations in Delft3D has been validated against Ribberink’s (1987) straight-flume experiments and Olesen’s (1987) curved-flume experiments (Sloff et al., 2001). 2.3.
Model settings and initial and boundary conditions
We applied a spatially uniform Che´zy value of 45 m1/2/s. The sediment mixture was divided into the six size fractions presented in Table 7.1. The representative grain sizes, Di, for each fraction were calculated as the geometric mean of the upper and lower size limits. We used the transport formula of Meyer-Peter and Mu¨ller with a calibration coefficient, Acal, equal to 11.2. The porosity of the bed was taken as equal to 0.4. The effect of transverse bed slopes on the direction of sediment transport was represented by Ash ¼ 0.8, Bsh ¼ 0.5, Csh ¼ 0 and Dsh ¼ 0. Table 7.1.
Division of sediment mixture into six separate size fractions.
Fraction number
1 2 3 4 5 6
Grain sizes (mm) Lower limit
Upper limit
Geometric mean (Di)
0.06 1 2 2.8 4 8
1 2 2.8 4 8 12.5
0.24 1.41 2.37 3.35 5.66 10.00
The importance of floods for bed topography and bed sediment composition
169
Two cases were computed, one with a constant discharge of 2400 m3/s and one with a constant discharge of 6000 m3/s. The corresponding Boven-Rijn water depths were on the order of 6 m and 11 m respectively. The 2400 m3/s discharge represents more or less the annual bed-forming conditions for the sand-bed Rhine branches further downstream. The 6000 m3/s discharge represents flood conditions that actually occur at a Rhine discharge of 6700 m3/s because the residual 700 m3/s pass over the floodplains that were not included in the model. Water levels at the downstream boundaries were calculated with rating curves derived from a 1D SOBEK model of the Rhine branches. The initial bed topography was composed as an average of the topographies measured annually in the years 1988–1991, because none of the individual measured topographies covered the full model area (top of Fig. 7.3). The thickness of the active layers was estimated from dune height measurements analysed by Wilbers and Ten Brinke (2003). This resulted in a 0.1 m thickness at 2400 m3/s and a 1.0 m thickness at 6000 m3/s. The bed sediment composition was derived from measurements by Gruijters et al. (2001). An initial bed sediment composition for the computations was obtained by averaging the mean grain sizes over width and by assigning uniform distributions of the resulting grain sizes to each cross-section. This schematized initial bed sediment composition showed long-stream variations with a marked segregation between sediments in the Waal and the Pannerdensch Kanaal but no 2D patterns within the branches (bottom of Fig. 7.3). Each computation simulated the development during a period of 100 days.
3.
Results and analysis
Figure 7.4 shows the results for a 2400 m3/s discharge, Fig. 7.5 those for a 6000 m3/s discharge. Remarkably, the bed topography hardly changed under the 2400 m3/s discharge despite substantial sediment transport in the computation. The fast development of a patchy sediment composition pattern provides an explanation for the lack of bed level changes, because it immediately reduces all gradients in sediment transport capacity to zero. The slower development of sediment composition under the 6000 m3/s discharge does not eliminate the gradients in transport capacity. The result is a combined evolution of both bed topography and bed sediment composition that produces a much smoother sediment composition pattern. This smoother composition pattern complies better with the measured sediment composition in Fig. 7.6. These results reveal the importance of the ratio of the time scales for bed topography development and development of bed sediment composition. This ratio can be derived from the following theoretical analysis along the lines of Ribberink (1987). The 1D quasi-steady flow equations read u
@u @zb @h gujuj þg þ 2 ¼0 þg @x @x @x C h
(7.13)
h
@u @h þu ¼0 @x @x
(7.14)
E. Mosselman, K. Sloff
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6
4000
5 distance (m) →
3500 4 3000 3 2500
2
1
2000 2000
2500
3000 3500 distance (m) →
4000
4500
0
0.005
4000
0.0045 distance (m) →
3500 0.004 3000 0.0035 2500
0.003
0.0025
2000 2000
2500
3000 3500 distance (m) →
4000
4500
0.002
Figure 7.3. Initial bed topography (top, in m above NAP) and mean sediment grain sizes (bottom, in m) at Pannerdensche Kop.
The importance of floods for bed topography and bed sediment composition
171
6
4000
5 distance (m) →
3500 4 3000 3 2500
2
1
2000 2000
2500
3000 3500 distance (m) →
4000
4500
0
0.005
4000
0.0045 distance (m) →
3500 0.004 3000 0.0035 2500
0.003
0.0025
2000 2000
2500
3000 3500 distance (m) →
4000
4500
0.002
Figure 7.4. Bed topography (top, in m above NAP) and mean sediment grain sizes (bottom, in m) at Pannerdensche Kop resulting from computation with 2400 m3/s.
E. Mosselman, K. Sloff
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6
4000
5 distance (m) →
3500 4 3000 3 2500
2
1
2000 2000
2500
3000 3500 distance (m) →
4000
4500
0
0.005
4000
0.0045 distance (m) →
3500 0.004 3000 0.0035 2500
0.003
0.0025
2000 2000
2500
3000 3500 distance (m) →
4000
4500
0.002
Figure 7.5. Bed topography (top, in m above NAP) and mean sediment grain sizes (bottom, in m) at Pannerdensche Kop resulting from computation with 6000 m3/s.
The importance of floods for bed topography and bed sediment composition
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Figure 7.6. Measured sediment grain sizes. (After Gruijters et al. (2001)).
The friction term in equation (7.13) can be neglected when focusing the attention on short spatial scales. Substitution of equation (7.14) into equation (7.13) then leads to the simplified flow equation @u u @zb ¼0 ¼ 2 @x hð1 Fr Þ @x
(7.15)
pffiffiffiffiffi in which the Froude number, Fr, is defined by Fr ¼ u= gh. For a 1D system, the sediment balance for the complete sediment mixture in equation (7.4) can be written as @zb @qs þ ¼0 (7.16) @t @x in which qs is the volumetric sediment transport rate per unit width (excluding pores). The sediment transport is a function of both flow velocity, u, and average sediment grain size, Dm: ð1 Þ
@qs dqs @u dqs @Dm ¼ þ @x du @x dDm @x
(7.17)
Substitution of this equation into equation (7.16) and elimination of @u=@x by applying equation (7.15) lead to @zb u dqs @zb 1 dqs @Dm þ ¼ @t ð1 Þð1 Fr2 Þh du @x ð1 Þ dDm @x
(7.18)
This equation can be interpreted as a kinematic bed topography wave forced by gradients in sediment composition. The corresponding celerity is cbed ¼
u dqs ð1 Þð1 Fr2 Þh du
(7.19)
This relation assumes a simpler form by introducing the degree of nonlinearity, b, of qs ¼ qs ðuÞ, which is defined by b ¼ ðu=qs Þðdqs =duÞ. The result reads cbed ¼
bqs ð1 Þð1 Fr2 Þh
(7.20)
E. Mosselman, K. Sloff
174 Equation (7.7) reduces in a 1D system to @pi;a d @z0 @q þ pi ðz0 Þ þ si ¼ 0 ð1 Þ @t @t @x
(7.21)
The active layer thickness, d, is assumed constant, so that @z0 =@t ¼ @zb =@t. The transport rate per fraction is written as qsi ¼ piT qs in which piT is the relative occurrence of sediment size fraction i in the bedload. Subsequently equation (7.16) is used to eliminate @qs =@x. The result is @p @zb @p (7.22) ð1 Þ d i;a þ ðpi ðz0 Þ piT Þ þ qs iT ¼ 0 @t @t @x Multiplication of all terms by Di and summation over all size fractions gives, assuming that the substratum has the same composition as the active layer ðpi ðz0 Þ ¼ pi;a Þ and noting that the values of Di are constants for the selected size fractions: @Dm @zb @DmT þ ðDm DmT Þ þ qs ¼0 (7.23) ð1 Þ d @t @t @x with Dm ¼
X
pi;a Di
(7.24)
i
DmT ¼
X
piT Di
(7.25)
i
Assuming a constant ratio of average bedload grain size to average active-layer grain size, m ¼ DmT =Dm , equation (7.23) can be written as @Dm mqs @Dm DmT Dm @zb þ ¼ @t dð1 Þ @x d @t
(7.26)
This equation can be interpreted as a kinematic bed sediment composition wave forced by bed level changes and a difference between the sediment compositions of the bedload and the bed. The corresponding celerity is mqs (7.27) cmix ¼ dð1 Þ The celerities in equations (7.20) and (7.27) define the time scales of morphological change and change in sediment composition. The ratio of these time scales reads T mix cbed b d ¼ ¼ T bed cmix mð1 Fr2 Þ h
(7.28)
In sand bed rivers, b has values of 3 to 5, but higher values are possible in conditions close to the initiation of sediment motion (Paintal, 1971). Furthermore, m is an order 1 parameter and Fr2 1 in the Dutch Rhine branches. Hence T mix d 5 T bed h
(7.29)
The importance of floods for bed topography and bed sediment composition
175
The ratio of time scales is hence proportional to the ratio of active-layer thickness to flow depth. If d h, the sediment composition of the bed responds immediately to the initial bed topography in a way that eliminates the gradients in sediment transport capacity, after which the bed topography remains unchanged. This is the case for the 2400 m3/s discharge with d ¼ 0.1 m. If d h, the evolution of the bed topography is forced by the initial sediment composition pattern, while the bed sediment composition remains unchanged. This resembles the nature of the computations in the 1990s using spatially varying grain sizes without physics-based process descriptions for changes in bed sediment composition. A combined evolution of bed topography and bed sediment composition is only possible if (five times) d and h have the same order of magnitude. This is the case for the 6000 m3/s discharge with d ¼ 1 m.
4.
Discussion and conclusion
The results and the analysis demonstrate the importance of the ratio of active-layer thickness to flow depth. A combined evolution of bed topography and bed sediment composition is only possible if the active-layer thickness has the same order of magnitude as about one fifth of the flow depth. In the Dutch Rhine branches, such conditions occur during the large but rare floods that can be ignored in discharge hydrograph schematizations for traditional morphological computations with uniform sediment. Apparently these floods must be accounted for when simulating the combined evolution of topography and composition. At lower flows, the bed topography produced by the previous flood forces a rapid re-arrangement of grain sizes that suppresses further bed level changes. However, inclusion of high floods still may not yield the full picture. The observation from measurements that erosion and sedimentation in the Pannerdensche Kop area occur at lower discharges as well, casts doubt on the common wisdom that the active-layer thickness is equal to half the dune height, or somewhat larger due to sporadic deeper troughs. This common wisdom seems to underestimate the true thickness of the active layer to be adopted in the model. Better estimates might result from the new depth-continuous modelling approach by Blom (2003) and Blom et al. (2003). Moreover, the actual active layer on larger time scales depends on all kinds of local bed level fluctuations generated by discharge variations, i.e., not on dunes alone. Examples are the sand waves generated by fast changes in discharge, the sand waves generated by the flow pattern changes due to the flooding of floodplains, and the stage-dependent variations of the transverse bed slope in river bends. Increased shear stresses due to navigation during low flows might have an effect as well. The final conclusion is that the thickness of the active layer is a key parameter in morphological modelling with graded sediment. Proper representation of its effect implies that floods need to be included when modelling the combined evolution of bed topography and bed sediment composition, even in the absence of armouring. At the same time, however, textbook values seem to underestimate the true thickness of active layers. An important implication is that the application of standard theories might easily lead to the false idea of a stable bed topography that, in reality, is not stable at all. This is an important topic for further research.
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176
Acknowledgements This study has been carried out with Doelfinanciering funds from the Dutch Ministry of Transport, Public Works and Water Management. It is part of a joint research programme of the Morphological Triangle, a thematic subdivision of the Netherlands Centre for River Studies (NCR) that co-ordinates the fluvial morphological research in the Netherlands. The data have been provided by Rijkswaterstaat RIZA. The set-up of the computations has been based on numerous previous morphological computations by Michele Bernabe` of the University of Trento, Italy, and Patrick Verhaar of Delft University of Technology, the Netherlands.
Appendix 1: List of symbols Acal Ash Bsh b C Csh C90 cbed cmix Di Dm DmT Dsh D90 Fr f fi g h I Ie pi(z0) pi,a pi,0 piT
calibration factor in sediment transport formula () coefficient in relation for effect of transverse bed slopes on sediment transport direction () exponent of Shields parameter in relation for effect of transverse bed slopes on sediment transport direction () degree of nonlinearity in qs ¼ qs ðuÞ (), defined by b ¼ ðu=qs Þðdqs =duÞ Che´zy coefficient for hydraulic roughness (m1/2/s) exponent of Di =h in relation for effect of transverse bed slopes on sediment transport direction () Che´zy coefficient for grain roughness (m1/2/s) celerity of infinitesimal perturbations in bed topography (m/s) celerity of infinitesimal perturbations in bed sediment composition (m/s) sediment grain size of fraction i (m) average grain size of sediment mixture (m) average grain size of bedload (m) exponent of Dm =Di in relation for effect of transverse bed slopes on sediment transport direction () 90% percentile of sediment grain pffiffiffiffiffi size distribution (m) Froude number (), Fr ¼ u= gh parameter weighing the influence of gravity pull along transverse bed slopes on transport direction of complete sediment mixture () parameter weighing the influence of gravity pull along transverse bed slopes on transport direction of sediment size fraction i () acceleration due to gravity (m/s2) flow depth (m) local instantaneous intensity of helical flow (m/s) equilibrium intensity of helical flow (m/s) relative occurrence of sediment size fraction i at upper level of substratum, z0 () relative occurrence of sediment size fraction i in active layer () relative occurrence of sediment size fraction i in substratum () relative occurrence of sediment size fraction i in bedload ()
The importance of floods for bed topography and bed sediment composition qs qsi qsx qsxi qsy qsyi R s Tbed Tmix t u ur us x y zb z0 as at D d e k m xi rs rw tb
177
volumetric sediment transport rate per unit width for complete sediment mixture (m2/s) volumetric sediment transport rate per unit width for sediment size fraction i (m2/s) volumetric sediment transport component per unit width in x-direction for complete sediment mixture (m2/s) volumetric sediment transport component per unit width in x-direction for sediment size fraction i (m2/s) volumetric sediment transport component per unit width in y-direction for complete sediment mixture (m2/s) volumetric sediment transport component per unit width in y-direction for sediment size fraction i (m2/s) radius of streamline curvature (m) local coordinate along streamline (m) timescale of changes in bed topography (s) timescale of changes in bed sediment composition (s) time (s) depth-averaged flow velocity (m/s) depth-averaged flow velocity component perpendicular to streamline (m/s) depth-averaged flow velocity component along streamline (m/s) horizontal coordinate (m) horizontal coordinate (m) bed level (m+datum) upper level of substratum (m+datum) angle between sediment transport direction and depth-averaged flow direction (rad) angle between near-bed flow direction and depth-averaged flow direction (rad) relative density of sediment under water (), D ¼ ðrs rw Þ=rw thickness of active layer (m) porosity of bed () Von Karman constant () ratio of average grain size of bedload to average grain size of active layer (), m ¼ DmT/Dm hiding-and-exposure correction () mass density of sediment (kg/m3) mass density of water (kg/m3) magnitude of bed shear stress (N/m2)
References Ashida, K., Michiue, M., 1972. Study on hydraulic resistance and bedload transport rate in alluvial streams. Trans. Japn. Soc. Civil Eng. 206, 59–69. Ashida, K., Michiue, M., 1973. Studies on bed-load transport in open channel flows. Proceedings of International Symposium on River Mechanics, IAHR, Bangkok, Thailand, Paper No. A36, pp. 407–418.
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Blom, A., 2003. A continuum vertical sorting model for rivers with non-uniform sediment and dunes. Ph.D. Thesis, Twente University, Enschede, The Netherlands. Blom, A., Ribberink, J.S., Parker, G., 2003. Sediment continuity for rivers with non-uniform sediment, dunes, and bed load transport. In: Gyr, A. and Kinzelbach, W. (Eds), Sedimentation & Sediment Transport: At the Crossroad of Physics and Engineering. Kluwer Academic Publishers, Switzerland, pp. 179–182. Egiazaroff, I.V., 1965. Calculation of non-uniform sediment concentrations. J. Hydraul. Div. ASCE 91 (HY4), 225–247. Engelund, F., 1974. Flow and bed topography in channel bends. J. Hydraul. Div. ASCE 100 (HY11), 1631–1648. Gruijters, S.H.L.L., Veldkamp, J.G., Gunnink, J., Bosch, J.H.A., 2001. De lithologische en sedimentologische opbouw van de ondergrond van de Pannerdensche Kop. Eindrapport, NITG 01-166-B, TNO, the Netherlands. Hirano, M., 1972. Studies on variation and equilibrium state of a river bed composed of non-uniform material. Trans. Japn. Soc. Civil Eng. 4. Jansen, P.Ph., Van Bendegom, L., Van den Berg, J., De Vries, M., Zanen, A., 1979. Principles of River Engineering: The Non-Tidal Alluvial River. Pitman, London. Kalkwijk, J.P.Th., De Vriend, H.J., 1980. Computation of the flow in shallow river bends. J. Hydraul. Res. IAHR 18 (4), 327–342. Kennedy, J.F., Nakato, T., Odgaard, A.J., 1984. Analysis, numerical modeling, and experimental investigation of flow in river bends. In: Elliott, C.M. (Ed.), River Meandering, Proceedings of Conference on Rivers 1983, New Orleans, ASCE, 1984, pp. 843–856. Lesser, G.R., Roelvink, J.A., Van Kester, J.A.T.M., Stelling, G.S., 2004. Development and validation of a three-dimensional morphological model. Coastal Eng. 51 (8–9), 883–915. Meyer-Peter, E., Mu¨ller, R., 1948. Formulas for bed-load transport. Proceedings of second Congress IAHR, Stockholm, Paper No. 2, pp. 39–64. Mosselman, E., Hassan, K.I., Sieben, A., 2003. Effect of spatial grain size variations in two-dimensional morphological computations with uniform sediment. In: Sa´nchez-Arcilla, A. and Bateman, A. (Eds), Proceedings of IAHR Symposium on River, Coastal and Estuarine Morphodynamics, Barcelona, 1–5 September 2003, Publication of IAHR, Madrid, Spain, pp. 236–246. Mosselman, E., Sieben, A., Sloff, K., Wolters, A., 1999. Effect of spatial grain size variations on twodimensional river bed morphology. Procedings of IAHR Symposium on River, Coastal and Estuarine Morphodynamics, Genova, 6–10 Sept. 1999, Vol. I, pp. 499–507. Nelson, J.M., Smith, J.D., 1989. Evolution and stability of erodible channel beds. In: Ikeda, S. and Parker, G. (Eds), River meandering, AGU, Water Resources Monograph 12. pp. 321–377. Odgaard, A.J., 1981. Transverse bed slope in alluvial channel bends. J. Hydraul. Div. ASCE 107 (HY12), 1677–1694. Olesen, K.W., 1987. Bed topography in shallow river bends. PhD thesis, Delft University of Technology, Communications on Hydraulic and Geotechnical Engineering, No. 87-1, Delft University of Technology, ISSN 0169-6548. Paintal, A.S., 1971. Concept of critical shear stress in loose boundary open channels. J. Hydraul. Res. IAHR 9 (1), 91–108. Ribberink, J.S., 1987. Mathematical modelling of one-dimensional morphological changes in rivers with non-uniform sediment. PhD thesis, Delft University of Technology, Communications on Hydraulic and Geotechnical Engineering, No. 87-2, Delft University of Technology, ISSN 0169-6548. Shimizu, Y., Itakura, T., 1985. Practical computation of two-dimensional flow and bed deformation in alluvial streams. Civil Engineering Research Report, Hokkaido Development Bureau, Sapporo. Sloff, C.J., Jagers, H.R.A., Kitamura, Y., Kitamura P., 2001. 2D Morphodynamic modelling with graded sediment. Proceedings of second IAHR Symposium on River, Coastal and Estuarine Morphodynamics, 10–14 September 2001, Obihiro, Japan, pp. 535–544. Struiksma, N., 1985. Prediction of 2-D bed topography in rivers. J. Hydraul. Engrg. ASCE 111 (8), 1169–1182. Struiksma, N., Olesen, K.W., Flokstra, C., De Vriend, H.J., 1985. Bed deformation in curved alluvial channels. J. Hydraul. Res. IAHR 23 (1), 57–79.
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Van Bendegom, L., 1947. Some considerations on river morphology and river improvement. De Ingenieur 59, B1–B11 (in Dutch; English translation: National Research Council Canada, Technical Translation 1054, 1963). Wang, Z.B., Fokkink, R.J., De Vries, M., Langerak, A., 1995. Stability of river bifurcations in 1D morphodynamic models. J. Hydraul. Res. IAHR 33 (6), 739–750. Wilbers, A.W.E., Ten Brinke, W.B.M., 2003. The response of subaqueous dunes to floods in sand and gravel bed reaches of the Dutch Rhine. Sedimentology 50, 1013–1034.
Discussion by R. Ferguson You demonstrate that the main morphodynamic response to moderate floods is size sorting of the bed, but the main response to big floods is erosion and deposition. I was very interested in this since I too find a combination of the two kinds of response in my own modelling work. You provide a neat explanation of your result in terms of a ratio of response times for bed composition and bed elevation, and show this reduces to the ratio of active layer thickness d to flow depth h. This inspired me to think about the possible mechanisms and I have a suggestion which is entirely consistent with your results and explanation. Consider the fractional Exner equation in the form @ðð1 lÞdF i Þ @z (7:30Þ ¼ ð1 lÞ ðPi E i Þ @t @t where l denotes bed porosity and Fi, Pi, Ei denote the fraction of size i in the active layer, the bedload, and the exchange material, respectively, at the base of the active layer. If l and d are assumed constant over time, and Ei is equated with Fi as is traditional, the equation reduces to ð@F i =@tÞ Pi F i ¼ d ð@z=@tÞ
(7:31Þ
This confirms that the rate of change of bed composition, relative to the rate of change of bed elevation, decreases with increased active layer thickness. It also quantifies the tendency for composition change to be more important when transport is more size selective (bigger difference between Pi and Fi). For fine fractions of the bed, Pi–Fi is positive and qFi/qt has the same sign as qz/qt; for coarse fractions the signs are reversed. As flow depth and shear stress increase during major floods, transport becomes less size selective until Pi converges on Fi and no further change in bed composition is possible.
Reply by the authors We thank Rob Ferguson for the additional insights. His equation basically complies with our equation (7.22) under the assumption that there are no gradients in the sediment composition of the bedload ð@piT =@x ¼ 0Þ. This assumption, however, is responsible for his conclusion that no further change in bed composition is possible
The importance of floods for bed topography and bed sediment composition
179
Van Bendegom, L., 1947. Some considerations on river morphology and river improvement. De Ingenieur 59, B1–B11 (in Dutch; English translation: National Research Council Canada, Technical Translation 1054, 1963). Wang, Z.B., Fokkink, R.J., De Vries, M., Langerak, A., 1995. Stability of river bifurcations in 1D morphodynamic models. J. Hydraul. Res. IAHR 33 (6), 739–750. Wilbers, A.W.E., Ten Brinke, W.B.M., 2003. The response of subaqueous dunes to floods in sand and gravel bed reaches of the Dutch Rhine. Sedimentology 50, 1013–1034.
Discussion by R. Ferguson You demonstrate that the main morphodynamic response to moderate floods is size sorting of the bed, but the main response to big floods is erosion and deposition. I was very interested in this since I too find a combination of the two kinds of response in my own modelling work. You provide a neat explanation of your result in terms of a ratio of response times for bed composition and bed elevation, and show this reduces to the ratio of active layer thickness d to flow depth h. This inspired me to think about the possible mechanisms and I have a suggestion which is entirely consistent with your results and explanation. Consider the fractional Exner equation in the form @ðð1 lÞdF i Þ @z (7:30Þ ¼ ð1 lÞ ðPi E i Þ @t @t where l denotes bed porosity and Fi, Pi, Ei denote the fraction of size i in the active layer, the bedload, and the exchange material, respectively, at the base of the active layer. If l and d are assumed constant over time, and Ei is equated with Fi as is traditional, the equation reduces to ð@F i =@tÞ Pi F i ¼ d ð@z=@tÞ
(7:31Þ
This confirms that the rate of change of bed composition, relative to the rate of change of bed elevation, decreases with increased active layer thickness. It also quantifies the tendency for composition change to be more important when transport is more size selective (bigger difference between Pi and Fi). For fine fractions of the bed, Pi–Fi is positive and qFi/qt has the same sign as qz/qt; for coarse fractions the signs are reversed. As flow depth and shear stress increase during major floods, transport becomes less size selective until Pi converges on Fi and no further change in bed composition is possible.
Reply by the authors We thank Rob Ferguson for the additional insights. His equation basically complies with our equation (7.22) under the assumption that there are no gradients in the sediment composition of the bedload ð@piT =@x ¼ 0Þ. This assumption, however, is responsible for his conclusion that no further change in bed composition is possible
The importance of floods for bed topography and bed sediment composition
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Van Bendegom, L., 1947. Some considerations on river morphology and river improvement. De Ingenieur 59, B1–B11 (in Dutch; English translation: National Research Council Canada, Technical Translation 1054, 1963). Wang, Z.B., Fokkink, R.J., De Vries, M., Langerak, A., 1995. Stability of river bifurcations in 1D morphodynamic models. J. Hydraul. Res. IAHR 33 (6), 739–750. Wilbers, A.W.E., Ten Brinke, W.B.M., 2003. The response of subaqueous dunes to floods in sand and gravel bed reaches of the Dutch Rhine. Sedimentology 50, 1013–1034.
Discussion by R. Ferguson You demonstrate that the main morphodynamic response to moderate floods is size sorting of the bed, but the main response to big floods is erosion and deposition. I was very interested in this since I too find a combination of the two kinds of response in my own modelling work. You provide a neat explanation of your result in terms of a ratio of response times for bed composition and bed elevation, and show this reduces to the ratio of active layer thickness d to flow depth h. This inspired me to think about the possible mechanisms and I have a suggestion which is entirely consistent with your results and explanation. Consider the fractional Exner equation in the form @ðð1 lÞdF i Þ @z (7:30Þ ¼ ð1 lÞ ðPi E i Þ @t @t where l denotes bed porosity and Fi, Pi, Ei denote the fraction of size i in the active layer, the bedload, and the exchange material, respectively, at the base of the active layer. If l and d are assumed constant over time, and Ei is equated with Fi as is traditional, the equation reduces to ð@F i =@tÞ Pi F i ¼ d ð@z=@tÞ
(7:31Þ
This confirms that the rate of change of bed composition, relative to the rate of change of bed elevation, decreases with increased active layer thickness. It also quantifies the tendency for composition change to be more important when transport is more size selective (bigger difference between Pi and Fi). For fine fractions of the bed, Pi–Fi is positive and qFi/qt has the same sign as qz/qt; for coarse fractions the signs are reversed. As flow depth and shear stress increase during major floods, transport becomes less size selective until Pi converges on Fi and no further change in bed composition is possible.
Reply by the authors We thank Rob Ferguson for the additional insights. His equation basically complies with our equation (7.22) under the assumption that there are no gradients in the sediment composition of the bedload ð@piT =@x ¼ 0Þ. This assumption, however, is responsible for his conclusion that no further change in bed composition is possible
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when the transport is no longer size selective. In principle, changes in bed composition remain possible if the composition of the bedload varies spatially. We do support Rob Ferguson’s remark that size selectiveness influences the tendency for composition change, but we believe the ratio of active-layer thickness to flow depth to be the main influencing factor.
Gravel-Bed Rivers VI: From Process Understanding to River Restoration H. Habersack, H. Pie´gay, M. Rinaldi, Editors r 2008 Elsevier B.V. All rights reserved.
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8 Review of effects of large floods in resistant-boundary channels Ellen Wohl
Abstract Gravel-bed channels formed in coarse sediment or mixed bedrock and coarse sediment have higher thresholds of resistance to fluvial erosion than channels formed in finergrained sediment. These higher erosional thresholds are likely to be exceeded only during large floods. Variables that influence the geomorphic role of floods in resistantboundary channels include the flood-generating mechanism (hydroclimatic and damburst processes), position within a drainage basin, erosional threshold, sediment supply, land use, in-channel wood, riparian vegetation, and time since last flood. Geomorphic effects of floods include transport of sediment and wood, alteration of channel and valley morphology, and channel incision. Ecological effects of floods include alteration of physical and chemical characteristics of the river and floodplain, and changes in riparian and aquatic community composition and structure. Channel restoration and management must account for the occurrence and effects of infrequent, large magnitude floods by focusing on river process rather than river form. The net result of downstream trends in numerous physical variables is that the aggregate population of large floods creates the greatest geomorphic effects in headwater channels, whereas individual large floods are likely to be most geomorphically important in the middle portion of drainage basins.
1.
Introduction
This paper summarizes research on the geomorphic and ecological effects of large floods in resistant-boundary channels, and the implications of this research for channel management and restoration. An extensive literature now exists for the geomorphic and ecological impacts of floods in a variety of channel types, with resistant-boundary channels receiving a great deal of attention, including numerous books and review articles that cover at least some of the material addressed here (e.g., Baker et al., 1988; Beven and Carling, 1989; Tinkler and Wohl, 1998; Mosley, 2001). This review differs from previous work in that it addresses both the geomorphic and ecological roles of E-mail address:
[email protected] ISSN: 0928-2025
DOI: 10.1016/S0928-2025(07)11125-1
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large floods in channels formed in either bedrock, coarse sediment, or some combination of the two substrates. In the context of this paper, effects refer to persistent features that are created during flooding. A persistent feature is one that endures until the next flood of similar magnitude occurs, as opposed to a transient feature that is altered by smaller flows following the flood (Brunsden and Thornes, 1979). Geomorphic flood effects include erosional and depositional features. Ecological flood effects include changes in species age distribution or composition in riparian and aquatic communities. Large floods have been defined in a variety of ways for different field settings, and the papers reviewed here use this phrase for flows with widely differing recurrence intervals and differing ratios with respect to the mean annual flood. In this paper, floods are referred to as being large if they are at least twice the magnitude of the mean annual flood. Use of the word large in this context does not necessarily imply that the flood will have geomorphic or ecological impacts that differ from those of the normal annual flood in all field settings; this depends very much on the details of channelboundary resistance to erosion relative to the hydraulic forces generated by the flood. Resistant channel boundaries are streambeds and/or banks composed of either bedrock, alluvium that is coarser than pebble size (Z60 mm), or some combination of bedrock and coarse alluvium. These channels behave in ways distinctly different from channels formed in silt and sand because some minimum or threshold hydraulic force must be exceeded before substantial channel change begins in resistant-boundary channels, as opposed to the nearly constant adjustment of bedforms to changing hydraulic conditions in sand-bed channels (Simons and Richardson, 1966). Although sand-bed channels can have thresholds of motion (e.g., van Rijn, 1984 predicts a critical velocity of 0.3 m/s for a flow depth of 1.5 m over medium sand), these thresholds are typically exceeded multiple times each year. In contrast, the much higher resistance thresholds of channels formed in coarser sediment or bedrock may be exceeded only a few times a year (e.g., Andrews, 1984), or once in decades or centuries (e.g., Grant et al., 1990; de Jong, 1994). Quantitative assessments of the geomorphic role of floods began with Wolman and Miller (1960), who proposed that the relative importance in geomorphic processes of extreme events can be measured in terms of (i) the relative amounts of work done on the landscape (which Wolman and Miller expressed as suspended sediment transport) and (ii) the formation of specific features of the landscape. Using sediment transport records from the United States, they concluded that in many basins the largest portion of the total sediment load is carried by flows that recur on average once or twice each year, an analysis expanded in Leopold et al. (1964). Although the original Wolman and Miller paper discusses the increasing importance of infrequent events with increasing channel resistance to erosion, and a few studies focused on field settings where extreme floods clearly dominated channel morphology or sediment transport (e.g., Tinkler, 1971; Baker, 1973), many subsequent investigators used the Wolman and Miller paper to develop a restrictive model of fluvial dynamics that emphasized the importance of frequent flows in most geomorphic settings. Nearly two decades elapsed before numerous ‘‘anomalous’’ case studies convinced the geomorphic community that some rivers are more likely to be dominated by floods of lower frequency. These rivers include channels with high seasonal and interannual flow variability, high
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ratios between discharge of infrequent floods and average annual flow, abundant coarse bedload, high channel gradient, resistant channel boundaries, and highly erodible channel boundaries such as those found in braided rivers (Baker, 1977; Gupta, 1983; Nolan and Marron, 1985; Kochel, 1988; Baker and Kale, 1998; Cenderelli and Wohl, 2001, 2003; Wohl et al., 2001). Recent studies indicate that small to moderate floods can be very important for transporting sediment and shaping channel morphology even in gravel-bed and other resistant-boundary rivers (e.g., McKenney, 2001), but many resistant-boundary channels are dominated by large floods. This paper briefly reviews the influences of flood-generating mechanism, position in a drainage basin, erosional thresholds, sediment supply, land use, in-channel wood, riparian vegetation, and time elapsed since the last geomorphically effective flood on the geomorphic role of floods. Land use, in-channel wood, and riparian vegetation indirectly influence the geomorphic role of floods by influencing erosional thresholds and sediment supply. They have separate subheadings in this paper because of their multiple roles. Examples of geomorphic and ecological impacts of floods are followed by discussions of the implications for channel management, and a synthesis of how the geomorphic role of floods varies across a drainage basin.
2. 2.1.
Variables influencing the geomorphic role of floods in resistant-boundary channels Flood-generating mechanism
Flood effects to resistant-boundary channels occur along a hydroclimatic spectrum in that climatic patterns creating flood-generating precipitation differ in magnitude and frequency among different regions (e.g., Hirschboeck, 1987, 1988; Church, 1988; Gupta, 1988; Schick, 1988; Webb and Betancourt, 1990). For example, compilations of flood records from the United States indicate that, for small-to moderate-sized basins less than approximately 30,000 km2, the largest values of peak discharge per unit drainage area occur in semiarid or arid regions (Costa, 1987), and in regions such as Hawaii where mountainous islands intercept moisture from convective systems and tropical storms (O’Connor and Costa, 2004). Focusing specifically on the western United States, Pitlick (1994) found that large floods where streamflow is dominated by snowmelt, frontal rainfall, or rain-on-snow can be two to four times the average annual flood and recur every couple decades, whereas large floods in drier regions dominated by convective rainfall can be more than ten times the average annual flood and recur only a few times each century. The much greater interannual variability of flood magnitude in drier regions and in some parts of the seasonal tropics means that erosional and depositional features created during large floods can persist during subsequent smaller flows either because the features exist in portions of the channel that are not submerged during smaller flows, or because the smaller flows do not exceed the erosional thresholds necessary to modify cohesive or very coarse-grained channel boundaries. These types of persistent flood effects have been described for gravel-bed and bedrock rivers in the seasonal
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tropics (Gupta and Dutt, 1989; Wohl, 1992a, b; Kale and Hire, 2004) and semiarid/ arid regions (Patton and Baker, 1976; Graf, 1988; Tooth, 2000). Climatic influences on flooding are also exacerbated by topography. The largest flood flows generally result from orographic enhancement of precipitation (Shroba et al., 1979; SturdevantRees et al., 2001; O’Connor et al., 2002). Topographic variability can also alter storm tracks and promote rapid runoff that enhances flooding (O’Connor and Costa, 2004). Substantial geomorphic change can result from floods that are not directly produced by precipitation, including floods from breached natural (landslide, moraine, ice) or artificial dams. These can be the most geomorphically effective floods within a channel network because they are capable of generating a discharge two or three orders of magnitude greater than meteorologically generated discharges for the drainage basin. Damburst and outburst floods are likely to be particularly geomorphically important in high relief valleys with unstable hillslopes that create tall landslide dams (e.g., Tianche et al., 1986; Hewitt, 1998; Korup, 2005), and in drainages that still have active glaciers (e.g., Maizels, 1991, 1997; Gomez et al., 2002). Numerous compilations (e.g., Costa and Schuster, 1988; Shroder et al., 1998; Cenderelli, 2000; O’Connor et al., 2002) and case studies (e.g., Baker, 1973; Carling and Glaister, 1987; Desloges and Church, 1992; O’Connor, 1993; Benito et al., 1998; Cenderelli and Wohl, 2003) describe the geomorphic effects of damburst and outburst floods in resistant-boundary channels.
2.2.
Position within a drainage basin
Several studies indicate that the relative geomorphic importance of floods varies with position in a drainage basin (e.g., Clark et al., 1987; Miller, 1990). Smaller sub-basins in the headwater portion of a drainage are more likely to have the resistant channel boundaries, abundant coarse bedload, and high channel gradient that promote major geomorphic response to flooding (Patton, 1988; Jacobson et al., 1989; Kale and Hire, 2004). These channels are frequently disturbed because their smaller drainage area often results in a high percentage of contributing area, and because proximity to adjacent hillslopes and lack of floodplain and valley bottom storage minimizes time for precipitation to concentrate in channels (Clark et al., 1987). Because geomorphic response to individual large floods decreases with decreasing time interval between large floods (Harvey, 1984; Cenderelli and Wohl, 2003), the geomorphic effectiveness of any single large flood is likely to be less in the headwaters than in other portions of the drainage. Large floods in the aggregate, however, are likely to dominate the headwater channels. The steepest, narrowest channel segments in headwater areas are also subject to disturbance from mass movements such as debris flows that originate on adjacent hillslopes (e.g., Froehlich and Starkel, 1987; Larsen and Roman, 2001; Korup, 2005). The relationship between floods and debris flows is spatially and temporally complex. Tributary debris flows can be a major source of sediment and wood mobilized during floods (Webb et al., 1989; Wohl and Pearthree, 1991; Benda and Dunne, 1997; Benda et al., 2003; Montgomery et al., 2003); debris flows can alternate with floods along the main channel over timespans of months to years (Seidl and Dietrich, 1992; Stock
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and Dietrich, 2003; Bunn and Montgomery, 2004); and individual large flows can alternate downstream between floods, hyperconcentrated flows, and debris flows as sediment concentration varies (Cenderelli and Wohl, 1998; O’Connor et al., 2001). As drainage area increases downstream, the probability that the entire basin will be contributing to a flood decreases. Storms capable of generating large floods are less common than in the headwaters portion of the drainage and frequency of large floods decreases. The attenuation of water and sediment discharges associated with floodplains also increases, further reducing the likelihood of large floods. The long intervals between large floods increases the likelihood that normal flows will transport volumes of sediment comparable to those transported by the large floods, as well as substantially reworking geomorphic features created during large floods. Working in southern New England, for example, Patton (1988) found that floodplain erosion and deposition during rare large floods was much less substantial in lowland drainages than in smaller, steeper highland drainages. As a result of downstream decreases in large flood recurrence interval and magnitude relative to annual floods, individual large floods can be most geomorphically effective in the middle portions of drainages where such floods are less frequent than in the headwaters, but still exceed erosional thresholds sufficiently to cause substantial sediment transport and channel change (Clark et al., 1987). Flooding in the central Appalachian Mountains of the United States associated with a dissipating tropical cyclone in 1985 provides an example. Prolonged and locally intense precipitation produced over 250 mm of rain during 3 days, and this followed an unusually wet month (Clark et al., 1987). The resulting floods exceeded the 100year discharge in some drainage basins and the 500-year discharge in other basins. Clark et al. (1987) found that basins draining 130–4,000 km2 were most geomorphically altered by the flood. Smaller basins receive comparable precipitation intensities during summer thunderstorms that occur much more frequently than the 1985 storm, and larger basins included sub-basins that received much less precipitation during the 1985 storm.
2.3.
Erosional threshold
The importance of floods in individual resistant-boundary channels will also depend on the frequency/duration of flows exceeding an erosional threshold governed by channel-boundary composition (Costa and O’Connor, 1995) (Fig. 8.1). Following Bull’s (1979) choice of stream power as an appropriate descriptor of threshold conditions for channel change, Magilligan (1992) and Wohl et al. (2001) proposed minimum values of stream power necessary to initiate substantial geomorphic change in alluvial and bedrock channels, respectively. Alternatively, Miller (1990) concluded that unit stream power alone is not a reliable predictor of geomorphic change for individual sites because of the complex interactions among channel width and gradient, channel pattern, spatial arrangements of roughness elements, and local flow obstructions. The geomorphic effectiveness of a flood will ultimately depend on the duration of flow(s) that exceed the erosional resistance of the channel boundaries. Erosional resistance is governed by bedrock and alluvial characteristics (Table 8.1). The ability
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a
b
Unit stream power (W/m2)
bedrock erosion threshold
energy available for geomorphic change
alluvial erosion threshold
c
Time Figure 8.1. Conceptual diagram of energy available for geomorphic change during floods as a function of flood magnitude and duration above thresholds for erosion of different types of channel substrate (see Costa and O’Connor, 1995, Fig. 11). The three curves represent three different types of idealized flood hydrographs: (a) could be a convective storm over a small basin, (b) could be a frontal rainfall storm, and (c) could be a seasonal snowmelt peak of longer duration but lower magnitude than (a) and (b).
of flow to exceed threshold resistance is not simply a matter of average shear stress. Fluctuations about the mean associated with turbulence can be more important in initiating bedrock erosion or particle entrainment that, once started, promotes a selfenhancing feedback by inducing further flow separation and turbulence (Nelson et al., 1995; Robert et al., 1996; Lawless and Robert, 2001). It has proven extremely difficult to adequately quantify the factors influencing boundary erosional resistance and hydraulic driving forces because these factors vary across temporal and spatial scales. For example, many resistant-boundary channels have both bedrock and alluvium exposed along the channel boundaries (Wohl, 1998). An effective approach is likely to be a probabilistic characterization of the key control variables (Powell, 1998; Graf, 2001), but hydraulic models that simulate the two- or three-dimensional flow properties necessary for such a probabilistic approach are just now becoming available to the research community (Miller and Cluer, 1998; Booker et al., 2001; Nicholas, 2001).
2.4.
Sediment supply
Sediment supply exerts a critical control on the type and magnitude of erosional and depositional features produced by a flood. Erosion of bedrock channels is greatest at moderate sediment supplies (Seidl et al., 1994; Sklar and Dietrich, 2004); for example, smaller amounts of sediment do not provide sufficient tools for abrasion of channel boundaries, and larger amounts of sediment mantle the channel bed and protect it
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Factors influencing erosional resistance in bedrock and gravel-bed channels.
Substrate characteristic
Associated erosional processes
Sample reference
Joint geometry (orientation, spacing, width, continuity) and analogous discontinuities (e.g., bedding planes) [bedrock] Porosity and permeability [bedrock]
Cavitation initiated along joints; quarrying lifts separated blocks
Baker and Pickup (1987), Miller (1991), Tinkler (1993), Hancock et al. (1998), Wohl and Springer (2005) Howard (1998), Wohl et al. (1999)
Crystal or grain boundaries [bedrock] Sediment cover [bedrock]
Clast size, shape, and sorting (mean size, sorting, particle shape, packing) [alluvial] Clast resistance [alluvial]
Bank stratigraphy [alluvial]
Channel and valley geometry [bedrock and alluvial]
Seepage and enhanced chemical weathering can produce surface irregularities that induce flow separation and accelerated abrasion Differential weathering produces microscale surface roughness that induces flow separation and accelerated abrasion Areal extent and thickness of alluvial veneer in bedrock channels determines effectiveness of sediment in either shielding bedrock surface from erosion, or promoting erosion through abrasion These characteristics influence entrainment threshold for drag and lift forces Resistance of clasts to chemical and mechanical weathering determines relative importance of disintegration in place versus downstream transport Influences importance of particle-by-particle erosion versus bank slumping or other forms of collapse Influences distribution of hydraulic variables by governing boundary roughness and generation of turbulence, which in turn influences cavitation, lift, and abrasion
Seidl et al. (1994), Sklar and Dietrich (1998, 2001)
Kirchner et al. (1990), Powell (1998), Shvidchenko et al. (2001) Kodama (1994), Sklar and Dietrich (2001)
Lawler (1992), Fonstad and Marcus (2003) Shroba et al. (1979), Miller and Parkinson (1993), Wohl et al. (2001)
from erosion. At the most general level, bed coarsening (e.g., Dietrich et al., 1989), or channel erosion result when transport capacity exceeds sediment supply during a flood in a predominantly alluvial channel. Deposition, which is usually localized in resistant-boundary channels, results when sediment supply exceeds transport capacity during a flood (e.g., Nolan and Marron, 1985; Wohl, 1992a). Sediment supply during a flood can reflect hillslope, valley bottom, and in-channel processes. Hillslope sediment inputs result primarily from slope instability triggered
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by surface runoff, increased infiltration, or undercutting of the slope by floodwaters (e.g., Williams and Guy, 1973). Valley bottom sediment can be mobilized by overbank flows that exceed the threshold shear stress for erosion of the floodplain and valley bottom, which depends on characteristics including grain size, vegetation, and land use. In-channel sediment supply resulting from bed and bank erosion, like the other sources of sediment supplied to floods, can be highly variable in time and space. The presence of a coarse surface layer is likely to be particularly important in controlling in-channel sediment supply in resistant-boundary channels. This coarse surface layer (which has been variously referred to as an armor, pavement, or censored layer; Carling and Reader, 1982) can reduce the sizes and amount of sediment transported (e.g., Gomez, 1983; Parker and Sutherland, 1990). The presence of a coarse surface layer does not imply that the bed is static. Numerous investigators have demonstrated transport of a majority of the particle sizes present on the bed while the coarse surface layer remains stable (e.g., Parker and Klingeman, 1982; Andrews and Erman, 1986). Powell (1998) and Parker and Toro-Escobar (2002) provide more detailed reviews of the mechanics of coarse surface layers and their effects on sediment transport.
2.5.
Land use
Contemporary or historical land use can strongly influence erosional thresholds and sediment during a flood. Channel erosional thresholds can be altered by channel stabilization techniques such as riprap (Kresan, 1988), by the location of structures such as dams, bridges, or road crossings (Anthony and Julian, 1999; Chin and Gregory, 2001), or by alteration of channel geometry and channel–floodplain connections as a result of dredging, channelization, or construction of levees (e.g., Brookes, 1988; Wyzga, 1996; Wohl, 2000a). Land uses such as timber harvest (e.g., Madej and Ozaki, 1996; Stover and Montgomery, 2001), agriculture (e.g., Klimek, 1987; Starkel, 1988; Mei-e and Xianmo, 1994; Clark and Wilcock, 2000), roads (e.g., Froehlich, 1991), or mining (e.g., Macklin et al., 1992), can result in large pulses of sediment to adjacent stream channels during periods of rainfall-induced flooding. Laboratory experiments (Lisle et al., 1997; Cui et al., 2003a), numerical simulations (Cui et al., 2003b), and field studies (Madej and Ozaki, 1996; Madej, 2001; Sutherland et al., 2002) suggest that these pulses move by translation and dispersion over time intervals dependent on flow magnitude and duration following introduction of the sediment pulse. Sediment pulses can alter the grain-size distribution, bedforms, and planform of the channel as the pulses move downstream (e.g., Knighton, 1989; Hilmes and Wohl, 1995; James, 1999). Conversely, urbanization generally reduces sediment supply during floods as a result of increased paved areas, and this commonly results in channel erosion (e.g., Wolman, 1967; Roberts, 1989; Booth, 1990). Dams and other forms of flow regulation also influence channel response to floods by changing the characteristics of both water and sediment discharge (e.g., Young et al., 2001; Grant et al., 2003). The details of these changes depend on the type of flow regulation. Dams generally reduce peak flows and increase base flows, but the
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magnitude of these effects varies markedly among individual dams (Graf, 1999). The most common scenario on dammed rivers is that the geomorphic role of moderate to large floods is substantially reduced because of reductions in the magnitude and frequency of these floods (e.g., Williams and Wolman, 1985; Collier et al., 1996; Magilligan et al., 2003). By trapping bedload and at least a portion of suspended load, dams can also cause downstream coarsening, bed incision, bank erosion, and change in channel planform (e.g., Collier et al., 1996; Kondolf, 1997).
2.6.
In-channel wood
The presence of wood along the channel can exert a substantial control on the location, volume, and stability of stored sediment (Lancaster et al., 2001; Abbe and Montgomery, 2003; Bunn and Montgomery, 2004). Wood jams in large streams can create nucleation sites for bars, and in some cases promote a multi-thread channel (Collins and Montgomery, 2001; O’Connor et al., 2003). Pieces of wood in smaller streams can be longer than the channel width and/or partially attached to the channel bank, and thus provide very effective points of stability for trapping sediment until the wood rots (Keller and Tally, 1979). This sediment trapping alters bedforms; creates bars, increases step height (Keller and Swanson, 1979; Thompson, 1995; Curran and Wohl, 2003; Gomi et al., 2003; MacFarlane and Wohl, 2003); reduces channel gradient (Faustini and Jones, 2003); promotes substrate heterogeneity and local fining (Kail, 2003); and creates alluvial reaches where bedrock would otherwise form the channel substrate (Montgomery et al., 1996). Wood also deflects flow and creates localized scour that increases pool volume and bank undercutting (Fausch and Northcote, 1992; Baillie and Davies, 2002), as well as promotes overbank flooding (Jeffries et al., 2003). Removal of wood from smaller channels commonly results in greater sediment fluxes as local sediment deposits are mobilized (Heede, 1985; Klein et al., 1987; Smith et al., 1993), and can trigger widespread channel instability in the form of bed and bank erosion (Brooks et al., 2003). When comparing forested rivers around the world, wood may not play as important a geomorphic role on European rivers with a long history of forest and channel management that effectively reduces the size and volume of wood recruited to stream channels (Pie´gay and Gurnell, 1997; Pie´gay et al., 1999).
2.7.
Riparian vegetation
Riparian vegetation can mediate channel response to flooding by increasing bank resistance through roots (e.g., Gray and Barker, 2004; Pollen et al., 2004; Rutherfurd and Grove, 2004; Pollen and Simon, 2005) and hydraulic roughness of overbank areas (e.g., Pie´gay and Bravard, 1997; Kean and Smith, 2004). Along some steep, coarse-grained streams, riparian vegetation may be critical in maintaining a singlethread channel with adjacent floodplains, rather than a braided planform extending across much of the valley bottom (Smith, 2004). Discontinuous vegetation may also direct flow toward the opposite bank and promote meandering (Bennett et al., 2002).
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Along multi-thread channels, vegetation reduces total channel width, braiding index, and relative mobility of channels (Tal et al., 2004). Vegetated areas between sub-channels in multi-thread channel systems can create threshold effects such that smaller discharges confined between vegetated areas are primarily erosive, whereas larger discharges that partially inundate hydraulically rough vegetated areas are primarily depositional (Merritt and Wohl, 2003). Vegetation helps to stabilize the interfluve areas and promote the formation of sub-channels that reduce flow resistance as flow depth increases (Wende and Nanson, 1998). In cases where vegetation establishment is facilitated by regulation-induced changes in flow regime, channels have changed from a braided to a meandering or anastomosing planform (Nadler and Schumm, 1981; Eschner et al., 1983; Johnson, 1994; Pie´gay and Salvador, 1997). 2.8.
Time since last flood
Another important component of flow duration above an erosional threshold is the time elapsed since the last geomorphically effective flood. Beven (1981) used hypothetical scenarios to demonstrate that geomorphic effectiveness should depend on the ordering of floods of differing magnitude, the time elapsed between subsequent floods, and the state of the channel at the time of a particular flood, such that real channels are most appropriately considered to have a time variable, rather than a fixed, threshold of erosion. Several investigators have found that when a channel is modified by a large flood, subsequent large floods cause very little geomorphic change if intervening lower flows did not modify erosional and depositional features created by the first large flood (Harvey, 1984; Cenderelli and Wohl, 2003). The time elapsed since the last large flood that destabilized a resistant-boundary channel and exposed new sources of sediment can also determine sediment supply. For example, the ratio of bedload transport volume to effective runoff increased substantially during the years following a 50-year flood in the Rio Cordon of Italy (Lenzi et al., 2004).
3. 3.1.
Geomorphic effects of floods Sediment dynamics
Both suspended and bedload transport can be orders of magnitude higher during a large flood than during average flows if the large flood exceeds the erosional threshold set by a coarse surface layer in gravel-bed channels (Inbar, 1987; Eaton and Lapointe, 2001). High rates of sediment transport can trigger channel-boundary erosion, resulting in destabilization of adjacent hillslopes (Scott and Gravlee, 1968; Burbank et al., 1996), change of local base level for upstream or tributary channel segments (Sloan et al., 2001), or loss of floodplain area. Increased sediment movement during floods can change a step-pool or pool-riffle channel to plane-bed morphology, although the pre-flood bed morphology generally gradually reappears over a period of months to years following the flood (Lisle, 1982; Sawada et al., 1983; Wohl and Cenderelli, 2000; Lenzi, 2001; Madej, 2001). The forces exerted by large masses of
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bedload can break or dislodge the in-channel wood that stabilizes high-gradient gravel-bed rivers and creates sediment storage sites along both high- and low-gradient gravel-bed channels (Keller and Swanson, 1979; Smith et al., 1993; Montgomery et al., 1995; Carling and Tinkler, 1998; Buffington and Montgomery, 1999; Buffington et al., 2002; O’Connor et al., 2003; Bunn and Montgomery, 2004). The great majority of studies measuring sediment transport in resistant-boundary channels during floods indicate that bedload transport in particular is highly variable in time and space, and not adequately modeled by transport equations developed for channels formed in finer-grained alluvium (e.g., Carson and Griffiths, 1987; Gomez and Church, 1989; Wohl, 2000b). Quantitative descriptions and predictions of sediment dynamics during floods in resistant-boundary channels remains an area where much more work is needed.
3.2.
Erosional and depositional features
Sediment supply interacts with channel and valley geometry to control erosional and depositional features created during floods along resistant-boundary channels. Floodplain erosional features include longitudinal grooves, stripping of alluvium, and secondary anastomosing channels (Miller and Parkinson, 1993). Flood-induced erosional features within cohesive-boundary channels include longitudinal grooves, potholes, inner channels, and various types of abraded facets (Baker and Pickup, 1987; Wohl, 1993; Hancock et al., 1998; Springer and Wohl, 2002). Erosion within non-cohesive channel boundaries can result in channel widening or deepening, coarsening of grain-size distribution on the streambed, or change in bedform configuration (Stewart and LaMarche, 1967; Williams and Guy, 1973; Miller and Parkinson, 1993; Wondzell and Swanson, 1999). Flood depositional features derive from fine sediments carried in suspension that create slackwater deposits (Baker, 1987; Baker and Pickup, 1987; Kite and Linton, 1993) and various types of channel-margin sandbars such as separation deposits or reattachment deposits (Schmidt, 1990; Schmidt and Rubin, 1995; Cenderelli and Cluer, 1998). Depositional features created from coarser sediment carried as bedload include expansion bars downstream from constricted reaches (Baker, 1978, 1984; O’Connor, 1993); longitudinal bars along valley margins at local flow expansions (Stewart and LaMarche, 1967; Carling, 1987; Zielinski, 2003); point bars along the inner margins of valley bends (de Jong and Ergenzinger, 1995); pendant bars downstream from obstructions (Scott and Gravlee, 1968); imbricate clusters upstream from obstructions (Cenderelli and Cluer, 1998); and, where floodwaters break through natural or artificial levees, gravel bars, sand sheets, and splay deposits on floodplains (Kite and Linton, 1993; Miller and Parkinson, 1993). As might be expected, a flood along any given channel is more likely to be erosional in steeper, narrower channel reaches and depositional in lower gradient, wider reaches (Stewart and LaMarche, 1967; Malde, 1968; Shroba et al., 1979; Cenderelli and Wohl, 2003). Because large floods generate extreme hydraulic forces capable of creating erosional and depositional features that subsequent lower discharges cannot substantially modify, some flood-induced forms can be used to estimate the magnitude of
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paleodischarges along a channel (O’Connor et al., 1986; Baker, 1987; Nott and Price, 1994; Zen and Prestegaard, 1994; Jansen and Brierley, 2004). The higher the erosional resistance of the channel boundary, the more likely that flood-induced forms will persist over time intervals equal to or greater than the recurrence interval of the flood magnitude that created the forms. 3.3.
Channel planform
Floods can also alter channel planform, most commonly creating a braided pattern along what was previously a straight or meandering channel (Warburton, 1994; Friedman et al., 1996), or alter channel location through processes such as avulsion (Lapointe et al., 1998). Channel morphology (bedforms, channel pattern), surface and subsurface grain-size distributions, stream size, and channel constraint all influence hyporheic exchange flows along high-gradient streams (Kasahara and Wondzell, 2003). Floods can alter hyporheic exchanges between instream and subsurface flow by altering channel morphology and grain-size distributions. Flood effects along fourthand fifth-order channels in the Lookout Creek catchment of Oregon, for example, varied from large changes in unconstrained stream reaches where the channel incised during the flood, to lesser changes in constrained stream reaches where bedrock boundaries limited the depth and area of sediment available to be reworked by the flood (Wondzell and Swanson, 1999).
4.
Ecological effects of floods
Ecological effects of floods include disturbance of aquatic and riparian communities. A disturbance is defined in this context as a relatively discrete event in time that disrupts ecosystem, community, or population structure, and that changes resources, availability of substratum, or the physical environment (Pickett and White, 1985). Flood-induced disturbances alter river and floodplain characteristics as diverse as instream water temperature and chemistry (e.g., Brunke and Gonser, 1997); lateral and longitudinal nutrient flows (Fisher et al., 1998); streambed grain size, heterogeneity, and stability (e.g., Erman et al., 1988); bedform type and dimensions (e.g., Fausch and Bramblett, 1991); hyporheic exchange patterns (Wroblicky et al., 1998); channel-margin germination sites for plants (e.g., Swanson et al., 1998); and floodplain habitat availability (Junk et al., 1989). Flood-related processes are essential to the existence of many aquatic and riparian organisms because the processes create and maintain habitat, and because they present recruitment opportunities for new organisms (e.g., riparian seedling germination) and species. Although the annual flood is not normally considered a disturbance (Sparks et al., 1990), this scale of flooding provides cues that species rely on for timing migration, spawning or seed dispersal, hatching or germination, and seasonal growth (Junk et al., 1989; Nilsson et al., 1991; Power et al., 1995; Merritt and Wohl, 2002). The annual flood also facilitates lateral, longitudinal, and vertical exchanges of nutrients, organic matter, and organisms, and increasingly provides a necessary diluting flow
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that disperses contaminants throughout the river ecosystem (Sparks et al., 1990; Ciszewski, 2001). Numerous adverse ecological impacts can thus result from changes in the magnitude or duration of the annual flood. Rarer and larger floods, by creating the quasi-permanent erosional and depositional features described earlier, structure the riverine environment in ways that govern the distribution of organisms (Fausch et al., 2002). For example, Everitt (1968) demonstrated that the lateral and longitudinal distribution of bands of even-aged cottonwood (Populus sargentii) along the Little Missouri River in North Dakota reflected flood history and associated seedling germination sites. Flow regulation and loss of flood peaks along analogous channels has resulted in substantial changes in species composition and community structure of riparian vegetation (Scott et al., 1996). Riparian vegetation is structured by the frequency, duration, and intensity of floods, as well as availability and stability of germination sites, supply of propagules, and water availability (Birkeland, 1996; Hupp and Osterkamp, 1996; Pie´gay and Bravard, 1997). Changes in any of these characteristics will change riparian vegetation communities (Nilsson and Jansson, 1995; Nakamura and Shin, 2001; Johansson and Nilsson, 2002). Similarly, changes in flood regime will alter instream characteristics including grain-size distribution, hyporheic exchange, nutrient retention, wood loading, pool volume, channel cross-sectional and planform geometry, bank stability, and habitat abundance and diversity, all of which are crucial to the survival of aquatic organisms such as macroinvertebrates and fish (McKenney, 2001; Pitlick and Wilcock, 2001).
5.
Implications of flood effectiveness for channel management and restoration
In a widely cited paper, Poff et al. (1997) emphasize the importance of the natural flow regime in a river as a ‘‘master variable’’ that limits the distribution and abundance of riverine species and regulates ecological integrity by influencing water quality, energy sources, physical habitat, and biotic interactions. They list five basic components of the flow regime – magnitude, frequency, duration, timing, and rate of change – that must be preserved in order to conserve ecological integrity. Geomorphologists also consider the sediment regime to be a primary determinant of channel morphology and process, particularly because alterations in sediment supply, as well as flow regime, have substantially changed many human-impacted rivers (e.g., Sear, 1994; Pitlick and Wilcock, 2001). The Colorado River in the Grand Canyon, for example, continues to have coarse sediment supplied by episodic debris flows on tributaries downstream from Glen Canyon Dam (Webb et al., 1989). The trapping of most finer, suspended sediment behind the dam, however, and the loss of large flood peaks that historically deposited this fine sediment high along the channel margins, has led to erosion of beaches and terraces that provide important riparian habitat, as well as cultural and recreational sites (Collier et al., 1996). What emerges from review of the literature is that floods are integral to physical and biological conditions along river corridors (Ligon et al., 1995; Graf, 2001; Bunn and Arthington, 2002). Changing flood magnitude and duration affects riverine species directly, through the loss of nutrients, habitat, and migration or dispersal corridors, and indirectly, through the loss of habitat-maintaining processes such as
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flushing of fine sediment from spawning gravels (Harvey et al., 1993), pools (Wohl and Cenderelli, 2000), and channel-margin bars (Auble et al., 1994; Elliott and Parker, 1997). Numerous studies indicate that some aspects of channel adjustment require floods in order to be maintained (Table 8.2). The magnitude and frequency of these formative floods varies between individual rivers and specific channel features, largely as a function of boundary resistance. Along many rivers, the annual flood can keep spawning gravels and pools flushed of fine sediment, for example, but less frequent large floods are necessary to redistribute hillslope-derived coarse sediment
Table 8.2.
Examples of channel adjustment dependent on floods.
Location
Description
References
Black Canyon of the Gunnison River, Colorado, USA
Deep, narrow gorge with dam upstream; continuing sediment inputs from valley walls and tributaries; lack of flood flows to flush fine sediment from canyon and redistribute coarse sediment along river Canyon with dam upstream; continuing sediment inputs from tributaries; lack of flood flows to bring fine sediment into suspension and deposit it high on the channel margins, and redistribute coarse sediment along river River in wide canyon; simultaneous introduction of exotic riparian plant tamarisk (Tamarix spp.), regulation of flow from dam upstream, and natural reduction in flood magnitudes caused channel narrowing Only large, rare floods are capable of mobilizing coarse sediment forming gravel bars and riffles/rapids in these canyon systems Only large, rare floods are capable of mobilizing very large clasts that anchor steppool sequences Periodic large floods reverse process of channel narrowing to a single channel, creating a braided pattern
Liquori (1995), Elliott and Parker (1997), Elliott and Hammack (2000), Dubinski, 2005
Grand Canyon of the Colorado River, Arizona, USA
Green River, Utah, USA
Boulder Creek, Utah, USA Burdekin River, Australia Tapi River, India Step-pool channel in British Columbia, Canada Gila River, Arizona, USA Glacial stream, Switzerland Plum Creek, Colorado, USA
Kieffer (1985), Collier et al. (1996), Wiele et al. (1996), Rubin et al., 1998
Graf (1978), Allred and Schmidt (1999), Merritt and Cooper, 2000
O’Connor et al. (1986), Wohl (1992a), Kale and Hire, 2004 Zimmermann and Church, 2001 Burkham (1972), Warburton (1994), Friedman et al., 1996
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Figure 8.2. Talus deposit impinging on the channel of the Gunnison River in the Black Canyon of the Gunnison, Colorado. Flow is from left to right. These coarse sediments introduced directly to the channel from adjacent valley walls can only be mobilized by flows that recurred on average once every 2–3 years (the flow has been regulated since 1966, increasing the recurrence interval of these flows to 40 years). Photograph courtesy of Ian Dubinski.
and maintain the downstream spacing of pools and riffles (O’Connor et al., 1986; Wohl, 1992a; Dubinski, 2005) (Fig. 8.2). The primary implication of the physical and ecological importance of floods on a wide range of river types is that rivers must be managed and restored for process rather than form, and process includes floods (Stanford et al., 1996). Restoring form without process by engineering a specific channel configuration that cannot be maintained over a period of decades or longer by the existing flow regime, for example, is likely to require continual, expensive artificial maintenance and is unlikely to replicate the conditions necessary for a fully functional river ecosystem (Kondolf et al., 2001; Wohl et al., 2005). Of equal importance to river management is recognition that flood prevention is a difficult matter. Perceived detrimental effects of floods have been mitigated by levees, reservoirs, and flood-detention basins, and other structural, warning, and zoning measures, but such efforts generally had only limited and partial success. Even smaller, apparently thoroughly controlled mountain streams that are extensively channelized and stepped over grade-control structures can, and will, experience unexpected large floods that remove these structures and thoroughly rework the channel boundaries (e.g., Gavrilovic and Matovic, 1991). Given the inevitability of floods, the most effective management strategies will be those that restore and maintain a nearly natural flow regime and sediment supply, and permit the river to adjust to fluctuations in water and sediment discharge within a riverine corridor that has the minimum possible structural constraints (Kondolf, 1996; Graf, 2001; Ward et al., 2001; Jaquette et al., 2005).
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Communicating the geomorphic and ecological importance of large floods to resource managers and the public remains a difficult task. Differentiating the role of large floods with respect to position in the drainage basin, as well as specific flood effects (e.g., winnowing fine sediments from spawning gravels), may facilitate communication.
6.
The geomorphic role of floods revisited
Wolman and Miller’s classic 1960 paper assumed that suspended sediment represented the greatest volume of material moved in most rivers, and that therefore the basic geomorphic role of rivers – that of gradually transporting sediment downstream – was most appropriately characterized in terms of the magnitude of flow that transported the most suspended sediment over a period of many years. As subsequent work has expanded concepts of the geomorphic role of floods to include the persistence of floodcreated landforms such as channel pattern, bedforms, and grain-size distribution, it has become more difficult to agree on a consistent, readily applicable method for quantifying the geomorphic role of any particular flow magnitude. Wolman and Miller (1960) focused on alluvial systems. Subsequent studies, as outlined in this review, gave more attention to resistant-boundary channels where, by definition, thresholds of changes are higher, more variable, and thus more challenging to define. As summarized previously, the geomorphic effectiveness of a flood depends on the duration of flow(s) that exceed the erosional resistance of the channel boundaries, but erosional resistance is a spatially and temporally variable factor that is difficult to quantify except as a mean state or a probability of exceedance. Attempts to quantify the sediment transport component of the geomorphic role of floods in resistantboundary channels have generally relied on empirical data of bed-material load transport in relation to discharge magnitude, combined with flow frequency and duration data (Andrews and Nankervis, 1995). These types of relations can be successfully applied across hydroclimatically similar regions (e.g., Surian and Andrews, 1999). Attempts to quantify the landform-modification component of the geomorphic role of floods are more likely to use hydraulic modeling in combination with estimated thresholds for processes such as clast entrainment or bedrock quarrying to specify a threshold discharge. Threshold discharge is then used in the context of flow frequency and/or duration to quantify the role of large floods in modifying specific fluvial landforms (e.g., Baker, 1977; Wohl, 1992a,b; Baker and Kale, 1998; Kale and Hire, 2004). Whether addressing primarily sediment transport or landform modification, quantification of the geomorphic role of multiple floods through time is complicated by the fact that channel configuration (e.g., planform, bedforms, grain-size distribution, gradient) can change substantially during a flood, potentially creating a constantly changing rather than stable relationship between discharge and sediment transport, or between discharge and erosional thresholds. Most assessments of the geomorphic impact of floods in resistant-boundary channels remain imprecise generalizations. These generalizations are nonetheless useful in recognizing the range of geomorphic and ecological river processes and forms that rely on the occurrence of floods. As
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more case studies are added to the literature, the scientific community is getting closer to being able to specify numerical values on the axes in Fig. 8.1, and to being able to quantitatively characterize the geomorphic role of specific flood magnitudes in a variety of channel settings. Generalized, basin-wide trends in the geomorphic importance of floods can be drawn from the literature reviewed in this paper, as illustrated in Fig. 8.3. This figure subdivides an idealized mountainous drainage basin into three general categories. The headwater channels are most likely to have small drainage areas, close connections to adjacent hillslopes, minimal development of floodplains, steep gradients, and very high boundary resistance associated with very coarse clasts, bedrock, or in-channel wood. Local exceptions to these generalizations certainly occur; mountainous channel networks are commonly longitudinally segmented, for example, creating downstream alternations between lower and higher gradient reaches (Wohl, 2000b). However, the general characteristics listed above lead to frequent disturbances from events such as debris flows and floods. These headwater channels correspond to the cascade, steppool, and plane-bed channel types of Montgomery and Buffington (1997), which are supply-limited reaches that are resilient to changes in discharge and sediment supply, and are thus designated transport reaches. In the middle section of Fig. 8.3a, the lower gradient channels have progressively larger drainage areas, greater development of floodplains, lower gradients, and high boundary resistance associated with moderate-sized clasts (cobble, pebble) and riparian vegetation. These channels correspond to Montgomery and Buffington’s (1997) planebed and pool-riffle channel types. These response reaches are transport limited and more likely to have sustained responses to changes in sediment supply and discharge. The downstream-most section of Fig. 8.3a includes low-gradient channels with extensive floodplain development, very large drainage areas, and finer sediment (pebble and smaller) that produces relatively low boundary resistance. These channels correspond to Montgomery and Buffington’s (1997) pool-riffle and regime-bed (dune-ripple) channel types, and are also transport-limited response reaches. The presence of extensive floodplains can moderate channel response to a large flood by providing a greater area for sediment deposition and flow energy dissipation than is present in the middle reaches of a drainage basin. The boundaries between these three sections in a given drainage basin could be defined based on drainage area (Clark et al., 1987), stream order (Froehlich et al., 1990), stream gradient (Shroba et al., 1979), or channel type (Montgomery and Buffington, 1997). These four characteristics are likely to have substantial overlap (e.g., channels with small drainage areas are more likely to have low stream orders, steep gradients, and cascade or step-pool morphology), thus facilitating the zonation of the geomorphic role of floods within the drainage basin. Returning to the characteristics of rivers dominated by lower frequency floods (Kochel, 1988), Fig. 8.3b schematically illustrates the downstream trends in these characteristics within a drainage basin. The first two characteristics, large seasonal and interannual flow variability, and a high ratio between the discharges of infrequent floods and average annual flow, are partly dependent on hydroclimatology. Both of these characteristics are likely, however, to reach a maximum in the intermediate portion of a drainage basin. The smaller drainage areas of channel segments in the
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steepest headwater channels: frequent disturbances from floods and debris flows; very high boundary resistance; large supply of coarse sediment; large ratio Qf/Qb;more likely to be dominated by relatively frequent large floods lower gradient channels: infrequent disturbances from floods and debris flows; high boundary resistance; moderate supply of coarse sediment; large ratio Qf/Qb; more likely to be dominated by infrequent floods lowest gradient channels: infrequent disturbances from floods; low boundary resistance; minimal supply of coarse sediment; small ratio Qf/Qb; likely to be dominated by frequent, smaller floods
(b) Flow characteristics
discharge ratio of infrequent flood to average annual flow
seasonal & interannual flow variability
Elevation
Maximum grain size
Distance downstream
Channel-boundary resistance
Distance downstream
riparian vegetation as a bank stabilizer
bank stability resulting from grain size distribution Distance downstream
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upper basin likely result in a higher percentage of contributing area during any given precipitation-generating event, resulting in less difference between large and normal floods. Conversely, the large drainage areas of channel segments in the lowest portions of the basin likely result in some portion of the upstream basin providing little or no contribution even during extreme events, and/or being attenuated by floodplain storage, again reducing the difference between large and normal floods (e.g., Clark et al., 1987). The third characteristic, coarse bedload, declines steadily downstream as stream gradient and proximity to steep valley side slopes decline. Boundary resistance is more complex in that it depends on bank grain-size distribution (including stratigraphy) and riparian vegetation. Bank grain-size distribution declines steadily downstream, but associated resistance rises as sediments become sufficiently fine to exhibit cohesion. The effectiveness of riparian vegetation in stabilizing banks is likely to be very region (i.e., climate) specific, but can be assumed to increase downstream as a first approximation. The net result of these trends is that the aggregate population of large floods is likely to geomorphically dominate the headwater portions of drainage basins, whereas individual large floods are likely to be most geomorphically important in the middle portion of drainage basins. This broad generalization will have many sitespecific exceptions, but case studies quantifying the downstream trends in Fig. 8.3 can help to determine the usefulness of this conceptual model. Resistant-boundary channels are most likely to be present in the upper and middle portions of a basin, which correspond to the regions where unit and total stream power, respectively, are hypothesized to reach a maximum value (Knighton, 1999). As a first approximation, the relative geomorphic importance of large floods in resistant-boundary channels can thus be generalized based on position within the drainage basin. There remains a Figure 8.3. (a) Schematic illustration of the distribution of characteristics that govern the geomorphic impact of floods across a drainage basin. The dark upper line represents the drainage divide, with a channel network developed downstream. In this idealized basin, the low-order channels in the uppermost basin (dark shading) have high boundary resistance associated with bedrock and very large clasts; a steep, laterally confined valley and channel geometry; and abundant coarse sediment supply. The ratio of flood flow to base flow (Qf/Qb) is large. Because of the small contributing area, floods are relatively frequent, and debris flows from the valley side slopes also disturb the channels. Proceeding downstream, gravel-bed channels (light shading) replace boulder-bed and bedrock channels. The gravel-bed channels have lower boundary resistance and a less abundant supply of coarse sediment than channels higher in the drainage basin. They also have lower gradients and less lateral confinement. The ratio of flood flow to base flow remains large. As contributing area increases, individual flood-generating storm systems are less likely to cover the entire drainage area, so large floods become less frequent. Extreme storms are still capable of covering much of the upstream area, however, and infrequent large floods can produce substantial erosional and depositional changes that subsequent, smaller flows are incapable of modifying. In the downstream-most portions of the drainage basin, low channel gradients, limited supply of coarse sediment, limited lateral confinement, and contributing areas too large to be covered by all but the most extreme and infrequent storms, all contribute to a decreasing incidence and geomorphic role of extreme floods. Superimposed on these trends are the frequency and duration of floods, the ratio of extreme floods to base flows, and the time since the last major flood, as these are influenced by hydroclimatology. (b) Schematic downstream trends in characteristics associated with channels dominated by large, infrequent floods. The shape of these curves is purely conceptual and is not meant to resemble power functions. The details of how grain-size distribution and riparian vegetation influence bank stability, for example, can be complex and site-specific.
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strong need for quantification of patterns of flood effects in resistant-boundary channels with respect to hydroclimatology, position within a drainage basin, erosional thresholds, sediment supply, and time since the last flood.
Acknowledgements This paper benefited substantially from reviews by Sara Rathburn, Jim O’Connor, and two anonymous reviewers.
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Applications of Paleoflood Hydrology. American Geophysical Union Press, Washington, DC, pp. 359–385. O’Connor, J.E., Hardison, J.H., Costa, J.E., 2001. Debris flows from failures of Neoglacial-age moraine dams in the Three Sisters and Mount Jefferson Wilderness Areas, Oregon. US Geol. Surv. Prof. Pap. 1606, 93. O’Connor, J.E., Jones, M.A., Haluska, T.L., 2003. Flood plain and channel dynamics of the Quinault and Queets Rivers, Washington, USA. Geomorphology 51, 31–59. O’Connor, J.E., Webb, R.H., Baker, V.R., 1986. Paleohydrology of pool-and-riffle pattern development: Boulder Creek, Utah. Geol. Soc. Am. Bull. 97, 410–420. Parker, G., Klingeman, P.C., 1982. On why gravel bed streams are paved. Water Resour. Res. 18, 1409–1423. Parker, G., Sutherland, A.J., 1990. Fluvial armour. J. Hydraul. Res. 28, 529–544. Parker, G., Toro-Escobar, C.M., 2002. Equal mobility of gravel in streams: The remains of the day. Water Resour. Res. 38, WR000669. Patton, P.C., 1988. Geomorphic response of streams to floods in the glaciated terrain of southern New England. In: Baker, V.R., Kochel, R.C., and Patton, P.C. (Eds), Flood Geomorphology. John Wiley and Sons, New York, pp. 261–277. Patton, P.C., Baker, V.R., 1976. Morphometry and floods in small drainage basins subject to diverse hydrogeomorphic controls. Water Resour. Res. 12, 941–952. Pickett, S.T.A., White, P.S. (Eds), 1985. The Ecology of Natural Disturbance and Patch Dynamics. Academic Press, Orlando, FL. Pie´gay, H., Bravard, J.-P., 1997. Response of a Mediterranean riparian forest to a 1 in 400 year flood, Ouveze River, Drome-Vaucluse, France. Earth Surf. Process. Landf. 22, 31–43. Pie´gay, H., Gurnell, A.M., 1997. Large woody debris and river geomorphological pattern: Examples from S.E. France and S. England. Geomorphology 19, 99–116. Pie´gay, H., Salvador, P.-G., 1997. Contemporary floodplain forest evolution along the middle Ubaye River, Southern Alps, France. Global Ecol. Biogeogr. Lett. 6, 397–406. Pie´gay, H., The´venet, A., Citterio, A., 1999. Input, storage and distribution of large woody debris along a mountain river continuum, the Droˆme River, France. Catena 35, 19–39. Pitlick, J., 1994. Relation between peak flows, precipitation, and physiography for five mountainous regions in the western USA. J. Hydrol. 158, 219–240. Pitlick, J., Wilcock, P., 2001. Relations between streamflow, sediment transport, and aquatic habitat in regulated rivers. In: Dorava, J.M., Montgomery, D.R., Palcsak, B.B., and Fitzpatrick, F.A. (Eds), Geomorphic Processes and Riverine Habitat. American Geophysical Union Press, Washington, DC, pp. 185–198. Poff, N.L., Allan, J.D., Bain, M.B., et al., 1997. The natural flow regime. BioScience 47, 769–784. Pollen, N., Simon, A., 2005. Estimating the mechanical effects of riparian vegetation on stream bank stability using a fiber bundle model. Water Resour. Res. 41, W07025. Pollen, N., Simon, A., Collison, A., 2004. Advances in assessing the mechanical and hydrologic effects of riparian vegetation on streambank stability. In: Bennett, S.J. and Simon, A. (Eds), Riparian Vegetation and Fluvial Geomorphology. American Geophysical Union Press, Washington, DC, pp. 125–139. Powell, D.M., 1998. Patterns and processes of sediment sorting in gravel-bed rivers. Progr. Phys. Geogr. 22, 1–32. Power, M.E., Parker, G., Dietrich, W.E., Sun, A., 1995. How does floodplain width affect floodplain river ecology? A preliminary exploration using simulations. Geomorphology 13, 301–317. Robert, A., Roy, A.G., De Serres, B., 1996. Turbulence at a roughness transition in a depth limited flow over a gravel bed. Geomorphology 16, 175–187. Roberts, C.R., 1989. Flood frequency and urban-induced channel change: Some British examples. In: Beven, K. and Carling, P. (Eds), Floods: Hydrological, Sedimentological and Geomorphological Implications. John Wiley and Sons, Chichester, UK, pp. 57–82. Rubin, D.M., Nelson, J.M., Topping, D.J., 1998. Relation of inversely graded deposits to suspendedsediment grain-size evolution during the 1996 flood experiment in Grand Canyon. Geology 26, 99–102. Rutherfurd, I.D., Grove, J.R., 2004. The influence of trees on stream bank erosion: Evidence from rootplate abutments. In: Bennett, S.J. and Simon, A. (Eds), Riparian Vegetation and Fluvial Geomorphology. American Geophysical Union Press, Washington, DC, pp. 141–152.
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Wohl, E., 1998. Bedrock channel morphology in relation to erosional processes. In: Tinkler, K.J. and Wohl, E.E. (Eds), Rivers Over Rock: Fluvial Processes in Bedrock Channels. American Geophysical Union Press, Washington, DC, pp. 133–151, Geophysical Monograph 107. Wohl, E.E., 2000a. Anthropogenic impacts on flood hazards. In: Wohl, E.E. (Ed.), Inland Flood Hazards: Human, Riparian, and Aquatic Communities. Cambridge University Press, Cambridge, UK. Wohl, E.E., 2000b. Mountain rivers. American Geophysical Union Press, Washington, DC, 320pp. Wohl, E.E., Angermeier, P.L., Bledsoe, B., Kondolf, G.M., MacDonnell, L., Merritt, D.M., Palmer, M.A., Poff, N.L. and Tarboton, D., 2005. River restoration. Water Resour. Res. 41, W10301. Wohl, E.E., Cenderelli, D.A., 2000. Sediment deposition and transport patterns following a reservoir sediment release. Water Resour. Res. 36, 319–333. Wohl, E., Cenderelli, D., Mejia-Navarro, M., 2001. Channel change from extreme floods in canyon rivers. In: Anthony, D.J., Harvey, M.D., Laronne, J.B., and Mosley, M.P. (Eds), Applying Geomorphology to Environmental Management. Water Resources Publications, Highlands Ranch, CO, pp. 149–174. Wohl, E.E., Pearthree, P.A., 1991. Debris flows as geomorphic agents in the Huachuca Mountains of southeastern Arizona. Geomorphology 4, 273–292. Wohl, E., Springer, G., 2005. Bedrock channel incision along the upper Rio Chagres basin, Panama. In: Harmon, R.S. (Ed.), The Rio Chagres: A multidisciplinary profile of a tropical watershed. Springer, Dodrecht, The Netherlands, pp. 189–209. Wohl, E.E., Thompson, D.M., Miller, A.J., 1999. Canyons with undulating walls. Geol. Soc. Am. Bull. 111, 949–959. Wolman, M.G., 1967. A cycle of sedimentation and erosion in urban river channels. Geogr. Ann. 49A, 385–395. Wolman, M.G., Miller, J.P., 1960. Magnitude and frequency of forces in geomorphic processes. J. Geol. 68, 54–74. Wondzell, S.M., Swanson, F.J., 1999. Floods, channel change, and the hyporheic zone. Water Resour. Res. 35, 555–567. Wroblicky, G.J., Campana, M.E., Valett, H.M., Dahm, C.N., 1998. Seasonal variation in surfacesubsurface water exchange and lateral hyporheic area of two stream-aquifer systems. Water Resour. Res. 34, 317–328. Wyzga, B., 1996. Changes in the magnitude and transformation of flood waves subsequent to the channelization of the Raba River, Polish Carpathians. Earth Surf. Process. Landf. 21, 749–763. Young, W.J., Olley, J.M., Prosser, I.P., Warner, R.F., 2001. Relative changes in sediment supply and sediment transport capacity in a bedrock-controlled river. Water Resour. Res. 37, 3307–3320. Zen, E., Prestegaard, K.L., 1994. Possible hydraulic significance of two kinds of potholes: Examples from the paleo-Potomac River. Geology 22, 47–50. Zielinski, T., 2003. Catastrophic flood effects in alpine/foothill fluvial system (a case study from the Sudetes Mts, SW Poland). Geomorphology 54, 293–306. Zimmermann, A., Church, M., 2001. Channel morphology, gradient profiles, and bed stresses during flood in a step-pool channel. Geomorphology 40, 311–327.
Discussion by G. Heritage and D. Milan E. Wohl notes the importance of large floods on influencing the geomorphology of resistant-boundary channels. The authors have also found this to be true for the bedrock influenced semiarid Sabie River, South Africa. Analysis of 1:10,000 scale aerial photographs of the morphologic response of the river to low, moderate, and extreme flows has revealed a complex response across all flows that may be rationalized when viewed at the reach and morphologic unit scale. Bedrock dominated channel types display little change in response to low to moderate flows whereas alluviated channel reaches change was variable in direction and degree. At the level
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Wohl, E., 1998. Bedrock channel morphology in relation to erosional processes. In: Tinkler, K.J. and Wohl, E.E. (Eds), Rivers Over Rock: Fluvial Processes in Bedrock Channels. American Geophysical Union Press, Washington, DC, pp. 133–151, Geophysical Monograph 107. Wohl, E.E., 2000a. Anthropogenic impacts on flood hazards. In: Wohl, E.E. (Ed.), Inland Flood Hazards: Human, Riparian, and Aquatic Communities. Cambridge University Press, Cambridge, UK. Wohl, E.E., 2000b. Mountain rivers. American Geophysical Union Press, Washington, DC, 320pp. Wohl, E.E., Angermeier, P.L., Bledsoe, B., Kondolf, G.M., MacDonnell, L., Merritt, D.M., Palmer, M.A., Poff, N.L. and Tarboton, D., 2005. River restoration. Water Resour. Res. 41, W10301. Wohl, E.E., Cenderelli, D.A., 2000. Sediment deposition and transport patterns following a reservoir sediment release. Water Resour. Res. 36, 319–333. Wohl, E., Cenderelli, D., Mejia-Navarro, M., 2001. Channel change from extreme floods in canyon rivers. In: Anthony, D.J., Harvey, M.D., Laronne, J.B., and Mosley, M.P. (Eds), Applying Geomorphology to Environmental Management. Water Resources Publications, Highlands Ranch, CO, pp. 149–174. Wohl, E.E., Pearthree, P.A., 1991. Debris flows as geomorphic agents in the Huachuca Mountains of southeastern Arizona. Geomorphology 4, 273–292. Wohl, E., Springer, G., 2005. Bedrock channel incision along the upper Rio Chagres basin, Panama. In: Harmon, R.S. (Ed.), The Rio Chagres: A multidisciplinary profile of a tropical watershed. Springer, Dodrecht, The Netherlands, pp. 189–209. Wohl, E.E., Thompson, D.M., Miller, A.J., 1999. Canyons with undulating walls. Geol. Soc. Am. Bull. 111, 949–959. Wolman, M.G., 1967. A cycle of sedimentation and erosion in urban river channels. Geogr. Ann. 49A, 385–395. Wolman, M.G., Miller, J.P., 1960. Magnitude and frequency of forces in geomorphic processes. J. Geol. 68, 54–74. Wondzell, S.M., Swanson, F.J., 1999. Floods, channel change, and the hyporheic zone. Water Resour. Res. 35, 555–567. Wroblicky, G.J., Campana, M.E., Valett, H.M., Dahm, C.N., 1998. Seasonal variation in surfacesubsurface water exchange and lateral hyporheic area of two stream-aquifer systems. Water Resour. Res. 34, 317–328. Wyzga, B., 1996. Changes in the magnitude and transformation of flood waves subsequent to the channelization of the Raba River, Polish Carpathians. Earth Surf. Process. Landf. 21, 749–763. Young, W.J., Olley, J.M., Prosser, I.P., Warner, R.F., 2001. Relative changes in sediment supply and sediment transport capacity in a bedrock-controlled river. Water Resour. Res. 37, 3307–3320. Zen, E., Prestegaard, K.L., 1994. Possible hydraulic significance of two kinds of potholes: Examples from the paleo-Potomac River. Geology 22, 47–50. Zielinski, T., 2003. Catastrophic flood effects in alpine/foothill fluvial system (a case study from the Sudetes Mts, SW Poland). Geomorphology 54, 293–306. Zimmermann, A., Church, M., 2001. Channel morphology, gradient profiles, and bed stresses during flood in a step-pool channel. Geomorphology 40, 311–327.
Discussion by G. Heritage and D. Milan E. Wohl notes the importance of large floods on influencing the geomorphology of resistant-boundary channels. The authors have also found this to be true for the bedrock influenced semiarid Sabie River, South Africa. Analysis of 1:10,000 scale aerial photographs of the morphologic response of the river to low, moderate, and extreme flows has revealed a complex response across all flows that may be rationalized when viewed at the reach and morphologic unit scale. Bedrock dominated channel types display little change in response to low to moderate flows whereas alluviated channel reaches change was variable in direction and degree. At the level
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of morphologic unit changes were most dramatic for unconsolidated bar deposits, which were eroded and re-deposited frequently. Larger macrochannel features remained static and cohesive bars displayed sporadic vertical accretion in response to moderate floods. Morphologic change is thus generally restricted to features associated with the base of the incised river, particularly those composed of unconsolidated sediment or those located close to high energy areas of the channel. The response to extreme flows was more dramatic with significant losses of cohesive deposits occurring in the base of the incised channel. Bedrock dominated channel reaches remained largely unchanged, whereas alluviated channel reaches experienced both erosion and deposition. Morphologic unit change was widespread with unconsolidated active channel bar deposits eroded. Macrochannel deposits appear largely unaffected by the extreme flood magnitudes associated with the contemporary flow regime. Such changes illustrate the variable response to floods of varying magnitude exhibited by the different morphologic units found in the Sabie River. More importantly, it also demonstrates the variable recovery rates seen between unit types. These response–recovery patterns have been summarized as a series of morphologic response models (Fig. 8.4). It is suggested that these would be useful to river managers as well as scientists who often need to place into context the apparently dramatic changes that occur to semiarid river systems subject to extreme flow regimes.
Figure 8.4. Morphological response models for the Sabie River, South Africa.
Gravel-Bed Rivers VI: From Process Understanding to River Restoration H. Habersack, H. Pie´gay, M. Rinaldi, Editors r 2008 Elsevier B.V. All rights reserved.
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9 Modelling river-bank-erosion processes and mass failure mechanisms: progress towards fully coupled simulations Massimo Rinaldi and Stephen E. Darby
Abstract This paper reviews recent developments in modelling the two main sets of bankerosion processes and mechanisms, namely fluvial erosion and mass failure, before suggesting an avenue for research to make further progress in the future. Our review of mass failure mechanisms reveals that the traditional use of limit equilibrium methods to analyse bank stability has in recent years been supplemented by research that has made progress in understanding and modelling the role of positive and negative pore water pressures, confining river pressures, and hydrograph characteristics. While understanding of both fluvial erosion and mass failure processes has improved in recent years, we identify a key limitation in that few studies have examined the nature of the interaction between these processes. We argue that such interactions are likely to be important in gravel-bed rivers and present new simulations in which fluvial erosion, pore water pressure, and limit equilibrium stability models are combined into a fully coupled analysis. The results suggest that existing conceptual models, which describe how bank materials are delivered to the fluvial sediment transfer system, may need to be revised to account for the unforeseen effects introduced by feedback between the interacting processes. 1.
Introduction
Bank erosion is a key process in fluvial dynamics, affecting a wide range of physical, ecological, and socio-economic issues in the fluvial environment. These include the establishment and evolution of river and floodplain morphology and their associated habitats (e.g., Hooke, 1980; Millar and Quick, 1993; Darby and Thorne, 1996a; Barker et al., 1997; Millar, 2000; Goodson et al., 2002), turbidity problems (e.g., Bull, 1997; Eaton et al., 2004), sediment, nutrient, and contaminant dynamics (e.g., Reneau et al., 2004), loss of riparian lands (e.g., Amiri-Tokaldany et al., 2003), and associated threats to flood defence and transportation infrastructure (e.g., Simon, E-mail address:
[email protected]fi.it (M. Rinaldi) ISSN: 0928-2025
DOI: 10.1016/S0928-2025(07)11126-3
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1995). Moreover, recent studies have shown that the contribution of bank-derived sediments to catchment sediment budgets may be higher than previously thought, although the precise fraction varies depending on the time-scale of measurement (Bull, 1997). For example, considering annual sediment yields, Walling et al. (1999) showed that bank sediments contribute up to 37% of the total (10,816 t/yr) suspended sediment yield, even in the relatively low-energy catchments of the UK, with the contribution rising to values as high as 80% of the total (75,000 t/yr) suspended sediment yield in some highly unstable, incised, channel systems (e.g., Simon and Darby, 2002). With such a significant fraction of material within the alluvial sediment system derived from river banks, it is evident that knowledge of the rates, patterns, and controls on bank-erosion events that release sediment to river systems is a pre-requisite for a complete understanding of the fluvial sediment transport regime. Naturally, much research has already been devoted to these issues. These contributions include a number of excellent reviews (Lawler, 1993; Lawler et al., 1997b; Couper, 2004), including those published by Grissinger (1982) and Thorne (1982) in the original Gravel-Bed Rivers volume (Hey et al., 1982). So what might ‘yet’ another review of bank-erosion processes actually achieve? As Fig. 9.1 shows, there is a growing number of bank-erosion investigations (38% of the publications appear after 1997) and a shift in the pattern of ‘hot’ topics in the discipline. In particular, new research has elucidated the role of riparian vegetation (e.g., Abernethy and 18 16
interaction
Number of papers
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others
12
vegetation
10
stability
8
erosion
GBR1
6 4 2 2005
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
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1971
1969
1967
1965
1963
1961
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Figure 9.1. Summary of the bibliographic review on river-bank-erosion processes conducted for this chapter (total of 194 papers considered). Erosion: papers focused on fluvial entrainment; stability: papers on mass failures and bank stability; vegetation: papers focusing on the role of vegetation; others: papers on other issues related to bank erosion (e.g., measurement of bank retreat, variables controlling rates of retreat, sediment delivery from bank processes, influence of bank processes on channel geometry, etc.); interaction: papers on modelling width adjustments and channel migration, and including to some extent the interaction between fluvial erosion and mass failures. Dates of major reviews of bank erosion in the first Gravel-Bed Rivers I proceedings volume in 1982 (GBR I) and the most recent major review in 1997 (dashed line) are also highlighted.
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Rutherfurd, 1998, 2000; Simon and Collison, 2002) and bank hydrology (e.g., Rinaldi and Casagli, 1999; Casagli et al., 1999; Rinaldi et al., 2004) as key controlling influences on bank stability. In contrast, although improvements in the modelling of near-bank flows are starting to be made (e.g., Kean and Smith, 2006a,b), there are still relatively few studies that have been concerned with the process of fluvial erosion (i.e., the removal of bank sediments by the direct action of the flow). Accordingly, little progress has been made in understanding fluvial bank erosion of cohesive sediments since the contributions of Arulanandan et al. (1980) and Grissinger (1982). Notable exceptions to this trend include some work that has sought to quantify entrainment thresholds and process rates (e.g., Lawler et al., 1997a; Simon et al., 2000; Dapporto, 2001). The role of weathering as a significant agent of erosion has also started to be recognised (e.g., Lawler, 1993; Prosser et al., 2000; Couper and Maddock, 2001), both in headwater reaches (where weathering may be the dominant mechanism by which sediment is removed from the bank face) and, elsewhere, as a mechanism for enhancing bank erodibility and promoting fluvial erosion. Fig. 9.1 also highlights another gap in the literature. While most studies recognise that bank retreat is the integrated product of three interacting processes (namely, weathering and weakening, fluvial erosion, and mass failure), they tend to adopt reductionist approaches that focus on a single set of processes, so interactions between different groups of processes are not usually considered. This is important because dynamic interactions and feedbacks between processes may lead to outcomes that are not predictable a priori. In short, viewing bank processes in isolation is unrealistic and introduces the possibility that conclusions derived from such studies are biased. Recognition of this problem is not new. Lawler (1992) introduced a conceptual model of changing bank process dominance in a hypothetical drainage basin (Fig. 9.2), emphasising that processes act not in isolation, but are always present to a varying degree. While Fig. 9.2 represents a conceptualisation of an idealised basin and the length scales therein are, therefore, deliberately omitted, it is instructive to attempt to contextualise the drainage basin locations within which recent bankerosion research has been conducted. Bearing in mind that these studies have typically sought to isolate the effects of individual process groups, it is noteworthy that they cluster in the mid- to downstream reaches, where process interactions are strongest. Interactions between mass failure and fluvial-erosion processes (as opposed to the role of individual processes acting in isolation) therefore have particular relevance in the context of gravel-bed rivers, as the zone of interaction coincides at least in part with the middle reaches of basins where gravel-beds are typical, and also because the dominance of subaerial processes is generally limited geographically to the headwaters of typical fluvial systems (Couper and Maddock, 2001). This paper therefore seeks to address two objectives. First, we review recent developments regarding the two main bank-erosion phenomena (fluvial erosion and mass failure) responsible for bank retreat in gravel-bed rivers. Second, we focus on studies which have sought to address the interactions between these two processes and mechanisms. Included in this synthesis are new findings from our own research which show that adopting a fully coupled modelling approach that views bank processes as interacting, rather than individual, entities leads to a distinctive vision of
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Effectiveness of process grousp
G C
S
A
Fluid entrainment
Preparation processes F re
eze
/th a
Mass failure
w
dessication
Distance downstream Figure 9.2. Conceptual model of process dominance in the fluvial system. (After Lawler (1992)). Also shown are the approximate locations within their respective basins (mapped as proportion of stream length) of the sites used in some recent bank-erosion studies: A ¼ River Asker, Dorset, UK; C ¼ Cecina River, Tuscany, Italy; G ¼ Goodwin Creek, Mississippi, USA; S ¼ Sieve River, Tuscany, Italy. (Reproduced with permission from Wiley and Sons, 1992.)
the ways in which bank-derived materials are delivered to the alluvial sediment transfer system.
2.
Modelling fluvial erosion
Fluvial erosion is defined as the removal of bank material by the action of hydraulic forces, although it generally occurs in combination with weathering processes that prepare bank sediments for erosion by enhancing their erodibility (Hooke, 1980; Thorne, 1982; Lawler, 1993; ASCE Task Committee on Hydraulics, Bank Mechanics, and Modeling of River Width Adjustment, 1998; Prosser et al., 2000; Couper and Maddock, 2001). Relative to mass failure, fluvial erosion is, at the scale of the flow event and once the critical entrainment threshold has been exceeded, a quasi-continuous process, with the volume of sediment delivered by fluvial erosion dependent on the duration of the competent flow. In general, fluvial-erosion rates depend on the near-bank flow intensity and physical characteristics (i.e., the erodibility) of the bank material. However, this simple conceptualisation masks enormous complexity that results from the inherent variability of the relevant controlling parameters. Thus, observed rates of fluvial-erosion range over several orders of magnitude (Hooke, 1980) and fluvial-erosion rates are predictable only to the extent that the controlling parameter values, and their inherent variability, can be estimated accurately.
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It is widely accepted that the rate of fluvial bank erosion can be quantified using an excess shear stress formula such as (Partheniades, 1965; Arulanandan et al., 1980): ¼ kd ðt tc Þa
(9.1)
where e (m/s) is the fluvial bank-erosion rate per unit time and unit bank area, t (Pa) is the boundary shear stress applied by the flow, kd (m2s/kg) and tc (Pa) are erodibility parameters (erodibility coefficient, kd, and critical shear stress, tc), and a (dimensionless) is an empirically derived exponent. It is important to note that although excess shear stress models of this type are widely accepted and used in a range of geomorphological applications (e.g., Arulanandan et al., 1980; Govers, 1991; Howard, 1994), no formal validation of this model has yet been undertaken. Thus some uncertainty remains over the value of the exponent a (which is commonly assumed to take a value close to 1 for most studies involving cohesive sediments, e.g., Partheniades, 1965). Perhaps more significantly, the physical basis of the excess shear stress model for bank erosion can be questioned. One problem is its reliance on a threshold value, which is difficult to incorporate into numerical models due to the sharp threshold between stability and failure, which in turn results in instabilities near the threshold value. Nevertheless, such threshold behaviour is appropriate, particularly on cohesive river banks. Any propagation of numerical error may, therefore, de facto require the erodibility coefficient (kd) to be treated as a calibration parameter, a problem highlighted recently by Crosato (2007). For the purposes of this review we assume that the basic form of equation (9.1) is robust and that predictive ability is limited by the need to estimate the necessary parameter values accurately. In subsequent sub-sections we therefore focus on recent developments concerned with improving estimates of the erosion rate, erodibility, and shear stress parameters.
2.1.
Erosion rate
A comprehensive review of the methods used to observe bank erosion was provided by Lawler (1993). Recently, techniques such as digital photogrammetry and laser scanning (e.g., Lane et al., 1994; Barker et al., 1997; Nagihara et al., 2004) can provide the opportunity to define river bank topography at unprecedented spatial resolution (surveys with point densities of ca. 107 points across a bank face are readily obtainable using terrestrial laser scanning) and accuracy (72 mm). Bank erosion can then be quantified using the survey data to construct Digital Terrain Models (DTMs) for time intervals and differencing to establish net change. However, logistical and safety concerns usually limit the frequency of monitoring to relatively coarse timescales, at best perhaps resolving individual flow events. This is problematic because the pre- versus post-flow event ‘window’ is not the same thing as the bank erosion event window, such that it is not usually possible to resolve process thresholds, timing, and rates (Lawler, 2005). To address this limitation, new quasi-continuous bank-erosion sensors based on the use of photoelectronic cells (PEEPs; e.g., Lawler, 1993; Lawler et al., 1997a) and thermal consonance timing (TCT; e.g., Lawler, 2005) have been
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developed, though they have not yet been widely deployed. While these approaches are promising, the use of sensors can disturb the bank face, while excellent temporal resolution is inevitably obtained at relatively low spatial resolution. While accurate and representative discrimination of bank-erosion rates therefore remains elusive, studies that combine high spatial/low temporal (e.g., photogrammetry) and high temporal/low spatial (e.g., PEEPs, TCT) resolution approaches may deliver exciting new results in the near future.
2.2.
Erodibility of bank sediment
For granular (non-cohesive) sediments, bank erodibility parameters are modelled based on the same methods that are used to predict the entrainment of bed sediments, albeit with modifications to take into account the effect of the bank angle on the downslope component of the particle weight (Lane, 1955) and the case of partly packed and cemented sediments (e.g., Millar and Quick, 1993; Millar, 2000). Determination of critical shear stress for cohesive materials is more complex, given that it is widely recognised that fluvial entrainment for cohesive sediments depends on several factors, including (amongst others) clay and organic content, and the composition of interstitial fluids (Arulanandan et al., 1980; Grissinger, 1982; Knapen et al., 2007). Consequently methods for predicting the erodibility of cohesive banks remain poor. To address this issue, recent studies have deployed in situ jet-testing devices (e.g., Hanson, 1990; Hanson and Simon, 2001) to obtain direct measurements of bank erodibility (e.g., Dapporto, 2001). This is achieved by directing a jet of water with known hydraulic properties at the bank material. The resulting deformation is measured periodically with a mechanical point gauge, until an equilibrium scour depth is attained. The measured deformation rate, scour depth, and known hydraulic properties are used to determine the erodibility parameters. While jet-testers offer in situ sampling, our experience is that their design (especially their large weight) makes their deployment to inaccessible sites difficult, and it is also hard to emplace them without disturbing the bank surface. Moreover, individual tests are time consuming (ca. 0.5 h), making it difficult to obtain the numbers of samples needed to adequately characterise the spatial and temporal variability of the bank materials. On resistant surfaces, errors involved in mechanically inserting the point gauge into the base of the scour hole can be similar in magnitude to the scour depth itself, while erodible materials generate scour depths that can exceed the extent of the gauge. Instruments such as the Cohesive Strength Meter (Tolhurst et al., 1999) appear to offer advantages over conventional jet-testing devices. The CSM is similar to these in that water jets of increasing strength are directed at the target surface. However, instead of measuring the resulting scour depth, the CSM detects erosion by monitoring optical transmission in an enclosed sampling head chamber. Thus, the moment of erosion corresponds to sudden reductions in optical transmission induced by the suspension of eroded sediment within the test chamber, with the jet properties at that threshold defining the critical stress. Tests are both automated and rapid (o3 min) so the device can easily be used to obtain large numbers of samples. So far
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it has only been deployed in estuarine environments (Tolhurst et al., 1999), but the CSM appears to offer a potentially fruitful avenue of bank-erosion research.
2.3.
Near-bank shear stresses
With the aforementioned recent developments in bank-erosion monitoring technology and in the quantification of bank erodibility, the ‘missing link’ in equation (9.1) remains the difficulty of characterising the fluid stresses that are exerted on river banks during the large flows that typically drive erosion. Bank boundary shear stress is highly variable both in space and time, dependent as it is on such factors as the bank geometry (which is itself highly variable), cross-section size and shape, channel curvature, and flow stage. This variability presents a challenge for anyone seeking to characterise the shear stress distribution via direct measurement. Sampling strategies would need to capture this natural variability, suggesting that the necessary flow velocimetry equipment would need to be deployed at high spatial and temporal resolution, during the (hazardous) high flow conditions associated with bank erosion. It is, therefore, unsurprising that such investigations are lacking, apart from some flume studies (e.g., Blanckaert and Graf, 2001) which are able to achieve the necessary sampling resolution, albeit under rather idealised conditions. If field data collection is impractical, the only viable alternative is to predict the shear stress values using hydraulic models. Some models have been developed using empirical data sets obtained from laboratory channels (Leutheusser, 1963; Kartha and Leutheusser, 1972; Simons and Sentu¨rk, 1977; Knight et al., 1984), but these can only be applied with caution to natural rivers, as the bank and channel forms present in flumes with regular geometry represent the problem rather poorly. Recently, progress has been made in using analytical models to quantify form roughness induced by the irregular bank morphology and partition the shear stress acting on the banks (e.g., Kean and Smith, 2004, 2006a,b; Griffin et al., 2005). Although these approaches are promising, it is not yet clear whether such approaches are entirely appropriate. Specifically, a lack of field data sets means that we simply do not yet know whether near-bank flows are dominated by the form drag induced by the topographic irregularities (e.g., embayments, slump deposits, etc.) associated with natural, eroding, banks (e.g., Thorne and Furbish, 1995), or by the effects of turbulence induced by strong lateral shear and the occurrence of wakes. If the latter is the case, then modelling near-bank flows would require the application of 3-dimensional Computational Fluid Dynamics (3D-CFD) modelling techniques. The practice of using 3D-CFD modelling techniques as a substitute for field data in river flows that are difficult or impossible to measure has now become established for a range of open-channel flow contexts (e.g., Nicholas and Walling, 1997, 1998; Hodskinson and Ferguson, 1998; Nicholas and Sambrook-Smith, 1999; Bradbrook et al., 2000; Lane et al., 2000; Darby et al., 2004). However, the application of 3DCFD to near-bank flows remains novel and replication of near-bank flows would depend on: (i) ensuring the discretised computational scheme accurately solves the underlying conservation equations; (ii) selecting an appropriate turbulence-closure model (TCM), and (iii) accurately defining the initial and boundary conditions
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(Darby et al., 2004). Accepted standards of computational mesh design (e.g., American Society of Mechanical Engineers (ASME), 1993; American Institute of Aeronautics and Astronautics (AIAA), 1998) are already available, with adherence to those standards ensuring that discretisation and numerical solution errors are minimised (Hardy et al., 2003). Consequently, we focus attention on the latter two issues, though we note that very high-resolution grids are likely to be needed to represent the complex flow structures in near-bank environments. This, in turn, may create additional problems, not only of large computational requirements, but in terms of defining the boundary conditions correctly. Regarding the parameterisation of turbulence, some studies have begun to investigate the potential for approaches such as Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) to deliver accurate hydraulic data (e.g., Rodi et al., 1997). However, even with the capabilities of modern computing, these approaches have only been applied to flows with fixed (non-deformable) channel boundaries. For morphological modelling, Reynolds averaging appears set to continue as the only feasible approach, at least for the foreseeable future. However, all such TCMs contain empirical elements, so model selection must be matched to the anticipated physical conditions, namely: (i) strong lateral shear; (ii) occurrence of separated flow around topographic irregularities (e.g., embayments, slump deposits, etc.) associated with eroding banks. These requirements suggests that an anisotropic TCM is required (e.g., So et al., 1993; Sotiropoulos, 2001; Blanckaert and Graf, 2001; Gerolymos et al., 2002), and a Reynolds Stress Model (RSM) appears most appropriate for the specific context of modelling near-bank flows.
3.
Modelling river bank failures
Mass failure is the collapse and movement of bank material under gravity. Relative to fluvial erosion, mass failure is discontinuous and large-scale and occurs by any of a number of mechanisms (Thorne, 1982), with a specific model required for each. The methods developed and used in the literature have concentrated only on a relatively few of these, in particular slides (planar or rotational) and cantilever failures. Referring to the classical mechanism of a planar slide (Lohnes and Handy, 1968), bank failure occurs when the destabilising forces, due to gravity, exceed the resisting forces, which are related to the shear strength of the bank materials expressed by the failure criterion of Fredlund et al. (1978) as: t ¼ c0 þ ðs ua Þ tan f0 þ ðua uw Þ tan fb
(9.2)
where t is the shear strength (kPa), c0 the effective cohesion (kPa), s the normal stress (kPa), ua the pore air pressure (kPa), f0 the friction angle in terms of effective stress (1), uw the pore water pressure (kPa), (ua–uw) the matric suction (kPa), fb the angle expressing the rate of increase in strength relative to the matric suction (1). In saturated conditions, the apparent cohesion (the third term on the right-hand side of
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equation (9.2) disappears so equation (9.2) reduces to the classical Mohr–Coulomb criterion. 3.1.
Methods of analysis
The application of stability analyses is common in the bank-erosion literature. The analysis of slide failures is typically performed using a Limit Equilibrium Method (LEM) to compute the factor of safety (F), defined as the ratio between stabilising and destabilising forces. Since the 1960s, specific methods of bank stability analysis have been progressively disseminated, with an increasing effort to define closed-form solutions for planar failures representative of characteristic bank geometries (Table 9.1). It is evident that research has progressively sought to account for: (1) a more realistic bank geometry and the influence of tension cracks (Osman and Thorne, 1988); (2) positive pore water pressures and hydrostatic confining pressures (Simon et al., 1991; Darby and Thorne, 1996b); (3) the effects of negative pore water pressures in the unsaturated part of the bank (Rinaldi and Casagli, 1999; Casagli et al., 1999; Simon et al., 2000); and (4) the influence of riparian vegetation (Abernethy and Rutherfurd, 1998, 2000, 2001; Simon and Collison, 2002; Rutherfurd and Grove, 2004; Pollen et al., 2004; Van de Wiel and Darby, 2004; Pollen and Simon, 2005; Pollen, 2006). Recently, more complex analyses have been utilised for river bank studies (Abernethy and Rutherfurd, 2000; Dapporto et al., 2001, 2003; Simon et al., 2002; Rinaldi et al., 2004) by using various LEM solutions extended to rotational slides (i.e., Bishop, Fellenius, Jambu, Morgestern, GLE) that include features that overcome many of the previous limitations. These analyses provide the following advantages: (1) rotational or composite slide surfaces and generic bank geometries can be defined; (2) either the Mohr–Coulomb or Fredlund et al. (1978) failure criterion can be selected depending on whether the soil conditions are saturated or unsaturated, respectively; (3) a generic pore water pressure distribution can be defined, and confining pressures due to the river can be accounted for; (4) it is possible to perform several analyses for a large number of different sliding surface types and positions, providing more confidence in the identification of the most critical failure surface. On the other hand, it is important to recognise that LEM analyses also have some important limitations (Duncan and Wright, 2005). The main one is probably the fact that the mass delimited by the sliding surface is assumed to not be subject to deformation. In other words, only the stresses along the failure surface are accounted for, not the stress distribution within the soil mass. In order to characterise this deformation processes, more complex and sophisticated models used for slope analyses, namely stress-deformation analysis, are required (Griffiths and Lane, 1999; Collison, 2001). Such models have not yet been employed specifically for riverbanks, due to some main reasons: (1) stress-deformation analyses are particularly data-demanding and complex to use; (2) riverbank failures typically occur rapidly, whereas stress-deformation analyses are typically applied to slow landslides, deep-seated deformation, and/or progressive failures on large slopes (e.g., Wiberg et al., 2005; Hu¨rlimann et al., 2006).
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Table 9.1.
Summary of methods of stability analysis applied to river banks. Mechanism of failure and bank geometry
New capabilities (compared to previous methods)
Main limitations
Typical applications
Main references
‘Culmann’
Planar failure, uniform bank slope
Simple to use
Massive silt or clay, incised rivers of southeastern – midwestern U.S.
Thorne et al. (1981); Thorne (1982)
Thorne & Tovey
Cantilever failure
Composite banks
Osman & Thorne (O&T)
Planar failure with tension crack; bank profile taking into account basal erosion and relic tension crack Planar failure, uniform bank slope
First method specific for cantilever failure More realistic geometry including effects of basal erosion
Simplified geometry; failure surface passing from the bank toe; pore water pressures not included Data required not easily available Failure surface passing from the bank toe; pore water pressures not included
Homogeneous, steep, cohesive banks
Thorne and Tovey (1981); Thorne (1982); Van Eerdt (1985) Osman and Thorne (1988); Thorne and Abt (1993)
Simplified bank geometry (no tension crack)
Homogeneous, steep, cohesive banks
Simon et al.
Failure surface not passing from the bank toe; positive pore pressures and confining pressures incorporated
Simon et al. (1991)
M. Rinaldi, S.E. Darby
Analysis
Planar failure with vertical tension crack, O&T geometry
Rinaldi & Casagli
Planar failure with vertical tension crack, uniform bank slope
Casagli et al.
Planar failure with vertical tension crack, O&T geometry
More realistic geometry
Simon et al.
Planar failure with vertical tension crack, O&T geometry Planar (wedge-type) failure
Layered bank materials
USDA Bank stability model Various commercial software packages
Slides (planar, rotational, composite); generic bank geometry
More realistic geometry with positive pore pressures and confining pressures incorporated Negative pore water pressures taken into account
Incorporates soil reinforcement and surcharge due to vegetation Generic bank geometry and failure surfaces; possible to account for main vegetative mechanical effects
Unsaturated conditions are not considered
Homogeneous, steep, cohesive banks
Darby and Thorne (1996b)
Simplified bank geometry; simplified assumptions on water table during drawdown Homogeneous material; Relation river stage – water table needs to be specified Relation river stage – water table needs to be specified Simplified bank geometry
River banks formed in partially saturated soils; rivers with relatively rapid drawdown
Rinaldi and Casagli (1999)
Homogeneous, steep, cohesive river banks formed in partially saturated soils
Casagli et al. (1999), Rinaldi and Casagli (1999)
Layered cohesive river banks formed in partially saturated soils Vegetated river banks
Simon et al. (2000)
Generally more datademanding; requires expertise
When pore water pressure changes at the intra-event scale need to be accounted; rotational or other non-planar failure surfaces and generic bank geometry
Simon and Collison (2002) Dapporto et al. (2001, 2003); Rinaldi et al. (2004)
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Effects of pore water pressures
Changes in pore water content and pressures are recognised as one of the most important factors controlling the onset and timing of bank instability (Thorne, 1982; Springer et al., 1985) and the incorporation of these factors in bank process models is one of the major areas of recent progress. Pore water has at least four main effects: (1) reducing shear strength; (2) increasing the unit weight of the bank material; (3) providing an additional destabilising force due to the presence of water in tension cracks (i.e., the force of the water on the sides of the cracks before it infiltrates into the soil material); (4) providing additional (stabilising or destabilising) seepage forces. A crucial point when accounting for pore water pressures is their extremely transient character, driven as they are by dynamic hydrological variables (rainfall, river hydrograph). The actual mechanisms and timing of failure induced by pore water pressure effects are difficult to predict if their temporal changes, both at seasonal and intra-event time scales, are not accounted for (Rinaldi and Casagli, 1999; Casagli et al., 1999; Simon et al., 2000). For this reason, bank stability response at the intraevent time scale requires knowledge of the dynamics of saturated and unsaturated seepage flows. Various studies (Dapporto et al., 2001, 2003; Rinaldi et al., 2001, 2004) have made use of the software Seep/w (Geo-Slope International Ltd) to perform two-dimensional, finite element seepage analyses (Fig. 9.3A) based on the mass conservation equation in a form extended to unsaturated conditions (Fredlund and Rahardjo, 1993): @ @H @ @H @y kx þ ky þQ¼ (9.3) @x @x @y @y @t where H is the total head (m), kx the hydraulic conductivity in the x-direction (m/s), ky the hydraulic conductivity in the y-direction (m/s), Q the unit flux passing in or out of an elementary cube (in this case an elementary square, given that the equation is in two-dimensions) (m2/m2s), y the volumetric water content (m3/m3), t the time (s). Positive and negative pore water pressure distributions obtained by the seepage analysis are then used as input data for the stability analysis; the latter performed using the software Slope/w (Geo-Slope International Ltd.) for application of the LEM. Findings derived from the Rinaldi et al. (2004) analysis have important implications for understanding mass failure processes in relation to the driving hydrologic variables and their dominance in the fluvial system. For example, they partly support Figure 9.3. Seepage and stability analysis of a riverbank of the Sieve River. (Modified from Rinaldi et al. (2004)). (A) Geometry of the problem, showing finite element mesh, bank material layers (a, massive silty fine sand; b1, sand; b2, sand with cobbles included; c, silty sand; d, packed sand, gravel, and cobbles; e, loosely packed gravel and cobbles), and their properties (c0 ¼ effective cohesion; f0 ¼ friction angle in terms of effective stress; fb ¼ friction angle in terms of matric suction; g ¼ bulk unit weight; n ¼ porosity; ksat ¼ saturated conductivity; n/a ¼ data not available). (B) Results of the 14/12/1996 flow event: rainfall, river stages, groundwater levels (referred to at a constant distance of 0.5 m from the bank profile), and trend of the safety factor. (C) Minimum safety factor for the simulated flow events as a function of peak river stage: (1) single-peak hydrographs; (2) multiple-peak hydrographs. (Reproduced with permission from Wiley and Sons, 2004.)
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previous authors (Thorne, 1982; Springer et al., 1985; Lawler et al., 1997b) who argued that bank failures occur primarily during the drawdown phase, but they are also better able to discriminate the details of this effect. In particular, it is evident that bank failure in this case often occurs in the very early stage of drawdown (Fig. 9.3B), due to relatively small changes in the motivating and resisting forces. Indeed, it is not necessary for the bank to be saturated to explain bank failure, as would be the case if stability was limited by ‘worst case’ conditions. A second implication is related to the finding that prolonged and complex hydrographs, with subsidiary peaks preceding the main one, are more destabilising than flow events with a single, distinct, rising phase (Rinaldi et al., 2004; see Fig. 9.3C). Given that the shape of the hydrograph tends to vary systematically with location in the drainage basin, it follows that different destabilising responses can be expected in different locations. In particular, the upper reaches of drainage basins are generally characterised by simple hydrographs with relatively low and distinct peaks, while the flood hydrograph generally tends to become more complex and have a longer duration in downstream reaches. Consequently, pore water pressure distributions may favour the triggering of mass failures in downstream reaches, consistent with the bank process dominance model introduced earlier (Fig. 9.2). It also follows that bank failure frequency and intensity can be promoted by climatic regimes and/or network configurations that favour multi-peaked rather than single hydrographs. A final development highlighted by Rinaldi et al. (2004) is the use of animated graphics as a means of visualising pore water dynamics, enabling the transient effects of these changes to be elucidated more clearly (e.g., ‘Simulation 1’ at http://www.dicea.unifi. it/massimo.rinaldi/private/simulations.htm). Despite these recent advances, further progress is still needed to better simulate pore water pressure changes and their impacts on mass failure. One critical point is the difficulty of including in a seepage analysis those banks where the profile is undergoing deformation as a result of fluvial erosion. This is because of the need to continuously adapt the finite element mesh used to model the problem. A first attempt to address this issue has been introduced by Dapporto and Rinaldi (2003), and this is discussed in detail later.
3.3.
Effects of vegetation
The effects of vegetation on river bank processes are many and complex, and most are difficult to quantify. A comprehensive review is beyond the immediate scope of this paper, but given that this field is one of the areas in which major recent advances in modelling bank stability have occurred, we provide a brief overview of progress made in quantifying the effects of vegetation on river bank failures. The impacts of vegetation on mass failure can be divided into mechanical and hydrological effects, some of which are positive in terms of their impact on bank stability and some of which are negative. The net change in stability induced by vegetation is, therefore, highly contingent on site-specific factors, both in terms of the characteristics of the bank (hydrology, shape, sedimentology) and the characteristics
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of the vegetation. Considering the mechanical effects of vegetation first, the net effect of vegetative surcharge can be either beneficial (increase in normal stress and therefore in the frictional component of soil shear strength) or detrimental (increasing the downslope component of gravitational force), depending on such factors as the position of the tree on the bank, the slope of the shear surface, and the friction angle of the soil (Gray, 1978; Selby, 1982). However, the most important mechanical effect that vegetation has on slope stability is the increase in soil strength induced by the presence of the root system, and considerable progress has recently been made in quantifying this effect (Gray, 1978; Wu et al., 1979; Greenway, 1987; Gray and Barker, 2004; Pollen et al., 2004; Pollen and Simon, 2005; Pollen, 2006). Surcharge and root reinforcement have been recently included in bank stability models (Abernethy and Rutherfurd, 1998, 2000, 2001; Simon and Collison, 2002; Van de Wiel and Darby, 2004; Rutherfurd and Grove, 2004; Pollen and Simon, 2005; Pollen, 2006). In terms of the influence of riparian vegetation on local-scale river bank hydrology, three main factors can be distinguished: (a) interception; (b) infiltration; (c) evapotranspiration. Although these various hydrologic effects are well understood at a conceptual level (e.g., Greenway, 1987; Thorne, 1990), they are in practice extremely difficult to quantify and include in river bank stability models. One exception is the study of Simon and Collison (2002), who quantified the balance between potential stabilising and destabilising effects based on monitoring data from a river bank along Goodwin Creek, Mississippi (USA). A key finding of their research is that the hydrologic effects are comparable in magnitude to the mechanical effects of vegetation, and can be either beneficial or detrimental, depending on antecedent rainfall. However, the rate and amount by which plants alter the watercontent distribution within a river bank depend on a great many factors related to vegetation type, soil characteristics, seasonal variations, and climatic conditions of the region. This again makes the effects of vegetation highly contingent and sitedependent, so that generalisation of results from this single study can only be attempted with extreme caution. In addition to the complexity induced by the several and interacting effects of vegetation, a further factor limiting the reliability of prediction can also be mentioned here. Specifically, the stability of a riverbank is not only dependent on the sitespecific characteristics of that bank, but it is also conditioned by channel processes operating at the reach scale. Van De Wiel and Darby (2004) have investigated this effect in a series of numerical experiments, demonstrating that reach-scale variations in bed topography induced by the presence of bank vegetation influences local river bank retreat in a spatially variable manner. The magnitude of this effect was found to be sufficiently variable that, in some circumstances, local-scale changes in bank retreat resulting from the presence of vegetation on the bank were less than the changes forced by reach-scale variations in bed topography induced by vegetation assemblages located on the banks in reaches upstream and downstream. These findings demonstrate that at-a-site analysis by itself is not always sufficient to determine the net beneficial or adverse impact on bank stability of a specific assemblage of riparian vegetation.
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Concluding discussion: Modelling hydraulic and geotechnical interactions
The preceding sections have identified how bank retreat involves an interaction between specific erosion processes and mechanisms. Moreover, in the middle reaches of drainage basins where gravels often dominate, retreat is likely to be driven by a combination of the hydraulic forces of the flow, and mass failures driven by gravity (Fig. 9.2). This is not to exclude the importance of weathering processes, but in this conceptualisation their role is confined to providing a controlling influence on temporal variations in sediment erodibility (e.g., Prosser et al., 2000, Couper and Maddock, 2001; Lawler, 2005), such that their effect can be accounted for implicitly within fluvial-erosion models. What is clear is that for large extents of gravel-bed reaches in drainage basins, hydraulic and geotechnical factors are both significant enough that neither can be ignored (Fig. 9.2). This is not just a question of ensuring that models are comprehensive in the sense that all relevant processes are included. Rather, it is also necessary to capture the interactions between these process groups. This builds on the idea that models that incorporate complex feedbacks, non-linearities, and dynamic interactions between system components are needed to predict behaviour that would otherwise be unforeseen (e.g., Slingerland et al., 1996; Paola, 2000; Bras et al., 2003). In this section we suggest that river bank systems may also behave in this way, by modelling the interactions between hydraulic and geotechnical processes and obtaining predictions with qualitatively different outcomes (in terms of the nature of the onset and timing of bank sediment delivery to the alluvial sedimentary system) than existing models that treat these processes in isolation. While adequate quantitative treatments that include interactions between fluvial erosion and mass failure processes are lacking, basic conceptual models are available. Specifically, Thorne (1982) has elucidated the concept of basal endpoint control as a framework for understanding the controls on riverbank retreat. The concept is based on the notion that the local bank retreat rate is determined by the status of the sediment budget at the toe of the bank, with Thorne (1982) defining three basal endpoint states as follows.
4.1.
Unimpeded removal
Banks which are in dynamic equilibrium have an approximate balance between the rate at which sediment is supplied to the basal area by fluvial entrainment and mass failure and the removal of this debris by the flow.
4.2.
Excess basal capacity
Here the rate of removal of sediment from the basal region exceeds the rate at which sediment is supplied to the toe, resulting toe erosion may destabilise the bank, increase the rate of retreat, and thus restore a dynamic equilibrium.
Modelling river-bank-erosion processes and mass failure mechanisms 4.3.
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Impeded removal
Impeded removal is where bank-erosion processes supply material to the base of the bank at a higher rate than it is removed by the flow, such that deposition occurs in the basal zone. Consequently, stability with respect to mass failure increases and the rate of retreat will decrease. The basal endpoint concept is helpful in visualising the coupling that exists between sedimentary processes operating on the banks and those operating in the channel as a whole. Also noteworthy is the point that the residence time of sediment stored at the bank toe is seen as the critical factor controlling long-term bank retreat rates. We return to the significance of this below.
4.4. A methodological framework for coupling fluvial erosion, seepage, and bankstability models One of the few attempts to investigate bank-erosion dynamics combining fluvial erosion, pore water pressure changes, and mass bank stability into a single, integrated, modelling approach is the work of Simon et al. (2003), who used three models (Seep/w in combination with the USDA Bank Stability and Toe Erosion (BSM) models) to simulate bank response to flow events. However, although this is undoubtedly a useful exploratory study, it is limited for the following reasons. First, and most significantly, the domain of the seepage model is not updated to account for changes in bank geometry caused by fluvial erosion. Instead, the pore waterpressure distributions are calculated for a fixed geometry prior to being imported into the BSM. Consequently, the three modelling components (fluvial erosion, seepage, and mass stability) are not fully coupled, but are instead performed independently. A second limitation of the Simon et al. (2003) study is that they employed a series of artificial, rectangular-shaped, hydrographs of specified height and duration in their simulations and it is not clear how these relate to natural flow events observed in the field. An alternative example of a numerical simulation of river bank retreat in which fluvial erosion, seepage, and mass failure models are fully integrated is a study of bank dynamics on the Sieve River in Italy (Dapporto and Rinaldi, 2003; Darby et al., 2007). The aim of this simulation was, firstly, to test the potential of this form of integrated modelling, and secondly to quantify the contribution and mutual role that the various different processes play in controlling bank retreat. What is significant is that this research is firmly grounded in reality (recall that the Sieve River study site had been the focus of earlier bank stability research by Casagli et al., 1999 and Rinaldi et al., 2004). A representative bank profile was used to perform the simulations, using the procedure summarised in Fig. 9.4. For this study we selected a single peak flow event (Q ¼ 792.8 m3/s), that occurred during 18th to 20th November, 1999. For the purposes of the seepage, erosion, and stability analyses, the flow event was discretised into a series of explicit time steps, so that the hydrograph was represented as a succession of steady-state conditions (stepped hydrograph). The time steps were not constant in duration, but were defined according to the variations
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in flow and rainfall, with shorter time steps during phases of rapidly varying flow. A total number of 25 time steps was considered appropriate to represent the flow hydrograph and rainfall inputs in sufficient detail (Fig. 9.5A). As shown in Fig. 9.4, the procedure for modelling riverbank retreat was: (i) to compute the magnitude of fluvial erosion and consequent changes in bank geometry, (ii) to determine the pore water pressure distribution via finite element seepage analysis, and (iii) to estimate the factor of safety using a slope stability analysis based on the LEM. This sequence is repeated for each subsequent time step, with the bank geometry updated in accordance with any retreat predicted by either of the fluvial erosion or mass failure analyses. Note that while each of the three modelling approaches has already been discussed individually, each requires a particular implementation within the context of the integrated simulation, and these aspects are now discussed.
Initial conditions New time step
near-bank shear stress distribution
τb > τc
Changes in bank geometry
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Figure 30.9. Length frequency of grayling in (a) channelised, (b) rehabilitated and (c) rehabilitated, but still hydrologically impacted sections (due to hydro-peaking) of the Drau River.
Individuals
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Table 30.2. Ecological evaluation of the channelised river stretch and the rehabilitated sites regarding habitat and fish.
Habitat Fish
River Drau channelised
Dellach rehabilitated
Kleblach I rehabilitated
Greifenburg rehabilitated
Kleblach II rehabilitated
Spittal rehabilitated
3.2 3.9
3.0 3.7
3.1 3.4
3.0 3.3
2.1 2.7
2.9 3.0
development of type-specific habitats such as slow-flowing shallow zones, riffle area, gravel and sand bars, and pioneer sites; (2) increased densities and improved population structure of key fish species (e.g., grayling) as a crucial prerequisite of an improved population structure. The re-initiation of fluvial dynamics and the development of pioneer sites along the gravel bars were proved by other biological investigations not mentioned in Section 2.3.1. For example, characteristic key plant species (e.g., M. germanica) newly colonised the sediment bars and islands and, in general, the riparian areas with pioneer vegetation communities increased considerably (Kucher et al., 2003). Also, the monitoring on the ripicolous arachnid and beetle faunas showed clear improvements (O¨koteam, 2003; Unfer et al., 2004b).
3.
Conclusions and perspectives
Land drainage, flood control by levees, river regulation by hydro-power plants, various alterations of the hydrological regimes due to water diversion, hydro-peaking etc., and especially measures truncating bedload transport followed by river-bed degradation isolate rivers from their floodplain and have been the major factors behind physical habitat degradation (Petts, 1996; Jungwirth et al., 2002). These impacts heavily alter the type-specific natural disturbance regimes that normally maintain the dynamic complexes of ecotones and that are the primary physical factors structuring river ecosystems (Ward and Wiens, 2001). The resulting decrease in hydromorphological dynamics, habitat turnover and hydrological connectivity reduces habitat diversity remarkably. This changes such systems from their original ‘‘shiftingmosaic steady-state type’’ (sensu Bormann and Likens, 1979a, b) to an ecologically truncated ‘‘static-state system’’ (Hohensinner et al., 2005a). At the same time those human impacts also limit future restoration programmes. The assessment of formerly braiding rivers in Austria (Section 1) shows that nearly no such river systems remain intact. The braiding river sections of the Drau River are a part of these altered and impacted river landscapes. These results underline both the urgent need for protecting the last remnants of intact systems and the great demand for comprehensive restoration action (Tockner and Stanford, 2002; Palmer et al., 2005). A major issue and challenge in all such efforts will be to re-establish the balanced erosion/sedimentation processes and hydrological connectivity conditions typical for the given natural systems prior to degradation. This has been exemplified by the alluvial Danube floodplain system described by Hohensinner et al. (2002) and Hohensinner et al. (2005b).
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In the case of the Drau River, the restoration concept – boosted by the implementation of the WFD in 2000 – went beyond many ‘‘standard’’ approaches that primarily focus on ‘‘form and structure’’ to also include ‘‘processes’’ that need to be re-established (compare Muhar and Jungwirth, 1998; Kondolf, 2000; Jungwirth et al., 2002). The ‘‘planning philosophy’’ and conceptual design was based on ‘‘physical processes’’, re-enabling fluvial dynamics and connectivity. This will ultimately promote the essential ‘‘biological processes’’, structures and habitats necessary for the key species and ecological guilds of gravel-bed rivers. In our opinion, this general restoration approach is crucial for ensuring that the habitats and the biocoenoses of the rehabilitated sites develop and correspond at least qualitatively to the type-specific characteristics of the given riverine system. Nevertheless, the long-term sustainability and success of the restoration efforts along the Drau River will heavily depend on the future possibilities to resolve two major problems in the catchment beyond structural alterations and habitat degradation: bedload transport and hydro-peaking. Although the connection to bedload sources still mostly exists, a continuous future reduction of bedload input to the restoration reaches would again promote the process of river-bed degradation, despite widening the river bed. The result: costly, rehabilitated river stretches would once again become decoupled from the floodplains. In general, the restoration concept and measures presented in this paper can certainly be applied to gravel-bed rivers of comparable hydraulic, sedimentological and morphological characteristics. The second still ongoing pressure decreasing the overall success of the restoration efforts is hydropeaking, affecting the habitat quality of the Upper Drau River. Its consequences as an overwhelming impact become obvious in the presented results. In contrast to ‘‘Klebach II’’, which is largely undisturbed hydrologically, the hydrological regime at ‘‘Spittal’’ is heavily influenced by hydro-peaking surges. Despite the comparable general availability of different habitat types at both sites, the population structure of the key fish species, the grayling, remains qualitatively and quantitatively distorted at ‘‘Spittal’’ (Fig. 30.7; Fig. 30.9c). The fish ecological monitoring thus clearly documents that the restoration efforts were unable to reduce the detrimental effects of hydro-peaking on the river system. Beyond these two major impacts, further habitat deficits must be taken into account: (1) until now, the extensive functional de-coupling of the river channel network and its surrounding floodplains allowed only comparatively small adjacent areas to be restored in terms of connectivity conditions corresponding to the former (potential) floodplains (see also Habersack and Pie´gay, this volume), (2) regarding the whole river system, only comparatively few areas of dynamically originated, typespecific habitats could re-establish and (3) many original migration pathways – as important links between different habitats in both longitudinal and lateral direction – are still blocked. The latter, migratory aspect reflects the disrupted longitudinal continuum by a downstream chain of hydropower plants and the still poor lateral connectivity. This has caused the stocks of the formerly important nase (Table 30.1) to become extinct. This species clearly depended on open migration routes between distinct habitats within the middle reaches and the Upper Drau River. These migration routes urgently need to be re-opened. One way to evaluate restoration success is to correlate the fish ecological evaluation of restored and channelised sections with the corresponding aquatic areas. For the Upper Drau River this correlation yields a perspective for future restoration
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1
fish ecological status
R2 = 0.81 2 Spittal 3.0
Kleblach II 2.7
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3
3.3 Greifenburg 4
3.9 channelised
3.7 Dellach
5 0
10
20 30 40 50 60 70 80 % aquatic habitat area (related to reference conditions)
90
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Figure 30.10. Fish ecological status correlated with the percentage of aquatic habitat area at different rehabilitation sites (100% ¼ reference situation).
programmes (Fig. 30.10). The linear regression shows that, despite the positive trend, even the highest surface area of aquatic habitat at site Kleblach II (94% of the reference condition value) fails to yield a fish ecological status better than 2.7 (compare Section 2.4.3). This reflects the multitude of further deficits of the riverine system at the given status, but note that the restoration efforts will continue in the frame of new LIFE Nature project and that additional measures will be carried out for flood protection purposes. The current population structure of the grayling in channelised and in rehabilitated sections shows that the stock in the Drau River has not benefited satisfactorily (Fig. 30.9a, b). Although older year classes (4170 mm) do not differ between sections, the first year class significantly increased within rehabilitated parts, providing a positive perspective. This contribution shows that the first stage of measures (few and small sized) failed to sufficiently improve the ecological status (Fig. 30.10). In a second stage, however, where additional and larger measures were realised, at least juvenile graylings did benefit (Figs. 30.7 and 30.9b). We assume that further expanding the ‘‘patchwork of isolated small-scale measures’’ to a network of measures will yield improvements for the entire grayling population. In order to regain the ecological integrity of impaired riverine landscapes (‘‘good ecological status’’ according to WFD), future restoration programmes at the Drau River must address problems associated with (1) the bedload regime, (2) the interrupted longitudinal continuum caused by downstream hydropower plants, (3) the intensively used floodplain area along with the loss of wetlands as well as the reduced lateral connectivity between river and floodplains and (4) the human-induced disturbances through hydro-peaking. This calls for higher-level programmes that focus on the catchment or sub-catchment scale. Here, WFD opens up a new perspective because the guideline specifies comprehensive efforts to re-establish ‘‘good ecological
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status’’, which also includes remote impacts within the whole catchment (jungwirth et al., 2005). This case study underlines the importance of such a broad spatial approach. It also emphasises the necessity of implementing additional measures along the Drau river landscape. Site-to reach-scale river rehabilitation does have the potential to be successful, for example in increasing the availability of appropriate habitats. This was documented in the case of the Drau River, regarding, e.g., improved habitat conditions within the aquatic area for gravel-spawning fish species, or the development of pioneer vegetation due to the re-establishment of naturally disturbed and re-shaped sediment bars (as shown by Kucher et al., 2003). Comparable examples are highlighted by Hughes et al. (2001). The authors demonstrate that riparian pioneer vegetation and floodplain woodlands can regenerate at these scales, but will only be self-sustaining over the long term if the restoration concept includes the re-activation of geomorphological processes. This once again underlines the need for a more challenging approach to river management across the catchment. Finally, comprehensively monitoring the Drau River was instrumental in analysing and documenting the various impacts; it was also crucial in determining which impacts were successfully addressed by the different restoration measures and to what degree. Such often neglected monitoring efforts are essential to avoid repeating mistakes and to develop an understanding of how rivers respond to restoration actions (Kondolf, 1998; Sear et al., 1998). The Drau River project is an example for this ‘‘learning process’’ by scientists as well as river managers. Here, over a period of more than 15 years, a step-by-step restoration concept has been developed; a chronology of the performance documents the gradual enhancement of the restoration measures. In conclusion, we can draw an optimistic perspective for the Drau River – in the event that the currently discussed design for future restoration measures comprises, stresses and solves the remaining problems. We identify these as the disturbed sediment budget, the hydrological deficits (in particular hydro-peaking), a more extensive lateral connectivity and large-scale solutions for restoring migration pathways within the Middle and Upper Drau River system.
Acknowledgements The findings presented in this paper are based on projects funded by the European Community (LIFE Nature ‘‘Restoration of wetland and riparian area at the Upper Drau River’’ 1999–2003) and the Austrian Ministry of Agriculture, Forestry, Environment and Water Management together with the Regional Governments and the local authorities. The authors thank those colleagues and students who supported these investigations by their field work as well as Michael Stachowitsch for professional scientific English proofreading. We would also like to thank the organising committee of the 6th International Gravel-Bed Rivers Workshop in St. Jakob/Austria for having provided the opportunity to attend and contribute to this workshop.
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Pie´gay, H., The´venet, A., Kondolf, G.M., Landon, N., 2000. Physical and human factors influencing potential fish habitat distribution along a mountain river, France. Geografis. Annal. Ser. A Phys. Geogr. 82 (1), 121–136. Roni, P., Hanson, K., Beechie, T., et al., 2005. Habitat rehabilitation for inland fisheries. Global review of effectiveness and guidance for rehabilitation of freshwater ecosystems. FAO Fisheries Technical Paper. No. 484. Rome, FAO. 116pp. Schmidt, F., 1880. Die Drauregulierung in Ka¨rnten, Seperatdruck aus. ‘‘O¨sterr.-Ungar. Revue,’’ Wien. Schmutz, S., Kaufmann, M., Vogel, B., et al., 2000. A multi-level concept for fish- based, rivertype-specific assessment of ecological integrity. In: Jungwirth, M., Muhar, S., and Schmutz, S. (Eds), Assessing the Ecological Integrity of Running Waters, Hydrobiologia 422/423, 279–289. Schmutz, S., Zauner, G., Eberstaller, J., Jungwirth, M., 2001. Die Streifenbefischungsmethode: Eine Methode zur Quantifizierung von Fischbesta¨nden mittelgroXer FlieXgewa¨sser. Oesterr. WasserAbfallwirtsch. 54, 14–27. Sear, D.A., Briggs, A., Brookes, A., 1998. A prelimininary analysis of the morphological adjustment within and downstream of a lowland river subject to river restoration. Aquat. Conserv. Mar. Freshw. Ecosyst. 8, 167–183. Sempeski, P., Gaudin, P., 1995a. Habitat selection by grayling – I. Spawning habitats. J. Fish Biol. 47, 256–265. Sempeski, P., Gaudin, P., 1995b. Habitat selection by grayling – II. Preliminary results on larval and juvenile daytime habitats. J. Fish Biol. 47, 345–349. Stanford, J.A., Ward, J.V., 2001. Revisiting the serial discontinuity concept. Regulated Rivers-Research & Management 17 (4-5), 303–310. Stanford, J.A., Ward, J.V., Liss, W.J., et al., 1996. A general protocol for restoration of regulated rivers. Regul. Rivers Res. Manage. 12, 391–413. Tockner, K., Stanford, J.A., 2002. Riverine flood plains: present state and future trends. Environ. Conserv. 293, 308–330. Unfer, G., Schmutz, S., Wiesner, C., et al., 2004b. The effects of hydro-peaking on the success of river-restoration measures within the LIFE-project ‘‘Auenverbund Obere Drau’’. In: Diego Garcia de Jalon and Pilar Vizcaino Martinez (Eds), Fifth International Symposium on Ecohydraulics, 12.09.200417.09.2004, Madrid; Proceedings of the Fifth International Conference on Ecohydraulics—Aquatic Habitats: Analysis and Restoration, 1, 741–746. Unfer, G., Wiesner, C., and Jungwirth, M., 2004a. Auenverbund Obere Drau—Fischo¨kologisches Monitoring – Endbericht. Studie im Auftrag des Amts der Ka¨rntner Landesregierung—Abt. 18 – Wasserwirtschaft: 94pp. Ward, J.V., Wiens, J.A., 2001. Ecotones of riverine systems: role and typology, spatio- temporal dynamics, and river regulation. Ecohydrol. Hydrobiol. 1, 25–36.
Discussion by M. Roberts Although braided rivers are a central component in the Leitbild approach to river restoration planning for gravel-bed rivers, it can be more apposite in some environments to consider using the properties of ‘wandering gravel-bed rivers’. This channel planform distinguished by multiple channels, armouring of the channel bottom and forested islands, which are often stable over decadal time periods, can be the most geomorphically appropriate planform to use in mountainous environments (Fig. 30.11). The analysis of historical maps from Alpine regions often reveals the presence of forested islands (e.g., Rhoˆne River near Aoste, France) suggesting that the wandering gravel-bed planform would be the most suitable to use for restoration work.
Restoring riverine landscapes at the Drau River
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Pie´gay, H., The´venet, A., Kondolf, G.M., Landon, N., 2000. Physical and human factors influencing potential fish habitat distribution along a mountain river, France. Geografis. Annal. Ser. A Phys. Geogr. 82 (1), 121–136. Roni, P., Hanson, K., Beechie, T., et al., 2005. Habitat rehabilitation for inland fisheries. Global review of effectiveness and guidance for rehabilitation of freshwater ecosystems. FAO Fisheries Technical Paper. No. 484. Rome, FAO. 116pp. Schmidt, F., 1880. Die Drauregulierung in Ka¨rnten, Seperatdruck aus. ‘‘O¨sterr.-Ungar. Revue,’’ Wien. Schmutz, S., Kaufmann, M., Vogel, B., et al., 2000. A multi-level concept for fish- based, rivertype-specific assessment of ecological integrity. In: Jungwirth, M., Muhar, S., and Schmutz, S. (Eds), Assessing the Ecological Integrity of Running Waters, Hydrobiologia 422/423, 279–289. Schmutz, S., Zauner, G., Eberstaller, J., Jungwirth, M., 2001. Die Streifenbefischungsmethode: Eine Methode zur Quantifizierung von Fischbesta¨nden mittelgroXer FlieXgewa¨sser. Oesterr. WasserAbfallwirtsch. 54, 14–27. Sear, D.A., Briggs, A., Brookes, A., 1998. A prelimininary analysis of the morphological adjustment within and downstream of a lowland river subject to river restoration. Aquat. Conserv. Mar. Freshw. Ecosyst. 8, 167–183. Sempeski, P., Gaudin, P., 1995a. Habitat selection by grayling – I. Spawning habitats. J. Fish Biol. 47, 256–265. Sempeski, P., Gaudin, P., 1995b. Habitat selection by grayling – II. Preliminary results on larval and juvenile daytime habitats. J. Fish Biol. 47, 345–349. Stanford, J.A., Ward, J.V., 2001. Revisiting the serial discontinuity concept. Regulated Rivers-Research & Management 17 (4-5), 303–310. Stanford, J.A., Ward, J.V., Liss, W.J., et al., 1996. A general protocol for restoration of regulated rivers. Regul. Rivers Res. Manage. 12, 391–413. Tockner, K., Stanford, J.A., 2002. Riverine flood plains: present state and future trends. Environ. Conserv. 293, 308–330. Unfer, G., Schmutz, S., Wiesner, C., et al., 2004b. The effects of hydro-peaking on the success of river-restoration measures within the LIFE-project ‘‘Auenverbund Obere Drau’’. In: Diego Garcia de Jalon and Pilar Vizcaino Martinez (Eds), Fifth International Symposium on Ecohydraulics, 12.09.200417.09.2004, Madrid; Proceedings of the Fifth International Conference on Ecohydraulics—Aquatic Habitats: Analysis and Restoration, 1, 741–746. Unfer, G., Wiesner, C., and Jungwirth, M., 2004a. Auenverbund Obere Drau—Fischo¨kologisches Monitoring – Endbericht. Studie im Auftrag des Amts der Ka¨rntner Landesregierung—Abt. 18 – Wasserwirtschaft: 94pp. Ward, J.V., Wiens, J.A., 2001. Ecotones of riverine systems: role and typology, spatio- temporal dynamics, and river regulation. Ecohydrol. Hydrobiol. 1, 25–36.
Discussion by M. Roberts Although braided rivers are a central component in the Leitbild approach to river restoration planning for gravel-bed rivers, it can be more apposite in some environments to consider using the properties of ‘wandering gravel-bed rivers’. This channel planform distinguished by multiple channels, armouring of the channel bottom and forested islands, which are often stable over decadal time periods, can be the most geomorphically appropriate planform to use in mountainous environments (Fig. 30.11). The analysis of historical maps from Alpine regions often reveals the presence of forested islands (e.g., Rhoˆne River near Aoste, France) suggesting that the wandering gravel-bed planform would be the most suitable to use for restoration work.
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Figure 30.11. Geomorphic-depositional elements of a wandering gravel-bed river (Roberts et al., 1997).
Reply by the authors
In general, the Leitbild approach is not only focusing on braided rivers but takes into consideration the rivertype specific morphology (Muhar et al., 2000). The Drau river is situated in a relatively narrow valley. Based on the analysis of historic maps it could be shown, that the river is a pendulous river type with partially braiding sections, where high bedload input occurred via torrential tributaries, causing highly dynamic changes in river morphology. Even ‘‘typical braided rivers’’ in New Zealand – like the Waimakariri river on the Southern Island – are characterised by braids and islands, that are partially covered with pioneer vegetation, being stable over years (Habersack and Smart, 1999). According to the classification schemes of Nanson and Knighton (1996) and Nanson and Croke (1992), in the pre-channalisation state, the alluvial Danube sections in Austria could be designated as gravel-dominated, laterally active anabranching river type that developed medium-energy, non-cohesive floodplains, i.e., wandering gravelbed river floodplains. Nevertheless the typical morphological character of the Danube river showed also sections with multiple channels and islands with pioneer vegetation, but within a short period of time (often less than decades) a complete turnover of bars etc. takes place (Hohensinner et al., 2004).
References Habersack, H. and Smart, G.M., 1999. Width of braided gravel bed rivers: implications for management in Austria and New Zealand, Proceedings of the IAHR-Symposium on River, Coastal and Estuarine Morphodynamics in Genova, pp. 575–584. Hohensinner, S., Habersack, H., Jungwirth, M., Zauner, G., 2004. Reconstruction of the characteristics of a natural alluvial river-floodplain system and hydromorphological changes following human modifications: the Danube River (1812–1991). J. River Res. Appl. 20, 25–41 ISSN: 1535-1467. Muhar, S., Schwarz, M., Schmutz, S., and Jungwirth, M., 2000. Identification of rivers with high and good habitat quality: methodological approach and applications in Austria. In: Jungwirth, M., Muhar, S., and Schmutz, S. (Eds), Assessing the Ecological Integrity of Running Waters, Hydrobiologia 422/423, 343–358. Nanson, G.C., Croke, J.C., 1992. A genetic classification of floodplains. Geomorphology 4, 459–486. Nanson, G.C., Knighton, A.D., 1996. Anabranching rivers: their cause, character and classification. Earth Surf. Process. Landf. 21, 217–239.
