Ocean Hydrodynamics: Ecohydrodynamics 12th: International Colloquium Proceedings

ECOHYDRODYNAMICS FURTHER TITLES IN THIS SERIES 1 J.L. MERO THE M INE R A L RESOURCES OF THE SEA 2 L.M.FOMlN THEDYNAMI...

Author: Jacques C.J. Nihoul

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ECOHYDRODYNAMICS

FURTHER TITLES IN THIS SERIES 1 J.L. MERO THE M INE R A L RESOURCES OF THE SEA 2 L.M.FOMlN THEDYNAMIC METHOD IN OCEANOGRAPHY 3 E.J.F.WOOD MICROBIOLOGY OF OCEANS A ND ESTUARIES 4 G.NEUMANN OCEAN CURRENTS 5 N.G. JERLOV OPTICAL OCEANOGRAPHY 6 V.VACQUIER GEOMAGNETISM I N MARINE GEOLOGY 7 W.J. WALLACE THE DEVELOPMENTS OF THE CHLORINITY/SALINITY CONCEPT I N OCEANOGRAPHY 8 E. L lS lTZ l N SEA-LEVEL CHANGES 9 R.H.PARKER THE STUDY OF BENTHIC COMMUNITIES 10 J.C.J. NI H OUL (Editor) MODELLING OF MARINE SYSTEMS 11 0.1. M A MA Y E V TEMPERATURE-SALINITY ANALYSIS OF WORLD OCEAN WATERS 12 E.J. FERGUSON WOOD and R.E. JOHANNES TROPICAL MARINE POLLUTION 13 E. STEEMANN NIELSEN MARINE PHOTOSYNTHESIS 14 N.G. JERLOV MARINE OPTICS 15 G.P. GLASBY MARINE MANGANESE DEPOSITS 16 V.M. KAMENKOVICH FUNDAMENTALS OF OCEAN DYNAMICS 17 R.A.GEYER SUBMERSIBLES AND THEIR USE I N OCEANOGRAPHY AND OCEAN ENGINEERING 18 J.W. CARUTHERS FUNDAMENTALS OF MARINE ACOUSTICS 19 J.C.J. NI H OUL (Editor) BOTTOM TURBULENCE 20 P.H. LEBLOND and L.A. MYSAK WAVES I N THE OCEAN 21 C.C. VON DER BORCH (Editor) SYNTHESIS OF DEEP-SEA DRI L LI NG RESULTS I N THE IN D IAN OCEAN 22 P. DEHLINGER MARINE GRA V I TY 23 J.C.J. NIHOUL (Editor) HYDRODYNAMICS OF ESTUARIES AND FJORDS 24 F.T. BANNER, M.B. COLLlNSand K.S. MASSIE (Editors) THE NORTH-WEST EUROPEAN SHELF SEAS: THE SEA BED AN D THE SEA IN MOTION 25 J.C.J.NIHOUL (Editor) MAR I N E FORECAST ING 26 H.G. RAMMING and Z. KOWALIK NUMERICAL MODELLING MARINE HYDRODYNAMICS 27 R.A. GEYER (Editor) MARINE ENVIRONMENTAL POLLUTION 28 J.C.J. NIHOUL (Editor) MARINE TURBULENCE 29 M. WALDICHUK. G.B. KULLENBERG and M.J. ORREN (Editors) MARINE POLLUTANT T ~ A N S F E RPROCESSES 30 A . VOlPlO (Editor) THE BALTIC SEA 3 1 E.K.-DUURSMA and R. DAWSON (Editors) MARINE ORGANIC CHEMISTRY

Elsevier Oceanography Series, 32

ECOHYDRODYNAMlCS PROCEEDINGS OF THE 12th INTERNATIONAL L l i G E COLLOQUIUM ON OCEAN HYDRODYNAMICS

Edited by JACQUES C.J. NIHOUL Professor of Ocean Hydrodynamics, University of LiGge L i$ge, Belgium

ELSEVIER SCIENTIFIC PUBLISHING COMPANY Amsterdam - Oxford - New York

1981

ELSEVIER SCIENTIFIC PUBLISHING COMPANY 1, Molenwerf, 1014 AG Amsterdam P.O. Box 211, 1000 AE Amsterdam, The Netherlands Distributions for the United States and Canada: ELSEVIER/NORTH-HOLLAND INC. 52, Vanderbilt Avenue New York, N.Y. 10017

Lihrary 01

(

o n g w \ \ Catalocing i n P u t i l l c a l l o i l U a l a

I p t e r n a t i o n n l Lihge Colloquiun on Ocean Hydrodynamics, L?tir: 1980. Ecoiiydrodynamics

.

(Elsevier oceano(;rapiiy s e r i e s : 3 2 ) BiSlioy,rapiiy: p . I n c l u d e s index. Conienis : Marine iiydrodynxrics a t e c o l o g i c a l s c a l e s / J . C . J . liiiioul -- F a t e 01 n u t r i e n t enriciinent on continental s h e l v e s as i n d i c a t e d by t h e C/N cnnterit o f bottom sediments / J . J . Walsi-1, F:.T. Prcmuzic, m d T . E . Whitledge -- Cross thermocline ; l o w on c o n t i n e n t a l shelves and tk.e l o c a t i o n s o f s!ielf fronts / A. Stigebrandt, - - [ e t , c . l 1. Marine ccolo~y--ConEresses. 2 . Oceanograpiiy-Cmgresscs. 3. Hydrod~amics--Con&resses. I. N i : i s u l , Jacques C.J.

111. S e r i e s .

11. T i t l e .

(a1541.5.s316 1980 ISBU 0-41d-41969-1

574.5'2636

01-4435 AACH.2

ISBN 044441969-1 (Val. 32) ISBN 0 4 4 4 4 1 6 2 3 4 (Series)

0 Elsevier Scientific Publishing Company, 1981 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior,written permission of the publisher, Elsevier Scientific Publishing Company, P.O. Box 330, 1000 AH Amsterdam, The Netherlands Printed in The Netherlands

V

FOREWORD

The International Liege Colloquia on Ocean Hydrodynamics are organized annually. Their topics differ from one year to another and try to address, as much as possible, recent problems and incentive new subjects in physical oceanography. Assembling a group of active and eminent scientists from different countries and often different disciplines, they provide a forum for discussion and foster a mutually beneficial exchange of information opening on to a survey of major recent discoveries, essential mechanisms, impelling question-marks and valuable suggestions for future research. The subject of the Twelfth Colloquium was initially described as "Marine Hydrodynamics, as a constraint on the dynamics of ecosystems". The emphasis was laid on hydrodynamical processes which had a determinant influence on the life of marine ecosystems by controlling, over appropriate scales of time and space, essential water characteristics such as temperature, salinity, the quantity and the quality of available nutrients, the penetration of light

...

These processes are not necessarily, -and actually rarely are- the most spectacular, from a physical point of view.

In many cases, the kind of information chemists

and biologists require is a small effect, a long term trend hidden somewhere in the results of hydrodynamical studies concerned in more intense, even if more transitory, phenomena. The determination of hydrodynamic constraints on ecosystems calls then for a new skill, learning to look for what one regarded before as minor residues and to parameterize mechanisms formerly regarded as essential. A new form of Hydrodynamics results, defined by distinctive time scales and length

scales, characteristic of the interactions between hydrodynamic and ecological processes. It is to emphasize the importance of such interactions that the word "Ecohydrodynamics" has been introduced and adopted as a title for the proceedings of the Twelfth Colloquium. One should however not be misled by the laconism of the title.

The present book

is not a manual or a textbook in Ecohydrodynamics. Its objective is to provide, with the help of well documented and often circumstantial case studies, illustrative examples of ecohydrodynamic problems, emphasizing the general features such problems have in common and their outstandinq importance for the understanding of hydrodynamic processes at ecological scales. Jacques C.J. NIHOUL.

This Page Intentionally Left Blank

VII

The Scientific Organizing Committee of the Twelfth International LiSge Colloquium on Ocean Hydrodynamics and all the participants wish to express their gratitude to the Belgian Minister of Education, the National Science Foundation of Belgium, the University of Liege, the Intergovernmental Oceanoqraphic Commission and the Office of Naval Research for their most valuable support.


IX

LIST OF PARTICIPANTS

ADAM, Y., Dr., Ministere de l'Environnement, Belgium. AITSAM, A., Prof., Academy of Sciences of the Estonian S S R , Tallinn, U.S.S.R. BAYENS, W., Dr., Vrije Universiteit Brussel, Belgium. BAH, A., Prof., Ecole Polytechnique de Conakry, Guinea,and Universite de Liege, Belgium. CLEMENT,

F.,

Mr., Universite de Liege, Belgium.

CREPON, M., Dr., Laboratoire d'oceanographie Physique du Museum, Paris, France. DISTECHE, ,A., Prof., Dr., Universit6 de LiGge, Belgium. DJENIDI, S., Ir., Universite de LiPge, Belgium. du PEUTY, J . , Mrs., CNEXO, Paris, France. ESTRADA, M., Dr., ~nstitutode Investigaciones Pesqueras, Barcelona, Spain. FLOS, J., Mr., Universidad de Barcelona, Spain. FRASSETTO, R., Dr., Laboratorio per lo Studio della Dinamica delle Grandi Masse, Venezia, Italy. GALLARDO, Y., Dr., Centre de Recherches Oceanographiques de Dakar-Thiaroye, Dakar, SBnBgal. GJERP, S.A., IT., Norwegian Hydrodynamic Laboratories, Trondheim, Norway. HAPPEL, J . J . ,

Ir., Universite de Liege, Belqium.

HENROTAY, P., Ir., Universite de Liege, Belgium. KLEIN, P., Dr., Institut de Mecanique Statistique de la Turbulence, Marseille, France.

I

LAGOS, P., Dr., Instituto Geofisico del Peru, Lima, Peru. LARSSON, A.M., Mr.,

University of Giiteborg, Sweden.

LEBON, G., Prof., Dr., Universite de Liege, Belgium. LEGENDRE, L., Prof., Dr., Universite Lava]., Quebec, Canada. LEWALLE, A., Ir., Universitf? de Liege, Belgium. LOFFET, A., Ir., UnivPrsite de Liege, Belgium.

A

MAITREJEAN, E., Mr., Universite de LiPge, Belgium MICHAUX, T., Ir., Universite de Liege, Belgium. NIHOUL, J.C.J.,

Prof., Dr., Universit6 de Liege and Universite de Louvain, Belgium.

O'BRIEN, J.J., Prof., Dr., Florida State University, Tallahassee, U.S.A. OZER, J., Ir., MinistPre de l'Environnement, Belgium. PARKER, R.A., Prof., Dr., Washington State University, Pullman, U.S.A. PICHOT, G., Dr., Ministere de l'Environnement, Belgium. RAMMING, H.G., Dr., Universitat Hamburg, F.R.G. ROMANA, L.A., Dr., CNEXO, COB, Brest, France. RONDAY, F.C.., Dr., Universite de Liege, Belgium. RUNFOLA, Y., Mr., Universite de Liege, Belgium. SALOMON, J.C., Dr., Universite de Bretagne Occidentale, Laboratoire d'oceanographie Physique, Brest, France. SMITH, N.P., Dr., Harbor Branch Foundation, Fort Pierce, F.A., U.S.A. STIGEBRANDT, A., VISSER, M.P., VOIGI,

Dr., University of Goteborg, Sweden.

Ir., K.N.M.I.,

De Bilt, The Netherlands.

K.F., Dr., UNESCO, IOC, Paris, France.

WALSH, J.J.,

Prof., Dr., Brookhaven National Laboratory, Upton, U.S.A.

WILLIAMS, P.J.L., YENTSCH, C.S., U.S.A.

Dr., University of Southampton, Dept. of Oceanography, U.K.

Dr., Bigelow Laboratory for Ocean Sciences, West Boothbay Harbor,

XI

CONTENTS

................................................................ ACKNOWLEDGMENTS ......................................................... LIST OF PARTICIPANTS .................................................... J.C.J. NIHOUL : Marine hydrodynamics at ecological scales ............... FOREWORD

J.J. WALSH, E.T. PREMUZIC and T.E. WHITLEDGE

:

V VI I IX 1

Fate of nutrient enrich-

ment on continental shelves as indicated by the C/N content of bottom sediments A. STIGEBRANDT

:

.....................................................

Cross thermocline flow on continental shelves and the

locations of shelf fronts C.S. YENTSCH

:

............................................

Vertical mixing, a constraint to primary production

an extension of the concept of an optimal mixing zone N.P. SMITH

:

13

51

:

................

67

An investigation of seasonal upwelling along the Atlantic

coast of Florida

.....................................................

79

A . BAH : Upwelling in the Gulf of Guinea. Results of a mathematical

model

................................................................

Y. GALLARDO sula

:

On two marine ecosystems of Senegal separated by a penin-

.................................................................

141

R.A. PARKER

:

Differential dispersion and nutrient-plankton distributions

A.M. AITSAM

:

Hydrodynamics as a limiting factor in the development of the

Baltic Sea ecosystem L. LEGENDRE

:

.................................................

Hydrodynamic control of marine phytoplankton production

the paradox of stability P.J.L.

155

165 :

.............................................

191

WILLIAMS and L.R. MUIR : Diffusion as a constraint on the biologi-

cal importance of microzones in the sea J.C.J.

99

NIHOUL and Y. RUNFOLA

P. KLEIN and M. COANTIC

:

:

..............................

The residual circulation in the North Sea

:

219

Modelling the physical mechanisms in the marine

.................. Seine estuary .........

upper layers with a second-order turbulence closure J.C. SALOMON

209

Modelling turbidity maximum in the

W. BAYENS, Y. ADAM, J.P. MOMMAERTS and

G.

PICHOT

:

273

285

Numerical simulations

of salinity, turbidity and sediment accumulation in the Scheldt estuary

319

XI1 Y. ADAM, W. BAYENS, J.P. MOMMAERTS, G. PICHOT

:

Mathematical modelling of

recent sedimentology in the shallow waters along the Belgian Coast SUBJECT INDEX

...........................................................

.._

333

351

MARINE HYDRODYNAMICS AT ECOLOGICAL SCALES

Jacques C.J. NLHOUL’ Geophysical Fluid Dynamics. University of Ligge, Belgium. ‘Also at the “Institut d ’Astronomie et de GPophysique”, University of Louvain, Belgium.

INTRODUCTION Marine chemists and marine biologists rely on physical oceanographers to provide information about currents, temperature and salinity distributions

_..

Marine hydrodynamics is often regarded as a constraint on ecosystems because marine ecosystems depend very much on the water characteristics, the quantity and the quality of available nutrients, the concentration of oxygen, the penetration of solar radiation

...

However, despite the enormous progress made in the recent years in understanding the physics of the sea, surprisingly little has been exploited by marine ecologists and most of the existing ecosystem models are still box models with a very crude representation of physical effects. This may be due, to a large extent, to the difficulty for chemists and biologists to determine the parameters of chemical and ecological kinetics as functions of space and time, in the sea, where the situation is often very different from laboratory conditions. It is, however, becoming more and more evident, that hydrodynamicists have also a responsability. They provide indeed very detailed information on the mechanisms which, to them, appear as essential but they often fail to understand the needs of the chemists and the biologists whose main interest lies frequently in phenomena which may be less spectacular but which have time scales and length scales more appropriate to the dynamics of ecosystems. In many cases, the kind of information chemists and biologists require is a small effect, a long term trend hidden somewhere in the results of hydrodynamical studies concerned in more intense, even if more transitory, phenomena. The determination of hydrodynamic constraints on ecosystems may call for a new skill, learning to look for what one regarded before as minor residues and parameterizing mechanisms formely regarded as essential.

2 T h i s may r e s u l t i n a new form of m a r i n e hydrodynamics c h a r a c t e r i z e d by d i f f e r e n t t i m e and l e n g t h s c a l e s , which one might t r y t o i d e n t i f y by t h e v o c a b l e "Ecohydrodynamics". A few examples a r e d i s c u s s e d i n t h e f o l l o w i n g .

SPAWNING AND MIGRATION OF PLAICE I N THE NORTH SEA P l a i c e p o p u l a t i o n s i n t h e N o r t h Sea a r e c h a r a c t e r i z e d by f a i r l y l a r g e s p r e a d i n g and s t r o n g s e a s o n a l v a r i a t i o n s . The s e a s o n a l v a r i a t i o n s a r e t h e r e s u l t o f m i g r a t i o n s from o r t o f e e d i n g g r o u n d s and spawning g r o u n d s . Spawning o c c u r s i n t h e w i n t e r (december - j a n u a r y ) . The r e q u i r e m e n t s f o r spawning a r e a t e m p e r a t u r e h i g h e r t h a n 5OC and a s a l i n i t y above 35

%.

(Oray, 1 9 6 5 ) .

These c o n d i t i o n s l i m i t t h e e x t e n s i o n o f spawning t o t h e N o r t h b u t a r e n o t , o t h e r -

w i s e p a r t i c u l a r l y s e v e r e . S t i l l , spawning a p p e a r s t o o c c u r , i n t h e N o r t h S e a , i n f i v e w e l l d e f i n e d and l i m i t e d r e g i o n s ( D e Veen and Boerema, 1959, D e C l e r c k and C l o e t , 1 9 7 7 ) . These a r e shown of f i g u r e 1 r e p r o d u c e d from D e C l e r c k and C l o e t ( 1 9 7 7 ) .

F i g , 1. Spawning g r o u n d s o f p l a i c e i n t h e N o r t h Sea (from De C l e r c k and C l o e t , 1 9 7 7 ) .

3 Experiments with marked specimens have shown that the fish always return to the same spawning ground. (De Veen and Boerema, 1959, De Veen, 1962, 1970). An extensive study of the plaice spawning in the Southern Bight was carried on with marked specimens from the North-Hinder area by the Belgian "Rijksstation voor Zeevisserij" (De Clerck and Cloet, 1977). Spawning in the Southern Bight takes place between the 7th and the 19th of January. After the spawning period, the fish progressively leave the spawning ground. This migration lasts from February to April and follows well defined directions from North-East to North. The distances covered by the fish vary from a hundred kilometers to six hundred kilometers according to the main direction of migration. The average migration velocity is typically of the order of a few centimeters per second. In trying to interpret these observations, the marine biologist will turn to the physicist €or explanation. It is obvious that migrations are motivated by the search for food and the return to the spawning grounds but the question remains why specific regions roughly the same every year appear to be suitable, exclusive of others. If specific water characteristics are required for spawning or for finding a suitable prey, what are these conditions and, most of all, how can one explain that the same areas, every year, appear to fulfil them. If currents, diffusion or other physical processes are responsible, one should be able to identify the mechanisms by which they operate, determine the areas with suitable ecological characteristics, foresee the changes which might follow modifications of the hydrodynamical regime and repeating the analysis for other species, predict what their preferential grounds will be. Thus, the marine biologist will turn to hydrodynamicists but he will find them engrossed in the study of tides and storm surges which, with current velocities of one m s-l or larger and surface elevations reaching several meters, constitute by far the most intense hydrodynamic processes in the North Sea. What other effect there may be appears as noise in current-meter data and in models; the instruments as well as the models being, since almost a half century, tuned to the dominant mesoscale signals.

However, mesoscale motions like tides and storm surges cannot possibly provide any direct explanation for the type of ecosystem patterns and dynamics which has been described above, The time scales, the length scales and the velocity scales are simply not right. Migration velocities are one or two orders of magnitude smaller than tidal velocities. Tides move the water back and forth some ten kilometers in a half day. The characteristic time of evolution of a typical weather pattern and of the atmospheric forcing on the sea is of the order of a few days. Spawning, on the other hand, lasts several weeks and migration several months

:

the corresponding time scales are one

4 or two orders of magnitude larger. Similarly, the length scales involved (sizes of the spawning grounds, distances covered by migration) are one or two orders of magnitude larger than, say, a typical tidal excursion. If this particular behaviour of a given ecosystem is the result of hydrodynamic constraints, one obviously must look into macroscale hydrodynamic processes such as the residual currents, fronts and eddies in the North Sea. Macroscale effects account for a small percentage of the North Sea kinetic energy at any instant but, in the long run, they survive changing and reversing mesoscale motions which more or less cancel out over periods of time of ecological interest although, through the non-linear terms, they have a determinant influence on the residual circulation pattern. Residual currents have velocities in harmony with the migration velocities quoted before, their length scales and time scales are in the right range and, in the spatial distribution of residual energy exchanges between macroscales and mesoscales, one can see structures which are reminiscent of spawning patchiness or other ecoloqical patterns (Nihoul, 1980). The macroscale hydrodynamics of the North Sea may not be the obvious objective of hydrodynamical investigations and it may be rather difficult to study, embedded as it is in much more energetic mesoscale motions. It is not clear whether it can be obtained, with enough accuracy, by measurements with classical instruments. Modelling may be the best way to approach the problem but models must be designed very carefully to make sure that the small residue one is looking for is indeed sorted out of the much stronger mesoscale effects without being tampered with by numerical or other errors (e.9. Nihoul, 1980).

HYDRODYNAMIC CONSTRAINTS ON ECOSYSTEMS IN THE SOUTHEASTERN BERING SEA A very interesting interdisciplinary study of the Bering Sea was conducted in the recent years under the name of PROBES (Processes and Resources of the Bering Sea). PROBES investigations have shown the existence of distinct ecosystems in the Southeastern Bering Sea, conditioned by hydrodynamic features. Major food webs leading to large stocks of pelagic fauna and benthic fauna are found well separated in space and organized in relation with a series of fronts (Iverson et al, 1979). Figure 2 shows the three fronts which have been observed. The shelf-break front which roughly follows the 200 m isobath along the continental slope near the shelfbreak is persistent for periods of years and marks a transition between oceanic and shelf waters (Kinder and Coachman, 1978). The inner front is located at the 50 m isobath where the water column is well mixed by tide-induced turbulence (Schumacher et al, 1979). Between these two fronts, lies a middle shelf front near the 100 m isobath (Coachman and Charnell, 1979).

5

BERING SEA

Fig. 2 . F r o n t s i n t h e S o u t h e a s t e r n B e r i n g Sea (from I v e r s o n e t a l , 1 9 7 9 ) .

The s h e l f b r e a k f r o n t and t h e middle s h e l f f r o n t a r e s e p a r a t e d by t h e o u t e r s h e l f zone which e x t e n d s o v e r some 100 km. A s d e s c r i b e d by I v e r s o n e t a 1 (19791, Open Bering Sea w a t e r s e x t e n d o n t o t h e s h e l f i n a bottom l a y e r o f a t h i c k n e s s o f some 30 m w h i l e s h e l f w a t e r s f l o w seawards above it.

(figure 3 ) . The u p p e r mixed l a y e r and t h e bottom t u r b u l e n t l a y e r a r e s e p a r a t e d , i n t h e o u t e r

s h e l f zone by a mld-depth r e g i o n where i n t e r l e a v i n g w a t e r l a y e r s produce a v e r t i c a l fine structure. The middle s h e l f f r o n t and t h e i n n e r f r o n t a r e s e p a r a t e d by t h e middle s h e l f zone which h a s a w i d t h o f 200 t o 300 km. The middle s h e l f zone i s c h a r a c t e r i z e d by a s t r o n g s e a s o n a l t h e r m o c l i n e and two d i s t i n c t superposed l a y e r s of f l u i d s w i t h o c c a s i o n a l mixing between t h e two l a y e r s d u r i n g s t o r m s . The bottom l a y e r i s c o l d and r i c h i n nutrients. The s o u r c e o f n u t r i e n t s f o r t h e s h e l f ecosystems i s l i m i t e d t o t h e bottom boundary l a y e r o f t h e m i d d l e s h e l f zone and t o t h e d e e p w a t e r s of t h e o u t e r s h e l f zone.

PHYTOPLANKTON

Y f L F BREAK FRONT OCEANIC ZONE

4

MIDDLE FRONT

OUTER SHELF ZONE

LASKA STREAM /

MlOOLE SHELF Z

INNER F M T

4

M

m T A L ZONf

---

,* '-

; WIND

MIXING

-0

Fig, 3, Cross-shelf hydrographic features and relative primary production in the Southeastern Bering Sea (from Iverson et al, 1979).

The major spring phytoplankton bloom occurs first in the shallow waters of the middle shelf zone. The herbivores can be separated into a shelf group community (confined to the region shoreward of the middle front) and an oceanic community (seaward of the front). The former consists of small animals rather ineffective in grazing the large chainforming diatoms which dominate the phytoplankton in the middle shelf zone. On the contrary, the oceanic zooplankton (composed in particular of large calanoid copepods) is an effective grazer of large phytoplankton. Almost negligible cross-shelf advection and the presence of the middle front acting as a barrier for diffusion restrict the large oceanic herbivores to the outer shelf zone, The small coastal herbivores which inhabit the middle shelf zone cannot graze the large diatoms there and the phytoplankton biomass accumulates and settles to the bottom. This promotes the development of benthic ecosyst-ems and large stocks of benthic infauna, demersal fish and crabs are found I n the middle shelf zone (Bakkala and Smith, 1978).

I n t h e o u t e r s h e l f zone, on t h e c o n t r a r y , t h e g r a z i n g o f t h e p h y t o p l a n k t o n by t h e l a r g e o c e a n i c z o o p l a n k t o n i n i t i a t e s an e f f e c t u a l p e l a g i c food c h a i n and l a r g e s t o c k s of b i r d s , mammals and p e l a g i c f i s h a r e found (Nasu, 1974, Bakkala and S m i t h , 1 9 7 8 ) . The s h o r t d e s c r i p t i o n g i v e n above o f t h e S o u t h e a s t e r n Bering Sea ecosystems f o l l o w s c l o s e l y t h e c o n c l u s i o n s o f I v e r s o n e t a 1 (1979) r e p o r t i n g on t h e r e s u l t s o f PROBES. I t shows c l e a r l y t h a t , f o r t h e a u t h o r s , t h e e c o l o g i c a l p a t t e r n s o b s e r v e d i n t h e

S o u t h e a s t e r n B e r i n g Sea r e s u l t from p h y s i c a l c o n s t r a i n t s on t h e system which l i m i t t h e t r a n s p o r t and t h e d i f f u s i o n o f n u t r i e n t s and p l a n k t o n s p e c i e s . However, a l t h o u g h t h e most i n t e n s i v e p h y s i c a l p r o c e s s e s a r e most c e r t a i n l y a s s o c i a t e d w i t h t i d e s , wind f o r c i n g and s t o r m s , t h e s e phenomena a r e s c a r c e l y mentioned and o n l y c a l l e d upon f o r t h e i r a v e r a g e mixing e f f e c t

:

p r e s e n c e and d e p t h of a wind-mixed

l a y e r , e x i s t e n c e of

a t u r b u l e n t bottom boundary l a y e r i n r e l a t i o n w i t h t i d a l c u r r e n t s and bottom f r i c t i o n , mingling o f t h e two l a y e r s d u r i n g s t o r m s i n t h e middle s h e l f r e g i o n and s u b s e q u e n t transfer'of

n u t r i e n t s i n t h e p h o t i c zone, f o r m a t i o n o f a f i n e s t r u c t u r e i n t h e o u t e r

s h e l f r e g i o n where t h e two mixed l a y e r s a r e s e p a r a t e d and a s s o c i a t e d i n t e r l e a v i n g o f s a l i n i t y and t e m p e r a t u r e enhancing v e r t i c a l d i f f u s i o n and v e r t i c a l t r a n s p o r t o f nut r i e n t s near t h e shel f break f r o n t . For t h e r e s t , t h e p i c t u r e a p p e a r s r a t h e r a s a s t e a d y o n e , i g n o r i n g s h o r t d i s t a n c e mesoscale e x c u r s i o n s and a d d r e s s i n g phenomena w i t h l e n g t h s c a l e s of t h e o r d e r o f 100 km o r more and t i m e s c a l e s r a n g i n g from s e a s o n s t o y e a r s . Very s m a l l r e s i d u a l cross-shelf

o r v e r t i c a l m o t i o n s seem t o matter much more t h a n c l e a r l y more i n t e n s i v e

wind-induced and t i d a l c u r r e n t s . One c a n s e e h e r e a g a i n a c a s e where t h e i n t e r e s t of t h e b i o l o g i s t d o e s n o t l i e p r i m a r i l y i n t h e most i n t e n s e hydrodynamic p r o c e s s e s b u t i n t h e p a r a m e t e r i z a t i o n o f t h e i r e f f e c t i n t h e mean and i n t h e d e t e r m i n a t i o n of t h e l o n g t e r m "ecohydrodynamic" c i r culation patterns.

TIDAL FRONTS ON THE EUROPEAN CONTINENTAL SHELF

Marked f r o n t a l s t r u c t u r e s have been o b s e r v e d on t h e European C o n t i n e n t a l S h e l f d u r i n g t h e summer months. These f r o n t s which s e p a r a t e well-mixed w a t e r s on one s i d e , and v e r t i c a l l y s t r a t i f i e d waters on t h e o t h e r , c a n be d e t e c t e d a t t h e s e a s u r f a c e by a t e m p e r a t u r e d i s c o n t i n u i t y and a r e q u i t e v i s i b l e on i n f r a r e d remote s e n s i n g images ( e . 9 . Simpson e t a l , 1 9 7 8 ) . A l l o b s e r v a t i o n s i n d i c a t e t h a t t h e f r o n t s a r e f a i r l y p e r s i s t e n t and a p p e a r a s a p p r o x i m a t e l y two-dimenslonal v e l o c i t y and d e n s i t y p a t t e r n s o s c i l l a t i n g back and f o r t h w i t h t i d e s . A v e r t i c a l c i r c u l a t i o n seems t o be a s s o c i a t e d w i t h t h e f r o n t a l s t r u c t u r e s a s

sketched i n f i g u r e 4. The e x i s t e n c e of a r e g i o n o f s u r f a c e convergence i s confirmed by t h e o b s e r v a t i o n , i n n e a r calm s u r f a c e c o n d i t i o n s , of a more o r l e s s c o n t i n u o u s s l i c k where j e l l y f i s h , seaweed, e t c . . .

a r e found t o a c c u m u l a t e . F r e q u e n t l y , a l s o , a minimum i s observed i n

t h e sea s u r f a c e t e m p e r a t u r e i n t h e mixed w a t e r j u s t b e f o r e c r o s s i n g t h e f r o n t .

8

Q

Y u R1

L(

8

u Q

:

temperature

w

Y convergence E

divergence distance in the cross-front direction

+J

u a0

aJ

A2

u

P

u

.c

t 7

.r(

2

distance in the cross-front direction

Fig. 4. Schematic vertical circulation at a front (from Simpson et al, 1978) This minimum is consistent with the existence of an upwelling and a region of surface divergence as shown in figure 4. (Simpson et al, 1978).

The fronts axe produced by variations in the level of wind and tidal mixing. The comparison of the different terms in the energy balance equation suggests that fronts are likely to be found in the regions where the Monin-Obhukov length scale is of the same order as the depth (Simpson and Hunter, 1974, Simpson et al, 1978, Garrett et al, 1978). When applied to a limited geographical area and a given period of time, the criterion can be simplified taking into account the relatively small variations of the mean atmospheric inputs. One can show, then, that the formation of a front can be associated with a given critical value of the mean rate of energy dissipation (Pingree and Griffiths, 1978, Nihoul, 1980).

9

Figure 5, reproduced from Nihoul (19801, shows the curves of equal value of

*

s

=

log

where

10 ER

E~

is the mean rate of energy dissipation per unit mass (m2 s - ~ )and

value of reference taken as

*= E

*

E

a

m2 s - ~ .

The havy line corresponds to the value

S = 1.5

which is generally accepted as the

critical value for the formation of fronts on the North European Continental Shelf.

Fig. 5. Curves of equal values of the Simpson-Hunter parameter in the North Sea (from Nihoul, 1980).

S = log10(10-4~~1)

10 I n f r a r e d s a t e l l i t e images and s h i p s u r v e y s c o n f i r m t h e e x i s t e n c e o f t h e c o a s t a l f r o n t s a t t h e N c r t h e r n S c o t t i s h c o a s t , i n t h e German B i g h t and o f f t h e c o a s t o f Denmark a s w e l l a s o f f r o n t a l s t r u c t u r e s c o r r e s p o n d i n g t o t h e Western and E a s t e r n e n d s o f t h e main c r i t i c a l l i n e c r o s s i n g t h e S o u t h e r n N o r t h Sea f r o m t h e E n g l i s h c o a s t t o t h e Dutch c o a s t ( f i g u r e 5). I n p a r t i c u l a r , s t r o n g e v i d e n c e e x i s t s of t h e Flamborough Head f r o n t , e x t e n d i n g seaward o f f t h e B r i t i s h c o a s t , i n v e r y good agreement w i t h t h e s h a p e o f t h e c r i t i c a l c u r v e i n t h a t r e g i o n ( P i n g r e e and G r i f f i t h s , 1 9 7 8 , Nihoul,

1980).

O b s e r v a t i o n s show t h a t f r o n t s a r e o f t e n u n s t a b l e and meanders of i n c r e a s i n g amplit u d e g e n e r a t e c y c l o n i c e d d i e s w i t h a s p a c i a l e x t e n t o f 20-40 km and a l i f e t i m e o f several days.

( P i n g r e e , 1 9 7 8 ) . I n t h e summer, s u c h c y c l o n i c e d d i e s p l a y a n i m p o r t a n t

r o l e i n t h e t r a n s f e r o f h e a t , s a l t and n u t r i e n t s a c c r o s s s t r a t i f i e d r e g i o n s . They p r e s u m a b l y have a c o g e n t i n f l u e n c e on p r i m a r y p r o d u c t i v i t y t h r o u g h t h e t r a n s f e r o f n u t r i e n t s and p h y t o p l a n k t o n a c c r o s s t h e f r o n t a l zone ( P i n g r e e e t a l , 1 9 7 9 ) .

5-50

h

I

5-30 W

i,

/

2 3

F i g . 6 . An example o f s u r f a c e d i s t r i b u t i o n s o f t e m p e r a t u r e , s a l i n i t y and c h l o r o p h y l l a , r e f l e c t i n g a c y c l o n i c eddy s t r u c t u r e .

11 Comparing the phytoplankton's growth rate and the life time of the cyclonic eddies, Pingree et a1 (1979) argued that the growth of the population may actually occur in the eddy transfer process. Figure 6 (reproduced from Pingree et al, 1979) shows a remarkable coherence between the surface distributions of temperature, salinity and chlorophyll a , reflecting the cyclonic eddy structure seen in the infrared image.

These admirable studies by Simpson, Pingree and others illustrate again the constraints which hydrodynamics processes impose on the dynamics of ecosystems. The hydrodynamic constraints result from energetic mesoscale motions such as tides and wind-induced currents but, as before, these processes, however essential they may seem to the hydrodynamicists, are not interesting per se. It is their ability or their inability to mix the water column which is determinant in the formation Of fronts. The data are corrected for tidal excursions which are otherwise disregarded and such phenomena as frontal circulation, frontal instabilities and cyclogenesis are interpreted by means of quasi steady-state pictures obtained by working in axes moving with the front or, as mentioned before, in relation with the residual circulation in the North Sea, by averaging over periods of time large enough to smooth out tidal and other mesoscale oscillations. The critical parameter used in predicting the locations of the fronts is written in terms of similarly average quantities such as the mean rate of energy dissipation (Pingree and Griffiths, 1978, Nihoul, 1980). Typical time scales of interest vary from seasons to a minimum of several days (for the growth of phytoplankton in the eddy like frontal excrescences). The formation and evolution of frontal structures in European shelf seas and their ecological implications, by the time scales, length scales and velocity scales involved, provide another example of these weak but persistent physical processes which deserve the solicitude of Ecohydrodynamics.

REFERENCES Bakkala R.G. and Smith G.B., 1978. Demersal fish resources of the Eastern Bering Sea: Spring 1976. Northwest and Alaska Fisheries Center Processed Report, U.S. Department of Commerce, National Marine Fisheries Service, Seattle, Washington, 234 pp. Coachman L.K. and Charnel1 R.L., 1979. On lateral water mass interaction. A case study. Bristol Bay, Alaska, J. Physical Ocean, 9: 278-297. De Clerck R. and Cloet N., 1977. Merkproeven of schol in de Zuidelijke Bocht. Mede lingen van het Rijksstation voor Zeevisserij, C.L.O. Gent, 124 B, 16. De Veen J.F., 1962. On the sub-populations of plaice in the Southern North Sea, I C E S CM 1962: 94. De Veen J.F., 1970. On the orientation of the plaice. I. Evidence from orientating factors derived from ICES transplantat.lor, experiments in the years 1904-1909, J. Cons. int. Explor. Mer, 33: 2. De Veen J.F. and Boerema L.K., 1959. Distinquishlng Southern North Sea spawning populations of plaice by means of otolith characteristics, ICES C.M. 1959: 91.

12 Garrett C.J.R., Keeley J.R. and Greenberg D.A., 1978. Tidal Mixing versus Thermal Stratification in the Bay of Fundy and the Gulf of Maine, Atmosphere-Ocean 16: 403-423, Iverson RIL., Coachman L.D., Cooney R.T., English T . S . , Goering J.J., Hunt G.L., Macauley M.C., MC Roy C.P., Reeburg W.S. and Whitledge T.E, 1979. Ecological significance of fronts in the Southeastern Bering Sea, in Ecological Processes in Coastal and Marine Systems. Ed by Robert J. Livingston, Plenum Publ., 437-466. Kinder T.H. and Coachman L.K., 1978. The front overlaying the continental slope in the Eastern Bering Sea, J. Geophys. Res.,83: 4551-4559. Nasu T., 1974. Movement of baleen whales in relation to hydrographic conditions in the Northern Part of the North Pacific Ocean and the Bering Sea, in Oceanography of the Bering Sea. Ed by D.W. Hood and E.J. Kelley, Institute of Marine Science, University of Alaska, Fairbanks, 345-361. Nihoul J.C.J., 1980. Residual circulation, long waves and mesoscale eddies in the North Sea. Oceanologica Acta, 3: 309-316. Oray I.K., 1965. Uber die Verbreitung der Fischbrut in der Sudlichen Nordsee. Ber. Dt. Wiss. Komm. Meeresforsch, 18: 1-11. Pingree R.D., 1978. Cyclonic eddies and cross-frontal mixing. J. mar. biol. Ass. U.K. 58: 955-963. Pingree R.D. and Griffiths D.K., 1978. Tidal fronts on the Shelf Seas Around the British Isles, J. Geophys. Res.,83: 4615-4622. Pingree R.D., Holligan P.M. and Mardell G.T., 1979. Phytoplankton growth and cyclonic eddies. Nature, 278: 245-247. Schumacher J.D., Hinder T.H., Pashinski D.J. and Charnel1 R.L., 1979. A structural front over the continental shelf of the Eastern Bering Sea, J. physical Ocean, 9: 79-87. SimpSon J.H. and Hunter J.R., 1974. Fronts in the Irish Sea. Nature, 250: 404-406. Simpson J.H., Allen C.M. and Morris N.C.G., 1978. Fronts on the Continental Shelf, J. Geophys, Res., 83: 4607-4614.

13

FATE OF NUTRIENT ENRICHMENT ON CONTINENTAL SHELVES AS INDICATED BY THE C/N

CONTENT O F BOTTOM SEDIMENTS

J O H N J. WALSH, EUGENE T.

PREMUZIC, AND TERRY E. WHITLEDGE

Brookhaven N a t i o n a l L a b o r a t o r y , Upton, NY, 11973

INTRODUCTION

I met a t r a v e l l e r from an a n t i q u e l a n d Who s a i d : "Two v a s t and t r u n k l e s s l e g s of s t o n e Stand i n t h e d e s e r t . Near them, on t h e s a n d ,

Half sunk, a s h a t t e r e d v i s a g e l i e s , whose frown, And w r i n k l e d l i p , and s n e e r of c o l d command, Tell t h a t i t s sculptor w e l l those passions read Which y e t s u r v i v e , stamped on t h e s e l i f e l e s s t h i n g s , The hand t h a t mocked them and t h e h e a r t t h a t f e d ; And on t h e p e d e s t a l t h e s e works a p p e a r ; 'My name i s Ozymandias, King o f K i n g s ; Look on my works, ye Mighty, and d e s p a i r ! ' Nothing b e s i d e r e m a i n s , Round t h e d e c a y Of t h a t c o l o s s a l wreck, b o u n d l e s s and b a r e The l o n e and l e v e l s a n d s s t r e t c h far away." (P.B.

S h e l l e y , 1817)

P h y t o p l a n k t o n growth p r o c e s s e s a r e r e a s o n a b l y well-known

f u n c t i o n s of l i g h t ,

t e m p e r a t u r e , and n u t r i e n t s : however, t h e i r l o s s p r o c e s s e s a r e c o m p a r a t i v e l y unknown.

For example, t h e l o w p r o d u c t i v i t y and n i t r a t e c o n t e n t o f m o s t o c e a n i c

s u r f a c e w a t e r s ( F i g . 1 ) r e f l e c t t h e slow upward rate of n u t r i e n t i n p u t a c r o s s t h e main t h e r m o c l i n e t o t h e e u p h o t i c zone. e.g.,

A t t h e c o a s t a l b o u n d a r i e s o f t h e ocean,

on t h e c o n t i n e n t a l s h e l v e s , d a i l y f l u x e s of n i t r a t e s u p p l y and e n s u i n g pro-

d u c t i v i t y a r e 1 t o 2 o r d e r s of magnitude l a r g e r (Walsh, 1976) a s a r e s u l t o f l o c a l l y i n t e n s i f i e d p h y s i c a l p r o c e s s e s of u p w e l l i n g , ing.

r i v e r r u n o f f , and t i d a l mix-

15N estimates o f n i t r a t e u p t a k e by p h y t o p l a n k t o n s u g g e s t t h a t o n l y 10% o f

t h e d a i l y n i t r o g e n demand of p h o t o s y n t h e s i s i s m e t by n i t r a t e i n t h e open ocean (Eppley and P e t e r s e n , 1 9 7 9 ) , w h e r e a s n i t r a t e i s 1.50% of t h e d a i l y n i t r o g e n s o u r c e f o r p h y t o p l a n k t o n i n coastal waters o f f P e r u (MacIsaac and Dugdale, 1 9 7 2 ) . N e w York (Conway and W h i t l e d g e , 1 9 7 9 ) , C a l i f o r n i a (R. Eppley, p e r s o n a l c o m u n i c a -

t i o n ) , and A l a s k a (J. G o e r i n g , p e r s o n a l communication).

N i t r a t e u p t a k e i s con-

s i d e r e d an e s t i m a t e of t h e "new" d a i l y p r o d u c t i o n (Dugdale and G o e r i n g , 1967) t h a t i s a v a i l a b l e f o r e x p o r t from an ecosystem and is a s s o c i a t e d w i t h t h e

14

3

NITRATE ( UG - ATOM I LITER) 10 I5 20

5

25

30

0

20

40

60

-

-E

-

ec

I

I-

n W

1oc

I2C

14C

ma

1ec

X

*

NORTH PACIFIC

0

= EASTERN MEDITERRANEAN

A

NORTW CENTRAL ATLANTIC

A

= PERU CURRENT = CALIFORNIA CURRENT = CANARY CURRENT

Fig. 1. The v e r t i c a l d i s t r i b u t i o n of n i t r a t e in t h e open ocean and w i t h i n t h e e a s t e r n boundary c u r r e n t s . o u t b r e a k of blooms of p h y t o p l a n k t o n p o p u l a t i o n s in c o a s t a l waters ( Y e n t s c h e t

al.,

1977).

Annual b u d g e t s , i n f a c t , s u g g e s t t h a t o n l y 1 0 % of t h e p a r t i c u l a t e

n i t r o g e n , f i x e d i n t h e open ocean, s i n k s o u t of t h e e u p h o t i c zone, b u t t h a t a s much as 50% of t h e p a r t i c u l a t e n i t r o g e n , f i x e d on t h e c o n t i n e n t a l s h e l f , may p e r h a p s be e x p o r t e d to t h e slope s e d i m e n t s (Walsh, 1 9 8 0 a ) . The t r a j e c t o r y and f a t e of t h i s p a r t i c u l a t e m a t t e r are p o o r l y u n d e r s t o o d pro-

cesses i n a s p a t i a l l y h e t e r o g e n e o u s c o a s t a l Ocean.

P a r a m e t e r i z a t i o n of a p p r o p r i -

a t e hydrodynamics f o r a q u a n t i t a t i v e d e s c r i p t i o n of t h e s e loss p r o c e s s e s must t h u s a w a i t d e f i n i t i o n of t h e i m p o r t a n t b i o l o g i c a l t i m e and s p a c e scales. t h e bottom s a n d s t e n d to " r e c o r d " t h e h i s t o r y of t h e w a t e r column, we have

Since

15 s e l e c t e d t h e C/N c o n t e c t of s h e l f s e d i m e n t s a s a p o s s i b l e t r a c e r of

1 ) s i t e s of

n u t r i e n t i n t r o d u c t i o n t o t h e s h e l f by v a r i o u s p h y s i c a l mechanisms, o f 2 ) a r e a s of subsequent downstream u t i l i z a t i o n by t h e p h y t o p l a n k t o n , and of 3 ) where loss of p a r t i c u l a t e matter might occur f r m t h e w a t e r column.

An a n a l y s i s i s made of

the

C/N p a t t e r n s of bottom s u r f a c e s e d i m e n t s i n r e l a t i o n to t h e n i t r o g e n s o u r c e s from

upwelling,

r i v e r r u n o f f , and t i d a l mixing on t h e P e r u v i a n , w e s t A f r i c a n ,

Amazonian, Gulf of Mexico, e a s t e r n U.S.,

B e r i n g , and North Sea s h e l v e s i n an

i n i t i a l a t t e m p t t o p r o s c r i b e t h e p a r t i c l e t r a j e c t o r i e s of o r g a n i c m a t t e r on t h e continental shelf. The r a t i o of carbon to n i t r o g e n ( C / N ) c o n t e n t i n most marine organisms i s l e s s than 6 , u n l i k e t h a t of l a n d p l a n t s which use more c a r b o h y d r a t e s f o r t h e i r s u p p o r t s t r u c t u r e s ( P a r s o n s , 1976) and have C/N r a t i o s >15 ( M u l l e r , 1977).

Detrital

p a r t i c l e s i n the sea a l s o have a C/N r a t i o g r e a t e r t h a n 10 a s a r e s u l t of t h e i n c r e a s e d r e c y c l i n g of n i t r o g e n compounds compared to slower decomposition of r e f r a c t o r y c a r b o n compounds (Degens, 1 9 7 0 ) .

For example, d u r i n g blooms of phyto-

plankton t h e C/N c o n t e n t of p a r t i c u l a t e matter i n t h e w a t e r column i s 1 % c a r b o n such t h a t t h e lower C/N r a t i o s of t h e s e slope r e g i o n s ( F i g . 2 0 ) a r e n o t a r e s u l t of s o r p t i o n of n i t r o g e n on c l a y m i n e r a l s { M u l l e r , 1977: SUeSS and M u l l e r , 1 9 8 0 ) , b u t r e f l e c t m a r i n e o r i g i n of t h e d e t r i t u s (Walsh, 1 9 8 0 b ) .

In

184C sediment samples t a k e n between 24O a n d 44ON (Hathaway, 1 9 7 1 1 , mean C/N r a t i o s < 6 are o n l y found on t h e slope a t 400-1800

m ( F i g . 20), w i t h > 1 % c a r b o n

sediments e x t e n d i n g from 8 0 0 - 2 2 0 0 m ( F i g . 1 9 ) . Although 613C v a l u e s of p l a n k t o n r a n g e from - 1 9 . 6

t o -30.6

(Sackett e t ale,

1965) between t h e t r o p i c a l and p o l a r o c e a n s , a t any g i v e n l a t i t u d e of t h e above s h e l v e s 613C v a l u e s 5 2 5 a p p e a r to i n d i c a t e c a r b o n of t e r r e s t r i a l o r i g i n and 5 2 1 of marine o r i g i n .

The w e a l t h o f i n f o r m a t i o n summarized i n t h i s a n a l y s i s s u g g e s t s

t h a t most t e r r e s t r i a l m a t e r i a l of a C/N > l o , w i t h a 613C L 2 5 , i s now e i t h e r trapped i n e s t u a r i e s o r h a s been d e p o s i t e d on t h e s h e l f - s l o p e d u r i n g g l a c i a l

2.0

I .6

z

g

1.2

[r

a 0 0.8

a (3 a: 0.4

8 0.c

-0.4 50

t--i + 350 650 950 1250 1550 1850 2150 24502750 3050 DEPTH INTERVAL ( m )

Fig. 1 9 . The c o m p o s i t e s h e l f - s l o p e d i s t r i b u t i o n of p e r c e n t o r g a n i c carbon w i t h i n s u r f a c e s e d i m e n t s from F l o r i d a to Maine ( a f t e r Hathaway, 1 9 7 1 ) .

42

. ...

c a

z W

c3 0

K

.

0 .

K

T--

---I

k z 5

0

300

600 900 1200 1500 1800 2100 2400 2700 3000 DEPTH INTERVAL (rn)

Fig. 20. The composite s h e l f - s l o p e d i s t r i b u t i o n of c a r b o n / n i t r o g e n s u r f a c e s e d i m e n t s from F l o r i d a t o Maine ( a f t e r Hathaway, 1 9 7 1 ) .

periods of t h e Pleistocene.

a C/N

within

The marine c a r b o n , mainly ungrazed p h y t o p l a n k t o n of

@L MIXING ZCNL

CHARLES S. YENTSCH Bigelow Laboratory for Ocean Science, West Boothbay Harbor, ME USA

04575

ABSTMC?'

The tieating by the sun's energy provides buoyancy to surface layers of tile oceans which limits vertical mixing of the entire water column. A water column stratified by tlie buoyancy of tne surface layers is low in important nutrients; thus, primary production and tne stocks of phytoplankton are small.

The buoyancy

of surface layers and resulting stratification of tlie water column is a constraint to primary production and in turn to the ecosystem as a whole.

Kenewewed vertical mixing of the water

column emphasizes the importance of an optimal depth of mixing: tnis is the zone of the mixed layer where stresses due to lignt limitation are balanced by the addition of nutrients to surface layers.

INTRODUCTION With the seasonal cnange in solar input which regulates the light intensity directly and the winds as stirring forces indirectly, tne mixeu layer depth can be viewed deepening and snoalinq in response to these forces.

At some zone an optimum is reached

wiien the detrimental effects of vertical mixing (i.e. lignt

limitation) are compromised by the benefits of vertical mixing (advection of nutrient-ricn water).

This depth, or more properly

"zone", is tne level of optimal mixing,

--

optimal conditicns for

phytoplankton production in a mixed water column. To introduce the reader, a famous model was proposed by Sverurup in 1953 which aemonstrated the role played by vertical mixing in light limiting primary production.

Later an important

contribution by Cu-shing (1962) emphasized the interaction of

68

photosynthesis, respiration and vertical mixing.

In the Sargasso

Sea Steele and Menzel (1962) applied light-limited concepts in concert with flux to describe the seasonal sequence of primary production. Thus the Steele and Menzel model 'introduced the concept of an optimal mixing depth. In my opinion, the general importance of this concept is still not fully appreciated. Although the dual-antagonistic role of vertical mixing has long been recognized, the concept of an optimal mixing depth zone and the factors regulating this zone are seldom addressed. The point of this paper is to extend the importance of this concept. Ily approach will be mechanically different from Steele and Menzel's, however, the concept is similar. One of the beauties of these models has been their simplicity. Thky tend to indicate specific topics where further research is needed either in the biological or physical processes of the system. Recent refinements have largely concerned the addition of physiological complexities. In my opinion, these recent formulations have tended to obscure the important interactions. But the point of this paper is not to discuss the inadequacies of these models, but to identify and reemphasize the degree to which mixing controls primary production. In the course of developing the optimal mixing depth concept, I believe the inadequacy of the modeling will become apparent. are ripe for future research.

It is these inadequacies which

Concepts concerning vertical mixing As the depth of thE mixed layer changes, the phytoplankton are subjected to changes in I) the average light quality and quantity and 2) the average nutrient concentration. As the mixed layer deepens, the average light intensity to the cells decreases, whereas the availability of nutrients depends on the scaler gradient of that substance distributed over the depth of the water column. It is the product of these two processes which establishes the potential for primary production in the water column. Thus, the mechanical effects of mixing on primary production concern two processes related to phytoplankton growth, namely light limitation of photosynthesis, and the availibility and uptake of nutrients. Light Limitation: In traditional mi.xing-production models, the depth where photosynthesis and respiration are equal is termed the critical mixing depth.

At the crux in the development

69

of these models is the relationship between the rate of phctosynthesis and the rate of respiration integrated over the depth in the mixeu water cclumn. For the persons unfamiliar with these models, I will very briefly describe the components. For more (1977). detail the reader is referred to Platt c t u Z . , The components of a so-called "integral model" are the relationship of photosynthesis and light, the so-called P vs I (photosynthesis vs. irradiance) curve and the distribution of downwelling irradiance, (Figure 1) .

k - - Pt

-~

Pt-P,= R

Pmax

z

/I/

+I I / 3

z,

-7

Fig. 1. (A) (B) (C) Components of the integral model. Curve A. The relationship between light and photosynthesis where P is total daily photosynthesis Pn is total daily net photosynthet sis. C is the compensation point and Ci is the compensention intensiEy. (Redrawn from Yentsch 1975). Curve B is the downwelling irradiance (I) in the water column of depth 2. Curve C is the product of A and B and represents the integral model in a water column of depth 2. Zc is the compensation depth and Ze the euphotic depth in meters. The prouuct of those two components yields the water column integral model shown in Figure lc. As the mixed layer deepens below the euphotic depth, the effect is to enlarge the influence of respiration. Therefore, as the mixed layer deepens, the relationship of (Pt:R) changes because of the increasing amount of R to the system. As previously mentioned, when (Pt:R) equals 1.0, there is no net production for the population. The depth of mixing responsible for this relationship is the critical mixing depth. Ir. the development of these models, one in forced to generalize

as to the interaction of light and photosynthesis and the assignment of the level of respiration.

The relationship between

70

photosynthesis and irradiance that I will use was obtained empirically from field data where the uptake of ca.rbon-14 was measured at light intensities ranging from 100% to 18 of sunlight (Yentsch, 1975 ) The model uses values for R expressed as a percentage of Pmax. Most commonly used is 10% which was an average obtained from field measurements by St.eemen-Nielsen and Hansen (1959). Using sensitive ETS measurements, Devol and Packard (1978) have found values for to'tal respiration to range between 2-45% with a mean around 5% of Pmax. There is no satisfactory method for measuring R specific for phytoplankton populations, and R undoubtedly varies a.s a function of species and population physiol.ogy. The values (Pt:R) were obtained by manually integrating the areas under the photosynthesis and respiration curves. The solar input and transmission features are generalized by selecting three euphotic depths which attempt to characterize the extremes founa in ocean environments (Figure 2).

01.O

2 .o i

3.0

4.0

5.0

t

I

I

A - COASTAL - Ze

30M

8-SLOPE - Z e

60M

C-

OFFSHORE Ze OCEANIC

6.0

1

I 2o

800 J

Fig. 2. Changes in Pt:R as a function of vertical mixing for three euphotic depths. (From Yentsch 1 9 7 5 ) .

( 2m )

The value (Pt:R) refers to the photosynthesis respiration ratio for populations where the mixed. layer depth in meters (Zm) is The results shown in equal to the euphotic depth in meters (2,). figure 2 demonstrates that the relationship between (Pt:R) and Zm is hyperbolic when Zm exceeds the d.epth of the euphotic zone

(Ze). Thus phctosynthetic to respiration ratios can be calculated for any mixed layer depth below the euphotic zone as follows: (Pt:R) = b/ZT,

(1)

Where b is a constant.

The two primary points on the curves

needed for the calculation are the euphotic depth (Ze) for a 0 given (Pt:R) and the critical depth (Zcr). Substitution in equation 1 , 0

(Pt:R) = b/Ze 1

=

and

(2)

b/Zcr.

(3)

From equation 2 one can write, 0

b = (Pt:R)

0

x Z and (Pt:R) = (Pt:R) e

x Ze/Z,.

The critical depth calculation is, Zcr =

(Pt:R)0 x Ze or,

(Pt:R)

=

Zcr/Z

m

(5)

(6)

The hyperbolic relationship between (Pt:R) and Zm demonstrates that the former decreases rapidly as the depth of mixing initially exceeds the euphotic depth. (Pt:R) declines more gradually as the critical depth is approached. For very transparent waters the critical depth (Zcr) resides at about 700 meters which is more than twice the observed isothermal layer depth in the Saryasso Sea. This suggests that if the assumption concerning respiration is correct then light limitation due to vertical mixing is never a severe problem to these populations.

The effect of decreasing the euphotic depth is to reduce the depth of critical mixing: In areas where the euphotic depth is shallow, small changes in vertical mixing markedly effect the ratio of photosynthesis to respiration. Therefore, the first point I wish to emphasize is that the role of vertical mixing - considering light effects alone - is to be a detriment to phytoplankton growth. And the severity of this detriment is strongly dependent upon the depth of the euphotic zone.

To emphasize this point, if we are to

72

dutrient Supply:

As tile mixed layer erodes the water column,

in autumn nutrient-rich water is advected into the euphotic zone. Consider the situation where a mixed layer gradually appears in a stratified water column. As the mixed layer deepens, it penetrates layers containing high concentrations of nutrients.

These are

entrained by the mixed layer. If the vertical distribution of nutrient concentration prior to mixing is known - the amount of nutrient (eg. nitrate) entrained (N m) is calculated by, 2'

m Nz,m =

0

NO -N 3

x

(7)

dz

To demonstrate the importance of the nutrient concentration compare the depth profiles for nitrate-nitrogen in the Sargasso Sea to that f o r the Gulf of Maine. Note that for mixing to entrain waters having 1.0 microgram atom per liter will entail a penetration to 30 meters in the Gulf of Maine while 100 meters in the Sarqasso Sea would be required. This difference illustrates the considerable difference in the amount of nitrate swept into the mixed layer (Figure 4). p g otoms liter

0

200

400

600

NO3-N ( p 4 O I O r 5 )

800

loci0

through deplh

I200

14

Zm

Fig. 4. The influence of concentration of nitrate as a function of depth and the level of entrainment of nitrate in the mixed layer. Data for Sargasso Sea ( S S ) taken on September 15, 1958, Lat. 32'10'N, Long. 64O3O'W. (Tech Rept. Bermuda Biol. Station 1960). Data for t the Gulf of Maine (GM) taken on September 2 1 , 1966 Atlantis 1001, Lat. 42°45'N, Long. 69O54'W. (T'ech. Report W.H.O.I. 67-27).

73

assume that respiration is approximately 10% of Pmax, then for a rough rule of thumb t,he depth of critical mixing can be estimated to be six times the euphotic depth. This estimate is very close to the measured values published by Gran and Brauud (1935). The effect of increasing the rate for respiration is to accentuate the influence of vertical mixing on the ratio of photosynthesis to respiration. Figure 3 illustrates the degree of accentuation.

1.0

2.0

3.0

5.0

4.0 I

1

I

6.0 10%

-cn -800I L

W

+ W

E

0

1.0 Ze

2.0

3.0

4.0

I

I

I

30%

20%

5.0

6.0

I 1 1 I

10O/O

v

E N

Fig. 3. Changes in Pt:R as a function of respiration for two euphotic depths (Ze). Here three values of respiration are shown in conjunction with two euphotic depths and demonstrates that if respiration is higher than 10% of Pmax then maximum isothermal mixed layers commonly observed (100-200m) are potentially capable of housing populations which are light limited.

74

For those unfamiliar, the emphasis on nitrate as a limiting substance may seem simplistic. Perhaps it is. However, conventional wisdon is that the amount of nitrate regulates and limits primary production in the sea. There are other forms of nitrogen. present however, it is the amount of nitrate which dictates net population growth. Tnus the low level of primary productivity in the Sargasso Sea as compared to the Gulf of Maine become apparent from the data shown in Figure 4. With the source of the limiting substance housed in layers below the euphotic zone and vertical mixing the principal means of transporting these to the surface - then for the same amount of work needed to mix the water columns the Sargasso Sea populations get much less than populations in the Gulf of Maine. Combination of light limitation with nutrient flux Assume that other than light, nitrate-nitrogen is limiting. The manner in which (Pt:R) change in the mixed layer can be estimated as follows. For comparison, the two areas, Sargasso Sea and the Gulf of Maine will be used. First, the critical depth (Zcr) is determined using equation 5. The value for Ze in the Gulf of Maine is 30 meters and 120 meters in the Sargasso Sea. The value (Pt:R)O is assumed to be 6.0 for populations in either area. For each, 10 meters of mixed depth (Pt:R) was calculated using equation 6. Phctosynthesis to respiration ratios are then placed in the context of net production (P,) , (Pt:R) values are normalized over the range 0 - 10 by,

The product of equation (7) and equation (8) yield the relative value of net production as a function of mixed layer depth,

where both the effects of light and nutrients are involved. At the optimal depth for vertical mixing ( Z opt) '

For the Gulf of Maine, Z centers around 90 met.ers. The opt critical depth (Zcr) for this region is 160 meters. For the

75

Sargasso Sea, Z centers around 250 meters with the critical opt depth Zcr at 700 meters.

I oc

20c 30C A

E 400 N v

500 600 700

Fig. 5. The influence of relative net production by the combined effects of light limitation and nutrient advection. For the Gulf of Maine (GM) Ze is 30 meters, for the Sargasso Sea ( S S ) 120 meters. These curves are interpreted to mean that as the penetrative mixing progresses to the optimum, the maximum amount of nutrient is entrained and the population is not overly stressed by light limitation. Further deepening of the mixing layer forces the population into a situation where nutrients are excessive, and light-limitation becomes the important factor. Obviously, mixing shallower than the optimum permits ample light yet the population is not supplied with enough nutrient to overcome a limitation.

76

Unlike the rather direct relationship between Z cr and Ze, no simple general relationship can be established between Z and opt Z or Zcr. This is largely because the Z is strongly influenced e opt by the depth distribution of the limiting nutrient. In general, the effect of either increasing respiration or decreasing the euphotic depth is to make the optimal depth shallower. DISCUSSION One dimension to two - the influence of baroclinicity For sake of this discussion it is convenient to divide the optimal mixing depth model into two compartments - light and

nutrients. In the "light" compartment it is possible to describe the relationship between mixed layer depth and (Pt:R) from fundamental principles of photosynthetic kinetics combined with assumptions concerning the magnitude of respiration. By contrast, the "nutrient" compartment requires knowing the depth profiles of the specific nutrient and an empirical calculation of entrainment. I n t h e one dimensional-depth t h e d e n s i t y d i s t r i b u t i o n of

model t h i s i s m a r k e d l y i n f l u e n c e d b y t h a t water mass; Furthermore

if

t h e nu-

t r i e n t - d e n s i t y r e l a t i o n s h i p i s p r o j e c t e d a s a c r o s s s e c t i o n of t h e w a t e r mass,

thereby adding t h e dimension of

distance,

the depth of

c r i t i c a l and o p t i m a l mixing w i l l be markedly a f f e c t e d by t h e d e n s i t y s t r u c t u r e i n w a t e r mass.

The degree of baroclinicity is proportional to geostrophic flow or mass transport in the horizontal direction. Thus the extremes in mass transport will reflect extremes in optimal and critical depths. To be specific, the large gyre as we have observed in Sargasso Sea will have deep critical and optimal depths. Whereas regions of active transport, e.g. where isopycnals are uplifted, will have shallow critical and optimal depths. The examples set down here as two extremes argues that in areas where high density nutrient rich water is near the surface (e.g. Gulf of Maine) the amount of nitrate supplied by mixing is greater than in the Sargasso Sea. Hence the standing crops of phytoplankton in the Gulf of Maine is proportionally greater than in the Sargasso Sea. This is clearly borne out by sea surface measurements (See Yentsch, 1974). This suggests that spatial patterns in primary production might be accurately assessed from estimates which combine baroclinicity and the depth of the mixed layer. The idea is not new, but

requires knowing the d.ensity distribution on a reasonably fine scale. It is possible to obtain the necessary data in areas where baroclinic change occurs over very short distances - for example in frontal regions. I have combined this approach with modeling to describe features such as the optimal and critical mixing depth. The model however fails in these frontal regions because there is no theory to combine isopycnal with vertical mixing. In other words, there is no way of estimating the mixing depth when isopycnals are anything less than vertical. SUMMARY The principal factors regulating phytoplankton growth in a mixed layer have been summarized. A two compartment model demonstrates 0(10-2), b u t i n t h e B a l t i c Sea .C > O(lO-’).

179 In the baroclinic case the potential vorticity is conserved according to the Ertel’s relation

f3

The condition for prevalence of topography over from the equality of and

frequency

disturbing the density

caused by

field

-effect may be obtained

the motion forced up the

to the frequency provided by

slope

6 -effect

alone in the following form (mines 1977)

fL a>------

(4)

R N .

Under conditions of the Baltic Sea, we obtain

a > In view of the fact that there is a great number

a >

in the Baltic, the

of

regions with the slope

appearance of topographic baroclinic waves is

most probable. Synoptic eddies in the Baltic Sea were observed first by Keunecke and Magaard in 1975. In 1976, topographic waves in the Bornholm Basin in the south-west part

were obtained by Simmons as a result of calculations on a

of the Baltic

multilayered model ( Simmons, 1976). In 1977,the BOSEX out in the Baltic Baltic Sea;

experiment of the ICES/SCOR

Joint Working Group was carried

Two mooring stations were installed, by the Department of the

one of them in the

the eastern corner of it. The

northern corner of the polygon and the other in

site of the BOSEX area in the Baltic is given in

Fig. 16, and the bottom topography as well as the locations of mooring stations in Fig. 17. Let us consider currents in deep

horizons of station

N

of 1977 polygon. In

Fig. l8,time series of the velocity components and of temperature at station N are presented, for period 400 hours. We see that inertial fluctuations are dominant there. After filtering out short periods, observed in the time series of the

fluctuations of low frequency can be

considered characteristics (Fig.19). The dominant

periods were found equal to 68 and 44 hours. In Fig. 18 and 19, we can see that the current velocity and temperature have the same dominant periods but with a phase shift. The effect can be

explained by topographic waves. In the

Baltic

Sea temperature increases with in the depth in bottom layers. Thus the upward

180

Fig.16. Location of the BOSEX area in the Baltic Sea.

Fig.17. Bottom-topography in the BOSEX-77 area.

181

15

ws 0

-15

11.70 OC

5.10

400 hrs

Fig.18. Variation of the velocity component and temperature at the 105 m level at

0

station

10

N

during

20

30

the

BOSEX experiment.

40

L,ig.19. Variation of the velocity component and temperature after high-frequency filtrations at the 105 m level during the BOSEX-77 experiment.

182 fluxes

along t h e slope t r a n s p o r t warm water up. When t h e d i r e c t i o n of v e l o c i t y

changes and water

begins t o move downwards, temperature must

have i t s maximum

value. d i s p e r s i v e r a t i o of bottom-trapped topographic waves i s w r i t t e n a s

The

[Rhines,l980)

w =

N a L

-

N K H

cth

where

k2

= k

f

2

+ L

2 k, R

-wave numbers along and

a For

c1 =

(5)

~

E

0.015 and

across the slope,

-bottom slope.

N = 0.015 sec

-1

from r e l a t i o n ( 5 ) , p e r i o d s equal t o o r

l a r g e r than 40 hours a r e obtained. This corresponds t o t h e observed p e r i o d s . By bottom-trapped topographic waves t h e k i n e t i c energy i n c r e a s e s with depth. I n F i g . 20 t h e v e r t i c a l d i s t r i b u t i o n of t h e ’ k i n e t i c energy

N

and

E i s presented.

about bottom-trapped

measured a t s t a t i o n s

I t can be seen t h a t i n accordance with t h e assumption

topographic waves a t s t a t i o n

N

k i n e t i c energy i n c r e a s e s

with depth. I n 1979, experiments t o study synoptic v a r i a b i l i t y on t h e BOSEX a r e a were repeated.

However, t h e dimensions and l o c a t i o n of t h e a r e a were a s l i g h t l y

changed ( F i g . 2 1 ) . I n 1979 cross-like,

autonomous mooring s t a t i o n s

(AMS) were i n s t a l l e d

so t h a t simultaneously t h r e e AMS were l o c a t e d along t h e bottom

slope and t h r e e i n t h e

t r a n s v e r s a l d i r e c t i o n . The d i s t a n c e between AMS was 10

miles. All t h e AMS were provided with Aanderaa RSM-4 c u r r e n t meters, whereas one of t h e instruments was always i n a bottom l a y e r . During t h e s t a g e o f c u r r e n t measurements and a f t e r it up t o the l a t e autumn,

8 d e n s i t y mappings with a N e i l Brown Mark I11 CTD probe were completed i n t h e a r e a . Each mapping

c o n s i s t e d of 2 1 s t a t i o n s

with a 5 m i l e s t e p . The

d u r a t i o n of a

mapping, one day, ensured q u a s i s t a t i s t i c a l approach. The d a t a obtained by CTD mappings w e r e l a t e r used t o i n v e s t i g a t e t h e s p a t i a l s t r u c t u r e of thermohaline f i e l d s and t o c a l c u l a t e dynamic topography with t h e aim of t h e i n d i r e c t determination

of a geostrophic c u r r e n t f i e l d i n t h e a r e a .

For a more d e t a i l e d study of t h e s p a t i a l d i s t r i b u t i o n of thermohaline

fields

i n t h e upper layer,experiments with a towed measuring complex were c a r r i e d o u t i n t h e a r e a . The complex,which was constructed i n t h e

Department of t h e B a l t i c Sea

of t h e I n s t i t u t e of Thermophysics and E l e c t r o p h y s i c s

of t h e Estonian S.S.R.

of t h e Academy of Sciences

i n 1978,enables us t o o b t a i n i n t h e 4 0 meters upper l a y e r

with a h o r i z o n t a l r e s o l u t i o n of 200 meters, temperature, s a l i n i t y and d e n s i t y s e c t i o n s . This i s achieved by t h e s t a b l e

wave-like motion of t h e

c a r r y i n g body

183

50

,

250 [cp */sec2

I50

I

I 20

40 60

80

100 120

Fig.20. V a r i a t i o n of k i n e t i c energy along t h e v e r t i c a l a t s t a t i o n s i n t h e BOSEX-71

of CTD

N

and

E

area.

r e g i s t e r s , being towed a f t e r t h e v e s s e l with t h e v e l o c i t y of 5-7 knots.

The r e s u l t s of t h e i n v e s t i g a t i o n s c a r r i e d o u t i n the a r e a a r e r e p o r t e d i n t h e paper by A i t s a m , Elken, Pavelson, Talpsepp ( 1 9 8 0 ) . I n t h e following, t h e main r e s u l t s are b r i e f l y discussed. For t h e i n d i r e c t determination of t h e v e l o c i t y f i e l d , t h e r e l a t i v e dynamic topography (RDT) ( d i f f e r e n c e between dynamical h e i g h t s ) was c a l c u l a t e d according

P

t o formula

where

pl;

g

- gravitational acceleration,

p

- water d e n s i t y , p2 - p r e s s u r e v a l u e s .

A s f a r a s t h e r e i s no

c l e a r l y expressed zero s u r f a c e i n t h e B a l t i c S e a , t h e

determination of t h e a b s o l u t e v e l o c i t y using t h e dynamic method remains undecided. RDT i s t h e stream f u n c t i o n of t h e r e l a t i v e v e l o c i t y and i n our c a s e , t o t h e change

of RDT

by 1 cm per 5 miles corresponds t h e r e l a t i v e v e l o c i t y change 8 . 6 5 cm/sec.

While compiling RDT maps, t h e q u e s t i o n about t h e

e x a c t n e s s of i t s

calculation

on t h e b a s i s of s i n g l e mappings without any time averaging a r i s e s . I n p r o f i l e s of

184

N

Po I

Fig.21. Location ( r i g h t ) and t h e map of t h e bottom-topography

( l e f t ) of t h e

BOSEX a r e a .

a s i n g l e mapping, high-frequency n o i s e i s p r e s e n t . Other causes of e r r o r s are t h e

asynchronism of measurements and t h e presence o f t h e time t r e n d of synoptic processes i n t h e obtained data. To e v a l u a t e e r r o r s , d a i l y s e r i e s of p r o f i l e s w e r e twice carried o u t a t t h e c e n t r a l s t a t i o n and t h e mean square e r r o r s o u t t h a t i n t h e presence of a pycnocline between l e v e l s square e r r o r

u

E

were determined. I t turned p1

and

p2

,

o f RDT along h o r i z o n t a l plane more than twice exceeds

is no pycnocline i n t h e l a y e r (pl

;

p 2 ) , then values o f

ff

and

E

are

t h e mean E

.

I f there

of the

same o r d e r of magnitude.

I n f i g u r e s 2 2 and 23, RDT maps c a l c u l a t e d by making use of o b j e c t i v e a n a l y s i s are presented.

185

Fig.22. Maps of t h e r e l a t i v e dynamic topography f o r surveys

On maps 1-4

1-4.

(Fig.22) a p o s i t i v e eddy-like p e r t u r b a t i o n of RDT w i t h a weak inten-

s i t y i s observed i n t h e upper c e n t r a l p a r t of t h e area. On the b a s i s of t h e s i n g l e mapping, it may be assumed t h a t t h e p e r t u r b a t i o n i s a random r e s u l t o f t h e i n t e r n a l wave noise.

However, t h e presence of t h e p e r t u r b a t i o n on maps o f r e p e a t e d mappings

allows u s t o show q u i t e convincingly t h a t t h e p e r t u r b a t i o n (lowering of i s o p y c n a l ) , R 20 km, Rx 2 15 km, i s o f synoptic o r i g i n . The v e l o c i t y of Y I t h e p e r t u r b a t i o n displacement i s o f t h e o r d e r of C ?. 1.5 cm/sec, whereas t h e ve-

with axes

l o c i t y i s d i r e c t e d along averaged i s o b a t h with shallower water l e f t t o t h e r i g h t . A t t h e c e n t r a l s t a t i o n t h e d i r e c t l y measured r e l a t i v e v e l o c i t y corresponds w e l l

enough t o t h e geostrophic v e l o c i t y determined from RDT. On maps 6 and 7 iFig.23) a n e g a t i v e eddy-like p e r t u r b a t i o n o f RDT (lift of isopycnal) of t h e whole water column w a s p r e s e n t i n August. meter of t h e almost c i r c u l a r p e r t u r b a t i o n i s placement

C

R

2 2 cm/sec, whereas t h e v e l o c i t y

The h o r i z o n t a l d i a -

2 20 km and t h e v e l o c i t y o f d i s i s d i r e c t e d along t h e i s o b a t h s

186

3 (90,101

I \

35,-16.08.79

Fig.23. Maps of the relative dynamics topography for surveys 6 - 7 .

187 a 3 f o r maps 1-4.

I n 10 days

t h e r e l a t i v e v e l o c i t y i n c r e a s e d b y a f a c t o r two.

Eddy-like p e r t u r b a t i o n s of RDT and t h e i r displacement may be described a s t h e

sums of two f l a t

1,

topographic waves with wave numbers ( -k,X

( k,R

).

The

averaged topography of t h e deep p a r t of t h e a r e a was approximatedby a plane with

a

values

= 5-10-~

Ax

.

S i t u a t i o n s , presented i n Fig.23 were modelled by Elken and

X

=40 km,

-f

Y

=-40 km were used. Numerically estimated phase v e l o c i t y

Cf = (0; -3) cm/sec and p e r i o d Tp = 1 5 . 6 days correspond t o t h i s case. The

fact

t h a t t h e phase v e l o c i t y of waves exceeds t h e v e l o c i t y of p e r t u r b a t i o n displacement -3

C = (0 ; -2)

cm/sec.

No i n s t r u m e n t a l

may be caused by t h e average c u r r e n t

measurements were r e a l i z e d during

"u

= (0 ; 1) cm/sec.

t h e period. R e l a t i o n s of t h e

geostrophic s h i f t s of v e l o c i t y i n thermocline and h a l o c l i n e correspond t o topographic waves. Doubling of t h e amplitude may be

explained by t h e v e r t i c a l s h i f t of t h e

100 m l e v e l , b u t i n t h a t case

average v e l o c i t y 1.3 cm/sec on t h e

t h e value of

t h e phase v e l o c i t y becomes worse. I n t e r p r e t i n g maps 1-4 f o r which values c u r r e n t measurements was estimated.

(Fig.22) wave l e n g t h s were estimated

i

as

t h e average

I n t h e presence of t h e average c u r r e n t

i s determined a s follows ;

+

Cf

=

+

Cf

km,A = 4 0 km, Y instrumental

, T = 23.8 days. From P c u r r e n t value i!i = (-0.4 ; 1.0) cm/sec

Cf = ( 0 ; 1 . 9 ) cm/sec

,

X =25

o=;I

with t h e displacement v e l o c i t y of t h e RDT

+

+ u

i

u = ( 0 ; V), t h e phase v e l o c i t y

and i t s value i s comparable

perturbation

-f

C

2

(0;

1.5) cm/sec.

From t h e experiments described above, it may be concluded t h a t low-frequency processes with s p a t i a l s c a l e s of t h e order of t h e Rossby i n t e r n a l r a d i u s and with time s c a l e s from s e v e r a l days t o s e v e r a l

decades become apparent i n t h e

BOSEX

a r e a . The r e s u l t s of t h e measurements c a r r i e d o u t i n 1977 may be i n t e r p r e t e d i n

t e r m s o f bottom-trapped waves. A considerably complicated s p a t i a l s t r u c t u r e of thermohaline f i e l d s w a s observed

i n t h e upper l a y e r . But p e r t u r b a t i o n s with s c a l e

R

2

30 km were v i s i b l e even

i n t h e s e d a t a . I n t h e d a t a of v e l o c i t y measurements a t mooring s t a t i o n s i n 1979, p e r t u r b a t i o n s of t h e synoptic scale become apparent, b u t t h e i r i n t e r p r e t a t i o n on t h e b a s i s of l i n e a r t h e o r i e s w a s found impossible.

Acknowledgements

The a u t h o r is o b l i g e d t o the whole s t a f f of t h e Section of t h e Marine Physics of t h e B a l t i c Sea Department f o r c a r r y i n g o u t experiments i n t h e BOSEX a r e a . H e i s p a r t i c u l a r l y thankful t o h i s follow s c i e n t i s t s J. Elken, J. Laanemets, J . Pavelson and L. Talpsepp by whom the experimental d a t a used i n t h e paper were processed and analized.

188

REFERENCES Aitsam A., Elken J., Pavelson J.,Talpsepp L . Preliminary results of the study of spatial and temporal characteristics of the synoptic variability in the Baltic (in press). Aitsam A., Laanemets J., Lilover J., 1978. Finestructure in the BOSEX polygOn.PrOC. of the XI Conference of Baltic Oceanographers,Rostock, pp.524-533. Aitsam A., Laanemets J., Lilover M.,1980. Finestructure of the Baltic Proper; The Study and Modelling of

processes in the Baltic,Tallinn (in press).

Ratchelor G.K.,1959. Small-scale variation of convected quantities like temperature in turbulent fluid. ,J.Fluid Mech., 5,l; pp.113-133. Bock K.H.,1971.Monastkarten der Dichte des Wassers in der Ostsee verschiedene

dargestellt fur

Tiefhorizonte.Deutsche Hydrographische Institut Hamburg.

Falkenmark M., Mikulski Z.,1974. Hydrology of the Baltic Sea International Hydrological Decade Project Document Nr.1. Stockholm-Warszawa. Fuglister F., 1972. Cyclonic rings formed by the Gulf Stream 1965-1966. Studies in physical oceanography

. v.1.A.

Gordon (Ed.) Gordon and Breach

Science Publishers.

Gregg M.C., 1976. Finestructure and Microstructure Observations During the Passage of a Mild Storm. J. Phys. Oceanogr. 6, pp.528-555. Kielman J., Krauss W., Keunecke K.H.,1973. Currents and

stratification in the Belt

Sea and the Arcona Basin during 1962-1968. Kieler Meeresforshungen. 29,2,pp.90-111. Keunecke K.M., Magaard L. 1975. Measurements by means of towed thermistor cables and

problems of their interpretation to mesoscale processes. Memoires Societe

des Sciences de Liege

6e serie, 7; 147-160.

Klemas V., Polis D.F.,1977. Remote sensing of estuarine fronts and their effects on pollutants. Programmetric engineering and remote sensing, 43; 594-612 Krauss W.,1973. Wind driven

oscillations of an encloused basin with bottom friction.

Deutsche Hydrographische Zeitschrift.,26, 1 ; 1-9. Laanemets J.,Lilover M.,1980. The Data Processing Scheme of the Measurements with Neil Brown Mark I11 CTD. The Study and Modelling of Processes in the Baltic

I

[in press). Matthaus W.,l979. Langzeitvariationen von Temperatur Salzgehalt und Sauerstaftgehalt der zentralen Ostsee

.

Beitr.zur Meereskunde,Nr.42;41-93.

Mooers C.N.K.,Flagg C.N., Boicourt W.C.,1978.

Prograde and Retrograde fronts. Oceanic

Fronts in Coastal Processes. Ed.by M.J. Browmann and Wayne E. Esiaias.Springer Werlag. Nygvist B., 1974. Osterjon blomnar. Forsking och

Framsteg. 6;l-2.

Platt T., Denman K., 1975. A general equation for the

mesoscale distribution of

phytoplankton in the Sea. Memoires Societe Royale des Sciences de Liege. 6e serie tome

7; 31-42.

Powell T.M., Richardson P.I., Dillon T.M., Dozier B.A., Godden D.A.,Myrup L.O.,1975.

189 Spatial scales of current speed and phytoplankton fluctuations in Lake Tahoe. Science 189; 1088-1090. m i n e s P., 197+. Edge-, bottom- and Rossby waves in a rotating stratified fluid. Geophys. Fluid Dyn.,l, 273-302. m i n e s P.,1977. The Tsernjakova A.M.,

dynamics of unsteady currents. The Sea VI.

Romanov A.S.,1980. Nonuniformities of the chemical fields in the

region of POLYMODE

caused by eddy structure.(in russian) Oceanology 20, I; 64-71.


191

+

HYDRODYNAMIC CONTROL OF MARINE PHYTOPLANKTON PRODUCTION: THE PARADOX OF STABILITY

L. LEGENDRE GIROQ, D6partement de biologie, Universitk Laval, Qukbec, QUEBEC

G1K 7P4

ABSTRACT Phytoplankton studies in a given environment

are generally conducted on a small

range of scales, so that no clear picture emerges as to the factors fundamentally critical to the dynamics of phytoplankton.

In the Estuary of the St Lawrence, where

a wide range of observation scales are covered, stability of the water column is the only hydrodynamic factor significant to phytoplankton that is observed on all spatiotemporal scales.

In various environments (estuarine,coastal, oceanic, frontal

regions) vertical stability is reported to influence phytoplankton on scales from 6.2 h to one year, the forcing mechanisms being climatic, river runoff, tides or

winds.

An apparent paradox is that neither stabilization nor destabilization of the

water column favours phytoplankton production: indeed, at any

spatio-temporal scale,

only the alternation of stabilization and destabilization is an hydrodynamic mechanism conducive to enhance primary production. A simple conceptual model of phytoplankton dynamics accounts for instances of the temporal succession of stratification and destratification of the water column, observed on a wide range of scales, and it may be applied to such structures as fronts and intermittent upwellings.

It is therefore proposed to characterize the phytoplankton production

potential of marine ecosystems by their frequency of stabilization-destabilization, since the resulting input of mechanical energy does enhance the primary production. Other factors such as temperature, turbidity, nutrient background, and so on, may limit the production potential built up by the alternation of stabilization and destabilization.

Contrary to marine ecosystems driven by nutrient regeneration,

which are vertically closed systems, those dominated by stabilization-destabilization vertically exchange nutrients regenerated at depth and energy stored by the phytoplankton at surface, which is one of the basic mechanisms of marine phytoplankton production.

'Contribution to the programme of GIROQ (Groupe interuniversitaire de recherches ockanographiques du Qukbec).

192 FACTORS CONTROLLING THE DYNAMICS OF PHYTOPLANKTON Understanding marine hydrodynamics, as a constraint on the dynamics of ecosystems, requires an assessment of its impact on the production of phytoplankton.

Indeed,

phytoplankton production is primarily responsible for the transfer of materials from the abiotic environment to the ecosystem, and also for the input of energy into the marine biosphere. Since the works of Denman (1976) and Denman and Platt (1975, 1976), oceanographers describe the spectral dynamics of phytoplankton in terms of an interplay between hydrodynamics and ecophysiology.

Using data series from the Estuary and the Gulf of

St Lawrence, these authors interpreted the variance spectrum of chlorophyll as a dependence of phytoplankton abundance on the rate of turbulent energy transfer at high wavenumbers, and a dominance of the lower wavenumbers by the rate of cell

-

.

reproduction.

On the contrary in the Middle Estuary of the St Lawrence, inhibition

of phytoplankton production, rather than growth, was invoked by Demers et al. (1979) as controlling the low frequencies of the chlorophyll spectrum. Furthermore, Lekan and Wilson (1978) observed, in Long Island Sound, characteristic scales on which phytoplankton distribution was respectively related to nutrients, hydrodynamics, and biological growth rate.

This new approach to marine phytoplankton (other papers are

cited below) stresses the fundamental importance of the spatio-temporal scales, and also the diversity of factors involved in the dynamics of phytoplankton according to the scales. However, despite this diversity, unifying concepts must be sought. For instance, a recent work by Fortier and Legendre (19791, in the St Lawrence Estuary, showed that fine-scale fluctuations of phytoplankton photosynthetic activity are related to the vertical by the Richardson number.

stability of the water column, as measured

The analysis of a stability spectrum gave some insight

into the low frequency control of phytoplankton dynamics by the hydrodynamics, thus potentially extending over a broad range of scales a unifying hydrodynamic concept. The main problem in defining such concepts is that, in a given environment, only a few studies are generally devoted to the phytoplankton, so that only a limited range of scales is covered.

On the contrary, many studies must be

conducted on various observation scales and on various phytoplankton parameters, for a clear picture to emerge as to the factors fundamentally critical to the dynamics of phytoplankton over a significant range of spatio-temporal scales. The phytoplankton of no marine ecosystem has yet been studied under such a broad perspective.

However a wide range of observation scales

tens of kilometres, and from a few minutes to months

- from a few metres to

- are covered by

19 of the

papers, recently published on the phytoplankton of the St Lawrence Estuary, in which phytoplankton biomasses (number of cells, chlorophyll, ATP) and production dynamics (primary production, photosynthetic capacity, photosynthetic efficiency)

are considered. According to the observation scale (Table 1: columns) and to the phytoplankton parameter investigated (within Table l), various environmental and/or endogenous factors are reported to influence the phytoplankton, on different spatio-temporal scales (Table 1: rows); M and M are the lunar fortnightly f 2 (327.9 h) and the principal lunar semi-diurnal (12.4 h) harmonic tidal components. It is obvious from Table 1 that, in the St Lawrence Estuary, many different environmental and biological factors interplay to shape the dynamics of phytoplankton The wind, which is a dominant factor in other coastal environments (see below), is not reported here since, in a stratified estuary, vertical mixing is caused mainly by the shear between layers with different relative velocities and densities rather than by the wind. and the observation scales

The relationship between the factors in Table 1

is striking, and it stresses dramatically the critical

importance of the observation window.

Biological oceanographic studies are

classically conducted on a monthly or a weekly basis, and on a grid of stations many nautical miles apart, which is clearly inadequate for estuarine or coastal phytoplankton. Another problem apparent from Table 1 is that only biomasses (especially in situ fluorescence, as an index of in vivo chlorophyll a: Lorenzen, 1966) may technically be sampled with high frequency; experiments on new methods to measure automatically primary production (Massol and Ballester, 1976; Roy and Legendre, 1979, 1980) will eventually overcome this constraint. In Table 1, hydrodynamic factors are evidenced at each observation scale; these factors also occur on various spatio-temporal scales. However, stability of the water column emerges as the only hydrodynamic factor, significant to phytoplankton, observed on all spatio-temporal scales. On a large geographic scale, Sinclair (1978) found that l o w phytoplankton biomasses in the St Lawrence Estuary are associated with areas of intense horizontal and vertical mixing, conditions that are not conducive to phytoplankton growth and may therefore explain the low biomasses.

On the contrary, regions

with greater stratification are potentially more productive environments, thus supporting higher biomasses.

Temporal variability of phytoplankton biomasses

and production in the Lower Estuary of the St Lawrence is interpreted by Sinclair (1978) in terms of the neap-spring (M ) tidal cycle. The increased tidal mixing f of the spring tide, with consequent reduction in stratification, is paralleled by reduced phytoplankton production; this is caused by an increased rate of loss of cells from the photic layer, due to higher vertical diffusivity and decreased upward advection.

The same is observed by Demers et al. (1979) in the Middle

Estuary, where phytoplankton cells, healthier during the neap tide, show higher chlorophyll concentrations per unit cell than during the spring tide. A l s o , pure endogenous rhythms of the photosynthetic capacity may be evidenced (Demers and Legendre, 1979) in the relatively homogenous environment resulting from the spring-tidal destratification.

194 TABLE 1 Schematic c o n c l u s i o n s of 1 9 s t u d i e s on t h e phytoplankton of t h e S t Lawrence Estuary.

I OBSERVATION SCALE FACTORS LARGE SCALE FACTORS

Month

Week

10-50 km

Seasonal v a r i a t i o n s Salinity gradients

CELLS ( C a r d i n a l and B6rardT h e r r i a u l t , 1976; C a r d i n a l and L a f l e u r , 1977)

Circulation

CHLOROPHYLL ( P l a t t , 1972; S i n c l a i r , 1978)

Nutrients

PRODUCTION (Sevigny e t a l . , 1979; Steven, 1974)

Vertical s t a b i l i t y

CHLOROPHYLL and ATP ( S i n c l a i r , 1978)

Turbulence Mf VARIATIONS


CHLOROPHYLL and PRODUCTION ( S i n c l a i r , 1978)

C r i t i c a l depth

CHLOROPHYLL and PRODUCTION ( S i n c l a i r , 1978)

Tidal incursion M2 VARIATIONS

Vertical s t a b i l i t y T and S g r a d i e n t s

I n t e r n a l waves

SLACK WATER VARIATIONS Vertical s t a b i l i t y LIGHT

Vertical d i s t r i b u t i o n High frequency v a r i a t i o n s [=1Hz) PHYTOPLANKTON Endogenous rhythms

C a r b o x y l a t i o n pathways Growth Senescence

195 TABLE 1 (continued)

OBSERVATION SCALE Hour 10-50 m

FACTORS

Minute -5 m

LARGE SCALE FACTORS

Seasonal v a r i a t i o n s S a l i n i t y gradients Circulation

Nutrients Vertical stability CHLOROPHYLL (Denman, 1976; Denman and P l a t t , 1975, 1976) PHOTOSYNTHETIC CAPACITY (Demers and Legendre, 1979)

CHLOROPHYLL (Demers e t a l . ,

Turbulence M

VARIATIONS f Vertical s t a b i l i t y

1979)

CHLORO. and PHOTOS. CAPACITY ( F o r t i e r and Legendre, 1979)

C r i t i c a l depth

CELLS (Demers and Legendre, 1979; L a f l e u r e t a l . , 1979)

Tidal incursion M

2

VARIATIONS


PHOTOSYNTHETIC CAPACITY ( F o r t i e r and Legendre, 1979) CELLS ( F o r t i e r e t a l . ,

1978)

T and S g r a d i e n t s

I n t e r n a l waves

CELLS ( L a f l e u r e t a l . , 1979) CHLOROPHYLL ( D e m n , 1976; CHLOROPHYLL ( T h e r r i a u l t and Denman and P l a t t , 1975, 1976) Lacroix, 1976) PHOTOSYNTHETIC CAPACITY ( F r e c h e t t e and Legendre, m s )

SLACK WATER VARIATIONS

CHLOROPHYLL (Auclair e t a l . , m s )

Vertical s t a b i l i t y LIGHT

PHOTOSYNTHETIC EFFICIENCY (Roy and Legendre, 1980)

Vertical distribution

PHOTOSYNTHETIC CAPACITY

High frequency v a r i a t i o n s (=I Hz)

( F r e c h e t t e and Legendre, 1978)

PHYTOPIANKTON

~

PHOTOSYNTHETIC CAPACITY (Demers and Legendre, 1979) CHLOROPHYLL ( A u c l a i r e t a l . , m s )

Endogenous rhythms

PHOTOSYNTHETIC CA PAC I TY ( F r g c h e t t e and Legendre, 1978)

C arboxy l a t i o n pathways

CHLOROPHYLL ( F o r t i e r and Legendre, 1979)

CHLOROPHYLL (Denman, 1976; Denman and P l a t t , 1975, 1976)

Growth

CHLOROPHYLL (Demers e t a l . , 1979)

Senescence

A l t e r n a t i n g stratification-destratification a l s o occurs, i n an e s t u a r y , on a semi-diurnal

(M

2

)

scale.

I n t h e S t Lawrence Estuary, F o r t i e r and Legendre (1979)

r e p o r t p e r i o d i c maxima of t h e p h o t o s y n t h e t i c c a p a c i t y coincident with maximum s t r a t i f i c a t i o n on a 12.5-h c y c l e , a s estimated by t h e Richardson number; high c a p a c i t y p e r s i s t s f o r about 1 t o 3 hours a f t e r t h e beginning of t h e v e r t i c a l mixing (low Richardson numbers).

( m s ) have observed

Furthermore, Auclair e t a l .

5 t o 6-h endogenous p e r i o d i c i t y of c h l o r o p h y l l , i n phase with s l a c k waters.

Turbulent mixing of phytoplankton c e l l s causes t h e i r l i g h t regime t o be l e s s

- according ( i n press) - i n

p r e d i c t a b l e , which r e s u l t s

t o t h e light-shade a d a p t a t i o n mechanism

described by Falkowski

t h e development of l a r g e i n t e r n a l

chlorophyll pools; conversely, a t t i m e s of s l a c k water, smaller concentrations of a c t i v e chlorophyll are observed. I n a d d i t i o n t o t h e S t Lawrence Estuary, o t h e r papers s t r e s s t h e i n f l u e n c e of v e r t i c a l s t a b i l i t y on phytoplankton.

The b e s t known a r e those of Gran and

Braarud (1935), Riley ( 1 9 4 2 ) and Sverdrup (19531, explaining t h e seasonal phytoplankton dynamics of temperate regions i n terms of v e r t i c a l mixing: t h e autumn bloom i s followed by a progressive i n t e n s i f i c a t i o n of t h e mixing, which l e a d s t o t h e l i g h t l i m i t a t i o n of w i n t e r phytoplankton and a l s o t o the replenishment of t h e s u r f a c e l a y e r i n n u t r i e n t s ; a t t h e end of t h e w i n t e r , i n c r e a s i n g s t r a t i f i c a t i o n ( c r i t i c a l depth: Sverdrup, 1953) r e s u l t s i n t h e s p r i n g o u t b u r s t , which r a p i d l y exhausts t h e a v a i l a b l e n u t r i e n t s , s o t h a t t h e following summer production depends e s s e n t i a l l y on t h e i n s i t u regeneration of n u t r i e n t s .

The

l e a d i n g f o r c e s of t h i s mechanism a r e c l i m a t i c , but r i v e r runoff may a l s o d r i v e t h e seasonal dynamics of c o a s t a l phytoplankton, a s i n Indian A r m , a f j o r d of WesteA Canada (Gilmartin, 1964) : t h e increased r i v e r runoff i n winter d e s t a b i l i z e s t h e water column and t h u s favours a replenishment of t h e p h o t i c l a y e r i n n u t r i e n t s , which a r e used by t h e phytoplankton a t springtime, when t h e water column s t a b i l i z e s v e r t i c a l l y with decreasing r u n o f f . Neap-spring t i d a l v a r i a t i o n s a r e known t o i n f l u e n c e t h e dynamics of phytoplankton i n c o a s t a l a r e a s .

I n t h e York River, a t r i b u t a r y of Chesapeake

Bay, s p r i n g - t i d a l d e s t r a t i f i c a t i o n r e d i s t r i b u t e s n u t r i e n t s and oxygen i n t h e water column (Webb and D ' E l i a , 1980). r e i n t e r p r e t e d d a t a from Winter e t a l . Northwestern United S t a t e s

-,

According t o S i n c l a i r (1978), who (1975) on t h e Puget Sound

s t r a t i f i c a t i o n , which p a r t i a l l y follows t h e neap-spring c y c l e . Pingree e t a l .

-a

fjord i n

primary production t h e r e i s w e l l c o r r e l a t e d t o Surveys by

(1975, 1976, 1977, 1978) on phytoplankton d i s t r i b u t i o n s on t h e

northwest European Shelf showed f r o n t a l movements, caused by t h e c y c l e of v e r t i c a l mixing induced by t h e a l t e r n a t i o n of neap and s p r i n g t i d e s .

Summer f r o n t s a r e

between regions of well-mixed and of w e l l - s t r a t i f i e d water: i n c r e a s e d t i d a l

mixing a t s p r i n g t i d e s modifies t h e p o s i t i o n of t h e f r o n t , by changing t h e s t r a t i f i c a t i o n of t h e w a t e r column.

The p e r i o d i c enrichment of s u r f a c e waters

i n n u t r i e n t s , followed by s t a b i l i z a t i o n a t neap t i d e s , d e l i n e a t e s a r e a s of t h e A s i m i l a r mechanism i s described by

ocean with high phytoplankton production.

Fournier e t a l . (1979) f o r the S c o t i a n Shelf (Eastern Canada), where changes i n w i n t e r c h l o r o p h y l l c o n c e n t r a t i o n s are c o r r e l a t e d t o t h e s t e e p n e s s of a subs u r f a c e shelf-break f r o n t ; according t o t h e f o r c i n g mechanism p o s t u l a t e d , t h e o s c i l l a t i o n p e r i o d of t h e f r o n t i s estimated between 15 and 60 days.

Decreased

f r o n t a l steepness reduces t h e depth of t h e mixed l a y e r , which enhances t h e phytoplankton production. The wind i s another d e s t a b i l i z i n g a g e n t , t o which t h e dynamics of phytoplankton responds.

Takahashi e t a l .

(1977) r e p o r t abrupt i n c r e a s e s i n n u t r i e n t s , ascribed

t o s t r o n g winds, i n t h e t o p 1 0 m of Saanich I n l e t (Western Canada), l e a d i n g t o occasional*summer phytoplankton blooms. noted by Webb and D'Elia

However, examination of t h e i r d a t a , a s

(1980), a l s o suggests a r e l a t i o n s h i p t o t h e neap-

Iverson e t a l . (1974) observed, i n Auke Bay (Alaska), -1 ) mixed n i t r a t e i n t o t h e p h o t i c l a y e r from deeper i n

spring t i d a l cycle.

t h a t high winds ( > 4 m ' s

t h e water column, r e s u l t i n g i n major summer phytoplankton blooms. Legendre e t a l .

Similarly

( m s ) p a r t i a l l y e x p l a i n t h e d i f f e r e n c e i n phytoplankton production

between s o u t h e a s t e r n Hudson Bay and i t s c o a s t a l Manitounuk Sound, i n t h e summer months, a s a response of phytoplankton t o l o c a l l y reduced wind stress, t h e more productive upper Sound being s h e l t e r e d behind t h e Manitounuk I s l a n d s . e t al.

Therriault

(1978) have demonstrated t h a t phytoplankton production is indeed

c o n t r o l l e d by wind s t r e s s induced turbulence, f o r wind v e l o c i t i e s g r e a t e r than

-1

4-5 m-s

S t a b i l i t y a l s o i n f l u e n c e s t h e phytoplankton t a x a found i n t h e w a t e r column. The seasonal succession of diatoms and d i n o f l a g e l l a t e s i n temperate regions p a r a l l e l s t h e seasonal v a r i a t i o n s i n primary production, and t h e v e r t i c a l s t r u c t u r e of phytoplankton communities responds ( I g n a t i a d e s , 1979) t o seasonal changes i n s t a b i l i t y . .

I n a r e a s s u b j e c t e d t o t i d e induced v a r i a t i o n s i n s t a b i l i t y ,

a s t h e C e l t i c Sea, p a t t e r n s of phytoplankton succession vary with t h e c h a r a c t e r i s t i c s of t h e mixing (Holligan and Harbour, 1977).

According t o Wangersky (1977),

s p e c i e s composition i n upwelling ecosystems r e f l e c t v a r i a t i o n s i n * n u t r i e n t s , which depend on t h e s u r f a c e s t a b i l i z a t i o n of upwelled water.

THE PARADOX OF STABILITY I t follows t h a t (Takahashi e t a l . ,

polar w a t e r s ,

[.- -3

1977)

' I . . .

p a r t i c u l a r l y i n temperate o r

t h e upper l a y e r s of t h e water column, where most p l a n t

a c t i v i t y occurs, a r e mixed or replaced with deep or i n t e r m e d i a t e depth w a t e r by v a r i o u s p h y s i c a l a c t i o n s : t i d e s , winds, r i v e r run-off

, and

currents

[..-3

FREQUENCY OF STAB1 LIZATION- DESTABILIZATION ( N o . sequences of rtabilizotion-destabilization per yeor)

Fig. 1. Frequencies of stabilization-destabilization significant to the dynamics of phytoplankton. Nonperiodic instances of stabilization-destabilization are also encountered. Unvarying environments are those seldom stabilized or destabilized.

Such water movements abruptly supply various nutrients to the surface

on

...‘I

a wide range of scales, as shown above, so t h a t the alternating stabilizationdestabilization of the water column emerges as a fundamental hydrodynamic control of phytoplankton production.

The available literature reports

periodicities significant to production from 5-6 h (Auclair et al. ms) to one year (traditional seasonal pattern), thus exceeding a range of three orders of magnitude (Fig. 1).

It must be noted that stabilization-destabilization is

not only of periodic character (astronomicalrhythms: seasons, tides) but may also be nonperiodic (meteorological factors such as the wind, or others).

The

stzatification-destratification mechanism thus appears as a unique environmental factor by its range of action and by its direct control of the phytoplankton dynamics. There is some degree of discussion in the literature as to the relationship between stability and production, some authors finding that reduced stability parallels reduced phytoplankton production, while others report an inverse correlation between stability and production.

This apparent paradox is

obviously the result of inappropriate observation scales, since neither stabilization nor destabilization of the water column favours phytoplankton production.

At any spatio-temporal scale, only the alternating stabilization

199 and d e s t a b i l i z a t i o n of t h e w a t e r column, i n time and/or i n space, i s an hydrodynamic mechanism conducive t o enhance primary production.

The g e n e r a l i t y

of t h i s mechanism i s e a s i l y understood using a simple conceptual model.

MODEL AND DISCUSSION

The conceptual model of phytoplankton production, schematized on F i g . 2 , s y n t h e s i z e s most of t h e conclusions reported above on t h e c o n t r o l of phytoplankton dynamics by a l t e r n a t i n g stratification-destratification of t h e w a t e r column. A s f a r as phytoplankton i s concerned, t h e water column s t a b i l i z e s when t h e

mixed l a y e r becomes shallower than t h e c r i t i c a l depth.

The b a s i c equations

modelling phytoplankton production a r e known s i n c e Riley ( 1 9 4 6 ) .

The curves f o r

t h e s t r a t i f i e d environment ( F i g . 2 ) a r e from S t e e l e ( 1 9 5 8 ) , as i n Riley ( 1 9 6 3 ) . The phase, of d e s t a b i l i z a t i o n i s dominated by increased mechanical energy, which r e s u l t s i n s t r o n g e r mixing and t h u s favours a replenishment of t h e p h o t i c l a y e r i n n u t r i e n t s , up t o maximum c o n c e n t r a t i o n s equal t o t h o s e i n t h e underlying waters ( i f they are n u t r i e n t - r i c h )

.

Phytoplankton production i s then l i m i t e d

by a shortage of l i g h t , r e s u l t i n g from t h e increased mixing t o g r e a t e r depth. On t h e o t h e r hand, t h e phase of s t a b i l i z a t i o n i s c h a r a c t e r i z e d by t h e a c t i v e use of s o l a r energy and m a t e r i a l s by t h e phytoplankton.

The i n i t i a l phytoplankton

bloom r a p i d l y exhausts t h e n u t r i e n t s a v a i l a b l e i n t h e p h o t i c l a y e r , s o t h a t subsequent production i s a f u n c t i o n of i n s i t u n u t r i e n t regeneration and of d i f f u s i o n of n u t r i e n t s from deeper w a t e r s , t h e l a t t e r being very l i m i t e d under s t r a t i f i e d conditions.

The phase of d e s t a b i l i z a t i o n i s t h e r e f o r e d r i v e n by

mechanical mixing, while t h a t of s t a b i l i z a t i o n i s dominated by b i o l o g i c a l processes, both being e q u a l l y e s s e n t i a l t o prevent t h e b i o l o g i c a l c y c l e from c l o s i n g up.

The i n p u t of e x t e r n a l mechanical energy a c t i v a t e s t h e turnover of

materials, incorporated i n t h e ecosystem by t h e phytoplankton under s t a b l e conditions.

N u t r i e n t s a r e t h u s r e d i s t r i b u t e d over t h e e n t i r e water column,

becoming a v a i l a b l e f o r t h e production of phytoplankton upon s t a b i l i z a t i o n .

The

i n p u t of mechanical energy t h e r e f o r e does enhance primary production. These c h a r a c t e r i s t i c s do shape t h e f o u r curves of F i g . 2 .

(1) Changes i n

s t a b i l i t y i n the marine environment a r e s h a r p , b u t obviously not a s much a s schematically drawn on Fig. 2 .

However, t h e d r a s t i c changes caused by winds

o r t i d e s , o r the f r o n t a l d i s c o n t i n u i t i e s , a r e examples of very s t e e p s t a b i l i t y t r a n s i t i o n s i n the oceans.

( 2 ) N u t r i e n t s a r e a p a s s i v e s c a l a r , c o n t r o l l e d by

t h e dominant r e a c t i n g parameter: v e r t i c a l mixing, i n t h e d e s t r a t i f i e d phase, uptake by phytoplankton and i n s i t u r e g e n e r a t i o n , under s t a b l e c o n d i t i o n s . Within t h e s t r a t i f i e d phase, n u t r i e n t s regenerated i n t h e mixed l a y e r a r e d i r e c t l y recycled i n t o t h e production of phytoplankton, t h e well-known d i n o f l a g e l l a t e blooms ( r e d t i d e s ) being supported by increased b a c t e r i a l

200

Unstable

St rat if ied

I

Unstable

Fig. 2 . Simple conceptual model of phytoplankton dynamics.

r e g e n e r a t i o n (Wangersky, 1 9 7 7 ) .

( 3 ) A s f a r a s t h e model i s concerned, production

is a t h r e s h o l d f u n c t i o n of both s t a b i l i t y ( l i g h t ) and n u t r i e n t s .

The concepts

of c r i t i c a l depth and of n u t r i e n t l i m i t a t i o n b o t h emphasize t h e independence of primary production above t h e s e t h r e s h o l d s , and i t s i n c r e a s i n g dependence below them.

( 4 ) Phytoplankton biomass depends on t h e balance between n e t

201 production and l o s s e s .

Under c o n d i t i o n s of high mixing, low production and

continuous d i s p e r s i o n i n t h e water column keep t h e biomass a t a very low l e v e l . I n t h e s t a b i l i z e d phase, g r a z i n g by t h e zooplankton, s i n k i n g of c e l l s , l y s i s of senescent c e l l s , e t c . t r a n s f e r t h e biomass produced i n t h e p h o t i c zone t o t h e remainder of t h e ecosystem.

Ecosystems with high production a r e o f t e n

c h a r a c t e r i z e d by s t r o n g h o r i z o n t a l advection, phytoplankton being exported a t t h e s u r f a c e and n u t r i e n t s imported a t depth. The model may be applied t o a l l temporal successions of s t r a t i f i c a t i o n and d e s t r a t i f i c a t i o n , on any t i m e s c a l e .

The seasonal production dynamics i s

obviously w e l l accounted f o r , a s a r e a l l o t h e r i n s t a n c e s of time changing production r e p o r t e d above, whatever t h e f o r c i n g agent may be

- tides

(M

f'

M2'

According t o the t i m e

s l a c k w a t e r s ) , winds, r i v e r r u n o f f , o r h e a t i n g .

c h a r a c t e r i s t i c s of t h e system ( h o u r s , weeks o r months), t h e time a b s c i s s a of F i g . 2 must only be d i f f e r e n t i a l l y expanded or c o n t r a c t e d , t h e phases of s t a b i l i t y and mixing being s u c c e s s i v e l y repeated a s many times as needed, from four times a day t o once a y e a r .

A peak i n phytoplankton production i s t h u s modelled a t

t h e beginning of each p e r i o d of s t r a t i f i c a t i o n , leading t o a phytoplankton bloom when o t h e r c o n d i t i o n s a r e p r o p i t i o u s (depth of t h e p h o t i c l a y e r , d u r a t i o n of t h e s t a b i l i z a t i o n , e t c . ) ; indeed, a s observed f o r i n s t a n c e i n t h e S t Lawrence Estuary by F o r t i e r and Legendre (1979), high photosynthetic p o t e n t i a l does not develop i n t o a biomass o u t b u r s t when t h e p h o t i c l a y e r i s t o o shallow.

If the

p e r i o d of s t a b i l i t y i s s h o r t enough, c o n d i t i o n s of n u t r i e n t l i m i t a t i o n a r e never encountered by t h e phytoplankton.

Periods of mixing, preceding and following

t h e p e r i o d of s t r a t i f i c a t i o n , a r e c h a r a c t e r i z e d by low phytoplankton production,

l o w phytoplankton biomass, and replenishment of n u t r i e n t s i n t h e p h o t i c l a y e r . B u r s t s of phytoplankton biomass t h e r e f o r e occur i n t e r m i t t e n t l y , t h e concept

Of

i n t e r m i t t e n c y r e f e r r i n g , as i n hydrodynamics (Mollo-Christensen, 1973), t o t h e

t i m e f r a c t i o n occupied by t h e "events"

- here

t h e phytoplankton blooms.

The model i s a l s o a p p l i c a b l e t o t h e h o r i z o n t a l s t r u c t u r e of f r o n t a l a r e a s . This s t r u c t u r e i s modelled by a s i n g l e sequence of u n s t a b l e and s t r a t i f i e d phases (two l e f t t h i r d s of Fig. 2 ) , t h e a b s c i s s a being then t h e c r o s s - f r o n t a l axis.

The i n c r e a s e i n s t a b i l i t y (Fig. 2 ) corresponds t o t h e f r o n t a l zone,

between w e l l mixed and w e l l s t r a t i f i e d regimes. t h e English Channel f o r i n s t a n c e (Pingree e t a l . ,

I n t h e Western Approaches t o

1975, 1976), t h e f r o n t i s

l o c a t e d between c o a s t a l regions of s t r o n g t i d a l stream, where t h e water column remains mixed throughout t h e summer, and s h e l f a r e a s , which a r e c h a r a c t e r i z e d by weak t i d e s , a s t a b l e thermocline and low s u r f a c e n u t r i e n t s .

According t o

t h e model ( F i g . 21, maximum phytoplankton biomass should be found on t h e s t r a t i f i e d s i d e of t h e f r o n t .

Pingree e t a l .

(1976) observed t h a t high s u r f a c e

c h l o r o p h y l l c o n c e n t r a t i o n s a r e d i s p l a c e d towards t h e s t r a t i f i e d s i d e of f r o n t a l

202 boundaries; furthermore Pingree e t a l .

(1977) reported a phytoplankton bloom f o r

both t h e s u r f a c e waters and t h e thermocline on t h e s t r a t i f i e d s i d e of t h e f r o n t . S i m i l a r l y on t h e Scotian S h e l f , Fournier e t a l .

(1979) found a sudden drop i n

c h l o r o p h y l l upon e n t e r i n g t h e well mixed slope water, t h e chlorophyll concentration being i n g e n e r a l d i r e c t l y r e l a t e d t o t h e s t a b i l i t y of t h e water column. I n a "permanent" upwelling, t h e r e i s l i m i t e d v e r t i c a l mixing over t h e e n t i r e water column (except a t t h e s c a l e of t h e World Ocean!), s i n c e most of t h e nutrient-rich advection).

upwelled water i s l a t e r a l l y advected ( l i m i t e d o r no downward

I n such a case both c o n d i t i o n s of n u t r i e n t enrichment and v e r t i c a l

s t a b i l i t y occur w i t h i n a r e l a t i v e l y small i n t e r v a l , l e a d i n g t o high phytoplankton production i n t h e r e c e n t l y upwelled water and export of biomass. upwelling ecosystems may show spatio-temporal

However,

changes i n t h e production and

biomass o f phytoplankton, r e l a t e d t o t h e v e r t i c a l s t a b i l i t y of t h e water column. The numerical model, developed by Wroblewski (1977) f o r t h e wind driven upwelling ecosystem o f f t h e Oregon c o a s t , p r e d i c t s t h e h i g h e s t phytoplankton biomass t o occur upon r e l a x a t i o n of s t r o n g winds, when t h e phytoplankton c e l l s remain longer i n t h e n u t r i e n t - r i c h p h o t i c zone. observed during f i e l d s t u d i e s .

Such phytoplankton blooms w e r e c l e a r l y

Whenthe model i s run with t h e observed

t i m e f l u c t u a t i n g wind r e c o r d s , t h e response of phytoplankton t o t h e r e s u l t i n g i n t e r m i t t e n t upwelling i s an i n c r e a s e i n primary production following each major i n t e n s i f i c a t i o n of t h e wind s t r e s s , t h e production maxima being always observed upon r e l a x a t i o n of winds ( F i g . 19 i n Wroblewski, 1977).

A

s e r i e s of phytoplankton blooms a r e t h u s forced during t h e season favourable f o r c o a s t a l upwelling, i n r e l a t i o n t o f l u c t u a t i o n s i n t h e wind s t r e s s . According t o Wangersky (1977) diatom growth responds t o s t a b i l i z a t i o n of nutrier& r i c h water, while d i n o f l a g e l l a t e s become dominant when t h e major source of n u t r i e n t s i s i n s i t u r e g e n e r a t i o n , from t h e degradation of dissolved organic m a t t e r by b a c t e r i a .

This r e l a t e s s p e c i e s composition t o t h e n u t r i e n t s t a t u s Of

t h e ecosystem, and provides a g e n e r a l scheme t o analyze succession and d i s t r i b u t i o n of s p e c i e s .

I n temperate r e g i o n s , t h e seasonal succession of diatoms and

d i n o f l a g e l l a t e s t h u s r e f l e c t s t h e n u t r i e n t changes caused by t h e mixing and t h e production of phytoplankton. northwest European Shelf

D i s t r i b u t i o n and succession of s p e c i e s on t h e

(Holligan and Harbour, 1977; Pingree e t a l . , 1978) show

diatoms t o be t h e most abundant taxa i n t h e n u t r i e n t - r i c h mixed water, while small f l a g e l l a t e s dominate t h e s u r f a c e water i n s t r a t i f i e d regions; populations of mixed diatoms and d i n o f l a g e l l a t e s , of d i n o f l a g e l l a t e s , and of small f l a g e l l a t e s , s u c c e s s i v e l y occupy t h e thermocline of s t r a t i f i e d w a t e r s , following t h e c h a r a c t e r i s t i c s of t h e mixing.

High phytoplankton c o n c e n t r a t i o n s i n f r o n t a l

regions a r e formed of a mixture of d i n o f l a g e l l a t e s and diatoms, which agrees with successive s t r a t i f i c a t i o n ( i n s i t u n u t r i e n t r e g e n e r a t i o n ) and d e s t r a t i f i c a t i o n

203 (upwelling of nutrient-rich water) on a fortnightly Mf cycle.

Wangersky (1977)

explains in the same way the differences in species composition observed from upwelling systems. The spatio-temporal sequence of stratification and destratification,despite the variety of hydrodynamic mechanisms encountered in the various oceanic conditions, therefore appears as a basic control of the phytoplankton dynamics. It follows that the frequency of stabilization-destabilization is a fundamental characteristic of any water column (except in shallow waters), as significant to phytoplankton production as temperature, turbidity, trace elements, or any other factor traditionally considered. For instance, summer chlorophyll concentrations in Auke Bay (Iverson et al., 1974) are about 40 mg.m-2, while they exceed 160 mg-m-2 in the wind driven summer blooms.

Maximum chlorophyll

concentrations in the spring and autumn blooms, reported by Takahashi et al. (1977)'for Saanich Inlet, are respectively 22 and 9 m9-m-3, while twelve summer blooms, between the two main blooms, range from 3 to 15 m9-m-3 at their peaks. -2 at a station of Puget

Annual production (Winter et al., 1975) is 275 9C.m

Sound with fairly uniform assimilation from March through September; it is 465 -2 gC-m at a station with a number of intense blooms between early May and September. On the northwest European Shelf (Pingree et al., 1975, 1976, 19781, -3

summer chlorophyll recorded in the tide driven frontal zones are 7 mgsm -3 -3 (Orkney - Shetland Isles), 19 mg-m (Ushant), and as high as 100 m9.m

(western English Channel), while the average surface concentrations on both -3 sides of the fronts are about 1 mg-m - On the Scotian Shelf (Fournier et al., 1979), intermittent growth for as few as 30% of the winter days increases the annual phytoplankton production in the frontal area by 25%. Takahashi et al. (1977) have already suggested that

"

...

a common feature in

temperate to sub-polar regions seems to be several Occasional phytoplankton blooms during summer caused by short term temporal nutrient increases and a possible supply of phytoplankton seed stock from deep or intermediate depth water by partial mixing, regional upwelling, or replacement of water masses. The seasonally changing pattern of phytoplankton bimodal or unimodal, based on seasonal climatic variations seems oversimplified. Summer blooms may contribute significantly to the total annual primary production

[. . .]

Summer blooms

probably occur frequently both in higher latitudes and coastal waters, and less frequently in open oceanic waters and in lower latitudes

. . _ ' I

In fact, this

mechanism is even more general (Fig. l), since winter blooms may contribute significantly to the annual production, as may do alternation of stabilization and destabilization on very short time scales.

It follows that seasonal patterns

with only two, one, or even no phytoplankton blooms, are extreme cases on a wide scale of frequencies (Fig. 1).

Even if they cover large geographic areas, these

ecosystems with a low periodicity of stratification-destratification must be studied within the framework of broad conceptual models, covering the full spectrum of frequencies significant to the dynamics of phytoplankton. According to Margalef (1978), "careful models of the dependence of primary production on light, nutrients, temperature, and so on, may be useful in many situations, but in upwelling areas they may be replaced, probably with advantage, by the simple dependence of primary production on the auxiliary energy made available.

It is like in agriculture, where yield can be simply related to the

input of subsidiary energy (in machines, oil power, fertilizers, irrigation)

."

Following the same approach, it is proposed here to characterize the phytoplankton production potential of marine ecosystems by their frequency of stabilizationdestabilization, defined as the number of sequences of stabilization and destabilization per unit time.

On this scale (Fig. l), a near zero frequency

identifies systems seldom stabilized or destabilized, while upwellings tend toward the upper limit of stabilization-destabilization;in the laboratory, the turbidostat is the best example of a system with maximum production, simultaneously taking advantage of both stabilization and destabilization of the water, and therefore characterized by a maximum frequency of stabilization-destabilization. As discussed above, the input of mechanical energy enhances primary production, so

that the frequency of stabilization-destabilizationis an index of potential

phytoplankton production.

However, factors such as temperature, turbidity, low

nutrient background, and so on, may limit the production potential built up by the alternating stratification-destratification,these limiting factors being passive, while the alternation of stabilization and destabilization is an active input of energy.

This concept does not apply to shallow environments, where

high mixing does not lead to light limitation of phytoplankton.

To become

operational, the concept of stabilization-destabilization must be translated into physical terms (spatio-temporal domain significant to phytoplankton, measurements at sea, etc.), and it must take into account the spatio-temporal characteristics of the phytoplankton (response times, growth rates, patchiness, etc.). Considering that vertical mixing plays a significant role in only a limited number of oceanic systems, Wangersky (1977) proposed that phytoplankton dynamics is mainly controlled by nutrient regeneration, which increases with the number of bacteria present, this number being in turn a function of the particle content of the water.

In contrast, the present work hypothesizes that stabilization-

destabilization of the water column is of general occurrence in most of the productive oceanic areas. This does not exclude, however, that production of phytoplankton may be significantly enhanced by increased nutrient regeneration, especially in areas with low frequency of stabilization-destabilization.

205 Ecosystems d r i v e n by n u t r i e n t r e g e n e r a t i o n , s u c h as the Sargassum f o r i n s t a n c e ,

are l i m i t e d t o t h e mixed l a y e r , by d e f i n i t i o n , and t h e y are t h e r e f o r e v e r t i c a l l y c l o s e d systems.

These e c o s y s t e m s , which a l s o i n c l u d e t h e r e d t i d e s , c o n c e n t r a t e

t h e o r g a n i c matter n e a r t h e s u r f a c e , i n a way somewhat a n a l o g o u s t o t h e bog lakes.

On t h e c o n t r a r y , e c o s y s t e m s dominated by s t a b i l i z a t i o n - d e s t a b i l i z a t i o n

are v e r t i c a l l y o p e n , s i n c e n u t r i e n t s r e g e n e r a t e d a t d e p t h and e n e r g y s t o r e d by p h y t o p l a n k t o n a t s u r f a c e are v e r t i c a l l y exchanged.

T h i s v e r t i c a l t r a n s f e r of

e n e r g y and m a t e r i a l s , d r i v e n by t h e s t a b i l i z a t i o n and d e s t a b i l i z a t i o n o f t h e

w a t e r column, i s one o f t h e b a s i c mechanisms of p r o d u c t i v e m a r i n e ecosystems.

ACKNOWLEDGMENTS The a u t h o r w i s h e s t o t h a n k P r o f . J. P. O'Kane

(University College, Dublin),

P r o f . P. Bougis, P r o f . P . N i v a l and D r . L . P r i e u r ( S t a t i o n marine de V i l l e f r a n c h e s u r - M e r ) , D r . M. E s t r a d a ( I n s t i t u t o de I n v e s t i g a c i o n e s P e s q u e r a s , B a r c e l o n a ) and D r . J. Flos

manuscript.

( U n i v e r s i d a d d e B a r c e l o n a ) , f o r t h e i r u s e f u l c r i t i c i s m s of t h e I n d i v i d u a l o p e r a t i n g g r a n t no. A9689 from t h e N a t u r a l S c i e n c e s and

E n g i n e e r i n g R e s e a r c h C o u n c i l o f Canada w a s i n s t r u m e n t a l i n t h e c o m p l e t i o n of t h i s work.

REFERENCES A u c l a i r , J . C . , D e m e r s , S . , F r b c h e t t e , M . , Legendre, L. and Trump, C . L . , m s . High f r e q u e n c y endogenous p e r i o d i c i t i e s o f c h l o r o p h y l l s y n t h e s i s i n e s t u a r i n e phytoplankton. In preparation. C a r d i n a l , A . and B i ? r a r d - T h e r r i a u l t , L . , 1976. L e p h y t o p l a n c t o n d e l ' e s t u a i r e moyen d u S a i n t - L a u r e n t e n amont d e 1 ' I l e - a u x - C o u d r e s (Qugbec). I n t . Revue g e s . H y d r o b i o l . , 61: 639-648. C a r d i n a l , A . and L a f l e u r , P . E . , 1977. L e p h y t o p l a n c t o n e s t i v a l de l ' e s t u a i r e maritime d u Saint-Laurent. B u l l . SOC. p h y c o l . F r a n c e , 22: 150-160. D e m e r s , S . L a f l e u r , P . E . , Legendre, L . and Trump, C . L . , 1979. S h o r t - t e r m c o v a r i a b i l i t y o f c h l o r o p h y l l and t e m p e r a t u r e i n t h e St. Lawrence E s t u a r y . J . F i s h . R e s . Board Can., 36: 568-573. D e m e r s , S. and Legendre, L . , 1979. E f f e t s d e s mar6es s u r l a v a r i a t i o n c i r c a d i e n n e d e l a c a p a c i t i ? p h o t o s y n t h 6 t i q u e d u p h y t o p l a n c t o n de l ' e s t u a i r e du S a i n t - L a m e n t . J . e x p . mar. B i o l . E c o l . , 39: 87-99. 1976. C o v a r i a b i l i t y o f c h l o r o p h y l l and t e m p e r a t u r e i n t h e s e a . Denman, K.L., Deep-sea R e s . , 23: 539-550. Denman, K.L. and P l a t t , T . , 1975. Coherences i n t h e h o r i z o n t a l d i s t r i b u t i o n s o f p h y t o p l a n k t o n and t e m p e r a t u r e i n t h e upper o c e a n . Mbm. SOC. R . S c i . LiGge, 6 , 7: 19-30. Denman, K . L . and P l a t t , T . , 1976. The v a r i a n c e s p e c t r u m o f p h y t o p l a n k t o n i n a t u r b u l e n t o c e a n . J . mar. R e s . , 34: 593-601. Falkowski, P.G., I n press. L i g h t - s h a d e a d a p t a t i o n and a s s i m i l a t i o n numbers. J. Plankton R e s . F o r t i e r , L . , L e g e n d r e , L . , C a r d i n a l , A . and Trump, C . L . , 1978. V a r i a b i l i t b h c o u r t t e r m e d u p h y t o p l a n c t o n d e l ' e s t u a i r e du S a i n t - L a u r e n t . Mar. B i o l . , 46: 349-354. F o r t i e r , L . and Legendre, L . , 1979. Le c o n t r 6 l e d e l a v a r i a b i l i t g 2 c o u r t t e r m e du phytoplancton e s t u a r i e n : s t a b i l i t i ? v e r t i c a l e e t profondeur c r i t i q u e . J . F i s h . R e s . Board,Can., 36: 1325-1335.

206 F o u r n i e r , R . O . , Det, M. van, Wilson, J.S. and Hargreaves, N . B . , 1979. Influence of t h e shelf-break f r o n t off Nova S c o t i a on phytoplankton standing stock i n w i n t e r . J . F i s h . R e s . Board Can., 36: 1228-1237. F r e c h e t t e , M. and Legendre, L., 1978. Photosynth6se phytoplanctonique: rkponse 2 un stimulus simple, i m i t a n t les v a r i a t i o n s r a p i d e s de l a lumihre engendr&s 15-25. p a r l e s vagues. J . exp. mar. Biol. Ecol., 32: Phytoplankton photosynthetic response F r g c h e t t e , M. and Legendre, L . , I n p r e s s . t o l i g h t i n an i n t e r n a l t i d e dominated environment. E s t u a r i e s . G i l m a r t i n , M . , 1964. The primary production of a B r i t i s h Columbia f j o r d . J . F i s h . Res. Board Can., 2 1 : 505-538. Gran, H.H. and Braarud, T . , 1935. A q u a n t i t a t i v e study of t h e phytoplankton i n t h e bay of Fundy and t h e g u l f of Maine (including observations on hydrography, chemistry and t u r b i d i t y ) . J. b i o l . Board Can., 1: 279-467. Holligan, P.M. and Harbour, D.S., 1977. The v e r t i c a l d i s t r i b u t i o n and succession of phytoplankton i n t h e western English Channel i n 1975 and 1976. J. mar. b i o l . ASS. U.K., 57: 1075-1093. I g n a t i a d e s , L . , 1979. The i n f l u e n c e of water s t a b i l i t y on t h e v e r t i c a l s t r u c t u r e of a phytoplankton community. Mar. B i o l . , 52: 97-104. Iverson, R . L . , C u r l , H . C . J r . , O'Connors, H.B. J r . , Kirk, D. and Zakar, K . , 1974. Summer phytoplankton blooms i n Auke Bay, Alaska, d r i v e n by wind mixing of t h e water column. Limnol. Oceanogr., 19: 271-278. L a f l e u r , P . E . , Legendre, L. and C a r d i n a l , A . , 1979. Dynamique d'une population e s t u a r i e n n e de Diatomkes planctoniques: e f f e t de l ' a l t e r n a n c e des marges de morte-eau e t de vive-eau. Ckeanologica Acta, 2 : 307-315. Legendre, L . , Ingram, R.G. and Simard, Y., m s Aperiodic changes of water column s t a b i l i t y and phytoplankton production i n Hudson Bay. I n p r e p a r a t i o n . Lekan, J.F. and Wilson, R . E . , 1978. S p a t i a l v a r i a b i l i t y of phytoplankton biomass i n t h e s u r f a c e waters of Long I s l a n d . Estuar. c o a s t . mar. S c i . , 6: 239-251. Lorenzen, C . J . , 1966. A method f o r t h e continuous measurement of i n vivo c h l o r o p h y l l concentration. Deep-sea Res., 13: 223-227. Margalef, R . , f978. What i s an upwelling ecosystem? I n : R. Boje and M. Tomczak ( E d i t o r s ) , Upwelling ecosystems. Springer-Verlag, B e r l i n , pp. 1 2 - 1 4 . Massol, R.H. and B a l l e s t e r , A . , 1976. Nueva metodologia p a r a l a determinacibn en continuo de l a a c t i v i d a d f o t o s i n t k t i c a de l a s a l g a s f i t o p l a n c t b n i c a s . Inv. Pesq., 40: 111-123. Mollo-Christensen, E . , 1973. I n t e r m i t t e n c y i n large-scale t u r b u l e n t flows. Ann. Rev. F l u i d Mech., 5 : 101-118. Pingree, R . D . , Holligan, P.M. and Head, R . N . , 1977. S u r v i v a l of d i n o f l a g e l l a t e blooms i n t h e western English Channel. Nature, 265: 266-269. Pingree, R.D., Holligan, P.M. and Mardell, G . T . , 1978. The e f f e c t s of v e r t i c a l s t a b i l i t y on phytoplankton d i s t r i b u t i o n s i n t h e summer on t h e northwest European S h e l f . Deep-sea R e s . , 25: 1011-1028. Pingree, R . D . , Holligan, P.M., Mardell, G.T. and Head, R . N . , 1976. The influence of p h y s i c a l s t a b i l i t y on s p r i n g , summer, and autumn phytoplankton blooms i n t h e C e l t i c Sea. J. mar. b i o l . A s s . U . K . , 56: 845-873. Pingree, R . D . , Pugh, P . R . , Holligan, P.M. and F o r s t e r , G . R . , 1975. Summer phytoplankton blooms and r e d t i d e s along t i d a l f r o n t s i n t h e approaches t o t h e English Channel. Nature, 258: 672-677. P l a t t , T., 1972. The f e a s i b i l i t y of mapping t h e chlorophyll d i s t r i b u t i o n i n Fish. R e s . Board Can. tech. Rep., 1332), 8 p. f t h e Gulf of S t . Lawrence. 20 f i g . Riley, G.A., 1942. The r e l a t i o n s h i p of v e r t i c a l turbulence and s p r i n g diatom J. mar. Res., 5: 67-87. flowerings. Riley, G . A . , 1946. F a c t o r s c o n t r o l l i n g phytoplankton populations on Georges Bank. J. mar. Res., 6 : 54-73. R i l e y , G . A . , 1963. Theory of food-chain r e l a t i o n s i n t h e ocean. I n : M.N. H i l l ( E d i t o r ) , The Sea, Vol. 2 . I n t e r s c i e n c e , N e w York, pp. 438-463.

207 Roy, S . and Legendre, L . , 1979. DCMU-enhanced f l u o r e s c e n c e a s an i n d e x of p h o t o s y n t h e t i c a c t i v i t y i n phytoplankton. Mar. B i o l . , 55: 93-101. Roy, S. and Legendre, L . , 1980. F i e l d s t u d i e s of DCMU-enhanced f l u o r e s c e n c e a s an i n d e x of i n s i t u phytoplankton p h o t o s y n t h e t i c a c t i v i t y . Can. J . F i s h . a q u a t . S c i . , 37: 1028-1031. S i n c l a i r , M . , El-Sabh, M . I . , P o u l e t , S . and Coote, A . , 1979. Sevigny, J . M . , Summer p l a n k t o n d i s t r i b u t i o n s a s s o c i a t e d w i t h t h e p h y s i c a l and n u t r i e n t p r o p e r t i e s of t h e n o r t h w e s t e r n Gulf of S t . Lawrence. J . F i s h . R e s . Board Can., 36: 187-203. S i n c l a i r , M . , 1978. Summer phytoplankton v a r i a b i l i t y i n t h e lower S t . Lawrence e s t u a r y . J . F i s h . Res. Board Can., 35: 1171-1185. S t e e l e , J . H . , 1958. P l a n t p r o d u c t i o n i n t h e n o r t h e r n North Sea. S c o t . Home Dep., Mar. Res. 1958, ( 7 ) : 1-36. Steven, D.M., 1974. Primary and secondary p r o d u c t i o n i n t h e Gulf of S t . Lawrence. M a r . S c i . C e n t . , M c G i l l Univ., Montreal, Quebec. MS Rep., ( 2 6 ) , viii 116 p .

+

Sverdrup, H.U., 1953. On c o n d i t i o n s for t h e v e r n a l blooming of phytoplankton. J . Cons. perm. i n t . Explor. M e r , 18: 287-295. Takahashi, M:, S i e b e r t , D.L. and Thomas, W.H., 1977. Occasional blooms of p h y t c p l a n k t o n d u r i n g summer i n Saanich I n l e t , B.C., Canada. Deep-sea R e s . , 24: 775-780. T h e r r i a u l t , J . C . and L a c r o i x , G . , 1976. N u t r i e n t s , c h l o r o p h y l l , and i n t e r n a l t i d e s i n t h e S t . Lawrence E s t u a r y . J. F i s h . Res. Board Can., 33: 2747-2757. T h e r r i a u l t , J . C . , Lawrence, D . J . and P l a t t , T . , 1978. S p a t i a l v a r i a b i l i t y of phytoplankton t u r n o v e r i n r e l a t i o n t o p h y s i c a l p r o c e s s e s i n a c o a s t a l environment. Limnol. Oceanogr., 23: 900-911. Wangersky, P . J . , 1977. The r o l e of p a r t i c u l a t e m a t t e r i n t h e p r o d u c t i v i t y of s u r f a c e w a t e r s . Helgolander w i s s . Meeresunters., 30: 546-564. Webb, K.L. and D ' E l i a , C.F., 1980. N u t r i e n t and oxygen r e d i s t r i b u t i o n d u r i n g a s p r i n g neap t i d a l c y c l e i n a temperature e s t u a r y . S c i e n c e , 207: 983-985. Winter, D . F . , Banse, K. and Anderson, G . C . , 1975. The dynamics of phytoplankton blooms i n Puget Sound, a f j o r d i n t h e n o r t h w e s t e r n United S t a t e s . Mar. B i o l . , 29: 139-176. Wroblewski, J . S . , 1977. A model of phytoplankton plume formation d u r i n g v a r i a b l e Oregon upwelling. J. mar. Res., 35: 357-394.


209

DIFFUSION AS A CONSTRAINT ON THE BIOLOGICAL IMPORTANCE OF MICROZONES IN THE SEA P.J.L. WILLIAMS and L.R. MUIRl Department of Oceanography, The University, Southampton, (England)

ABSTRACT Excretion patches produced by marine zooplankton have length scales on the order of to metres, and their dissipation is controlled by molecular diffusion. These microzones have been considered by many biologists and are thought to explain certain features of plankton production. It is shown that there cannot be enough of these patches, nor can they persist for long enough to be of importance in maintaining primary productivity in the ocean. The question of how phytoplankton maintain their observed growth rates is still open. INTRODUCTION Planktonic processes and events have space scales ranging from lo3 metres to metres if molecular processes are ignored. Parsons, Takahashi and Hargrave (1977) show that the major biological activity in the oceans is associated with small organisms whose size is between loW3and metres and their awareness will be primarily on a scale not too far removed from their own size. Our comprehension of planktonic processes on the molecular level is quite good as is our knowledge of processes on scales of more than one metre. However, in the critical region between I and metres our notions are hazy. We have, for example, no indication of the variability of important chemical parameters for algal growth (e.g., inorganic nitrogen and phosphorous sources, or chelating ability) on scales less than 10-1 metre.

Classical experimental methods for the determination of plant nutrients offer no sign of providing resolution on scales finer than metres while de-

tailed profiling of chlorophyll (Derenbach, et al, 1979) demonstrates variability on a

lo-’ metre length scale with indications that there is variability on even

finer scales. One could argue that if we have no understanding of processes on the microscale, then the usefulness of information on larger scales cannot be known. There is, therefore, no direct experimental evidence for assuming either homogeneity or variability on length scales between

and

metres.

Inevitably,

Permanent address: Ocean and Aquatic Sciences, Canada Centre for Inland Waters, P.O. Box 5050, Burlington, Ontario, Canada.

210 this lack of firm experimental evidence has meant that the subject of microzones in the marine environment is open to speculation. The notion of microzones is not new and a variety of biological observations have been explained by the assumption that there exist small patches of high chemical concentration which dominate the bulk chemical properties of the natural oceanic waters.

Since biological activity

is associated with small organisms which are discrete sources and sinks, then some chemical variability, on the approximate length scales of the organisms must inevitably occur. The approximate Reynolds number of the flows being considered is less than 1, and this would indicate that molecular diffusion rather than turbulent diffusion is the most important dissipation mechanism for these microzones. In this paper, we shall be concerned with the excretion patches of zooplankton as a source of nutrients for photosynthetic algae. We shall consider molecular diffusion to be the most important dissipation process and we shall mainly be to metres. We shall attempt conce'rned with length scales on the order of to answer the question : may the number, size and duration and chemical concentration in these patches be such that they are of importance in maintaining the primary productivity?. We show that, given the current knowledge of planktonic processes, microzones cannot play any important role. 2.0

PREVIOUS WORK

It has been argued for some time (Goering, Dugdale

&

Menzel, 1964; Beers and

Kelly, 1965 and Dugdale, 1967) that there is a close link between the excretion products of marine zooplankton and the phytoplankton, since these excretion products provide nitrogen which is essential for photosynthesis. Recent developments on this theme are given in the papers by Goldman, McCarthy and their co-workers (McCarthy and Goldman, 1979; and Goldman, McCarthy and Peavey, 1979). The argument runs as follows: The effect of nitrogen limitation on the rate of algal growth in cultures is reflected in the amount of inorganic nitrogen in the cell which is determined experimentally as the C/N ratio. When nitrogen limits the rate of growth, the nitrogen content of the cell is reduced, thus raising the C/N ratio. By measuring the C/N ratio of natural populations it is found that these ratios are indicative of growth rates which are too great to be sustained by the ambient inorganic nitrogen concentrations. However, these ambient nitrogen concentrations are measured as averages over relatively large volumes. Goldman and McCarthy draw attention to the fact that planktonic algae can assimilate their nitrogen in relatively short periods of time when exposed to high inorganic concentrations. They then speculate that:

211

"Such situations could conceivably exist when cells randomly and perhaps frequently pass into microenvironments in which nitrogenous nutrient concentrations are elevated as a result of either metabolic waste excretion by animals or the degradation of organic matter by bacteria." They produce, as an example, a calculation for the diatom Thalassiosira which indicates that the organism would need to spend 3% (40 minutes per day) of its time in an excretion patch produced by an adult calanoid zooplankter. The notion has been made more sophisticated by introducing the effect of nutrient status on buoyancy.

Steele and Yentsch (1960) haveobserved that under

nutrient deficient conditions, the phytoplankter Skeletonema costatum became negatively buoyant. Thus one could extend the McCarthy and Goldman hypothesis to suggest that algae could actively seek out and exploit nutrient rich zones by becoming negatively buoyant and sinking when they are deficient in nitrogen and then adjusting their buoyancy, when entering a patch, to maintain themselves in that patch. So long as the phytoplankter can find enough patches of high enough concentration to spend at least 3% of its time in these patches, then it is of no consequence to the phytoplankter that the ambient average nitrogen concentrations are too low to maintain its growth rate. 3.0

PATCH DYNAMICS

In the above argument, the critical assumption is that the patches produced by the zooplankton persist long enough that the mean length of time that a phytoplankter can spend in one or more patches exceeds 3%. Before we can have a quantitative discussion of the patch dynamics, it is necessary to define what is meant by a patch. We assume that the boundary of a patch will be defined as a concentration which significantly exceeds the background environment and which allows the algal growth rate to approach a maximum. Ammonia concentrations in the offshore environment are typically less than 0.5 pg-atoms N / 1 and a value between 0.05 and 0.2 may be regarded as a background concentration. The relationship between algal growth and the ambient nutrient concentration may be described by a hyperbolic curve which contains a constant (the uptake constant), and this uptake constant is numerically equal to the nutrient concentration which gives rise to one half of the maximum growth rate. McCarthy and Goldman consider algal growth rates, in nutrient rich patches, within 17% of the maximum growth rates. Such growth rates will be realized at nutrient concentrations which are approximately five times greater than the uptake constant. Typical values for the uptake constant for ammonia are in the region of 0.5 pg-atoms N / 1 (MacIsaac and Dugdale, 1969).

These two lines of argument

imply that a value between 2.5 and 15 pg-atoms N / 1 would be an appropriate value

212

to adopt for the boundary of an ammonia rich patch.

We shall consider a patch to

consist of a concentration higher than 2.5 pg-atoms N / t to allow the most favourable condition for the patch. Throughout the remainder of this paper, when alternatives or uncertainties exist, we shall assume the case which would be most favourable for the persistance of a patch and which would therefore strengthen the argument for the importance of the microzones. Zooplankton exhibit two types of motion.

The first is continuous motion which

produces an excretion plume behind the zooplankter. Jackson (1980) has considered this type of motion and has found that the plumes cannot contribute significantly to the growth of phytoplankton. intermittant motion.

We have assumed the other alternative, that of

We assume that the zooplankter is stationary while excreting

and then moves away from the spherical patch without disturbing it with its swimming appendages. We also assume that the zooplankter excretes through its body surface and that 'the growth and subsequent decay of the patch is controlled by molecular diffusion.

By assuming that the zooplankter is stationary while excreting, we

obtain the maximum patch size, and by assuming that it does not disturb the patch with its swimming appendages while moving away, we allow the patch to exist for the maximum period of time. There are two possible models for the method of excretion by the zooplankter. The first model assumes that the zooplankter excretes material at a constant rate through its body surface, and this leads to an expression for the concentration at any time during the excretion process and at any distance from the body surface which is (Carslaw and Jaeger, 1 9 4 7 , p. 261) c(x,t) =

2ERFC [ 2 4

4nDx

where;

c = concentration

D = diffusion coefficient x = distance from the body surface

Q

=

flux of material from the source

t = time

and ERFC is the complement of the Error Function. The difficulty with this model is that the concentration at the body surface is infinite and this is clearly impossible. If we assume, alternatively, that the body surface concentration is a constant and that we have spherical symmetry, then initially the zooplankter may be considered to be a semi-infinite source with a constant internal concentration of 2c for t > 0 the concentration is given by

.

Then

213

=

coERFC

I2G)

and while the zooplankter is excreting, the body surface concentration is constant at c

.

The average rates of amonia excretion from a variety of zooplankton have been determined (Ikeda, 1970), but the concentration of material in the body fluids and the precise excretion mechanism is not well known. However, if after a time, T a total mass M has been excreted, then m

M

4nc(x,T)xzdx

= 0

and

so,

during the excretion phase, 0

< t
T ) we assume that the concentration distribution in the patch is still described by (2) but that the concentration at the centre of the patch decays and is given by cob> =

M

(4)

2 0 . 6 6 G ~ ~t3I2 /~

In what follows, we shall assume that the dynamics of the patches are given by and that the body surface concentration is given by (3) while the animal is excreting and the patch is growing. The zooplankter then moves away without disturbing the patch, and during the decay phase, the concentration at the centre of (2)

the patch is given by ( 4 ) 4.0

MODEL RESULTS

McCarthy and Goldman (1979) used a mean excretion rate for Oithona and Clausocalanus of 2.6 x g-atoms N-NH3 in about 5 seconds and this is consistent with values determined by Ikeda (1970). We used this rate of excretion for the zooplankton to calculate a mean surface concentration during the growth

214

.

phase of the patch, using equation ( 3 ) , of 0.1 g-atoms m3 We assume the boundary concentration of the patch to be defined by a concentration of 2.5x103~g-atoms/m3 and a mean molecular diffusion coefficient of 1.5 x lo-’ m2/s which is consistent with Pasciak and Gavis (1974) and with Jackson (1980). The maximum radius of the patch, may be calculated by solving (2) numerically A plot of maximum patch radius using various values of the growth time, T g versus growth time is given in Figure 1. It shows that if the zooplankter remains

.

stationary and excretes continuously for 200 seconds (which is an unreasonably long time) the maximum patch radius is approximately 0.9 mu.

, - l s 0

0 .oo

40.00

GRUHTH

Fig. 1.

80.00

120.00

TIME OF

160.00

.

200 00

PflTCH

Maximum patch radius vs. zooplankter excretion time.

By rearranging (41, making use of ( 3 ) , and defining cb as the boundary concentration, the time taken for the patch to decay is given by

215

(5) =

1.52 T

g

and after this time, the concentration at the centre of the patch is below the boundary concentration. We have assumed that the zooplankton remains stationary while it excretes for T

g

seconds and then moves instantly to a new location while the original patch

decays in Td seconds. Hence the number of discrete patches present at any given time due to a single zooplankter is given by

By varying either cb or c or both, it is possible to get a variation in the decay time as a function of the growth time and so to get a variation in the number of patches present. of

cb and

c

However, the limits that are possible in choosing the values

will not make very much difference to N

.

Now that we know the patch dynamics and the mean number of patches that one zooplankter produces it is possible to calculate the expected exposure time for a randomly distributed algal cell once we know the number of zooplankton per unit volume of seawater and the mean excretion time for these zooplankton.

It is not an easy matter to obtain a value for the mean number of zooplankton per F i t volume of seawater. However, it is possible to put an upper limit on the number that would be expected in an oceanic environment. Using data from the CEPEX study (Grice et al, 19801, which was conducted near Vancouver Island where zooplankton numbers are higher than would be expected in oceanic locations, and assuming that all species and both the adult and the copepodite stages may be treated alike, gives a rough estimate of about 10 individuals per litre.

Inde-

pendant calculations of oxygen consumption for the wjor species and their individual larval stages, when converted to ammonia excretion rates, using molar O:N of 2 0 : 1 , gives very similar answers.

If it is further assumed that the copepods account for

approximately 50% of the overall animal excretion of nitrogen then a reasonable upper limit on the zooplankton population is about 20 individuals per litre. Hence there would be, on average, about 5.0

x

lo4 patches per cubic metre at any given

instant in time, The probability of a randomly distributed algal cell being in a patch at any particular instant is given by the ratio of total patch volume per unit volume of seawater. Hence the exposure time for a particular algal cell is given, in seconds

216

per day as

E

=

4 7 r3N

86400

(7)

where r = mean patch radius N = number of patches per cubic metre and there are 86400 seconds in a day. It is very difficult to calculate the mean patch radius, however, if we assume that the mean patch radius is given by the maximum radius, then we shall be conservative.

XO u s b*

a a-

zg -,’.

w

N

r -

C? &

aW I--

u

Wg

k =W 0

?

0

0 .oo

Fig. 2.

I

1

40.00

1

1

80.00

I

1

120.00

I

I

160.00

I

1

200.00

GROWTH TIME OF P A T C H

Expected time in patch (secondsfday) for a randomly distributed algal cell versus mean zooplankter excretion time.

If the zooplankton remain stationary for an average of 200 seconds then the exposure time for an algal cell would be approximately 32.3 seconds per day. The exposure time is plotted versus the average time of excretion in Figure 2. The argument by McCarthy and Goldman required exposure times of about 2600 seconds which is about two orders of magnitude longer than the maximum time available. Assuming that the phytoplankton do have 2600 seconds of exposure time, then the zooplankton would have to remain stationary but metabolically active for more

217 than 3 . 5 hours. Alternatively, if they do not excrete for longer than 200 seconds in one place then the zooplankton population must be in excess of 4000 individuals per litre. Both of these possibilities seem unrealistic biologically, even though they are very conservative estimates, since we have always erred on the side of allowing the patch to persist longer than it would in nature. So far, we have not made any allowance for the larval stages of the zooplankton. Data is not readily available for the nitrogen excretion rate of the small larval stages but as a first approximation, since the excretion rate is a function of the surface area and the biomass of the larvae is approximately 0.01 of the biomass of the adults, then the excretion rate should be about 0.05 of the excretion rate of the adult. Hence, although there will be more larvae, the patches produced by them would diffuse away even faster than those produced by the adults, since the patches would be much smaller. In the same way, it is possible to ignore the effects of the bacterial decay of organic matter. There are many bacteria, but their patches decay away too rapidly to be of any use. The remaining factor to be considered is the possible effect of the algae settling into patches by adjusting their bouyancy. This argument assumes that the algae are settling at a rate which is greater than the rate of contraction of the patch.

Bienfang (1979) has recently published data on careful measurements of the

settling rates of marine algae, both in cultures and in the natural environment, and the mean value is close to 1 metre per day. A rough shrinking rate for the patch may be calculated by dividing the maximum radius by the decay time.

If the

mean excretion time is less than 15 seconds, the patches decay too quickly for the phytoplankton to fall into them., but if the mean excretion time is 200 seconds, the shrinking rate is about 0.1 metres per day.

In any case, the expected ex-

posure time may still be calculated by equation (7) but with the number of patches, N

, increased by the factor

(1. + net settling velocity).

This would mean that

the maximum exposure time could be increased by perhaps a factor of two over the exposure time that would be expected if the algae did not settle. 5.0

CONCLUSIONS

The present study has shown that molecular diffusion is sufficient to disperse microzones far too rapidly for them to be of any particular importance in providing for the nitrogen requirements of the marine phytoplankton. The qualitative arguments that were given at the beginning of this paper are very attractive, but assuming values that would tend to make the patches persist for the maximum length of time shows that molecular diffusion disperses the patches at least 50 times too fast. If other forms of dispersion are important, or if smaller numbers of zooplankton are present, or if they do not excrete for long periods of time, the discrepancies will become even greater. Hence the question of how marine phytoplankton manage

218

to obtain their nitrogen requirements from water that is deficient (on large length scales) in nitrogen remains an open question. ACKNOWLEDGEMENTS This research was done while the second author was on educational leave at the University of Southampton, and he wishes to thank the Government of Canada for their financial support during this period. REFERENCES Beers, J.R., and Kelly, A.C., 1965. Short-term Variation of Amnonia in the Sargasso Sea off Bermuda. Deep-sea Res., 12:21-25. Bienfang, P.K., 1979. A New Phytoplankton Sinking Rate Method Suitable for Field Use. Deep-sea Res., 26:719:729. Carslaw, H.S. and Jaeger, J.C., 1947. Conduction of Heat in Solids. Oxford University Press. Derenbach, J.B., Astheimer, H., Hansen, H.P. and Leach, H., 1979. Vertical Microscale Distribution of phytoplankton in Relation to the Thermocline. Marine Ecology, 1:187-193. Dugdale, R.C., 1967. Nutrient Limitation in the Sea: Dynamics, Identification and Significance. Limnology and Oceanography, 12:685-695. Goering, J.J., Dugdale, R.C., and Menzel, D.W., 1964. Cyclic Diurnal Variations in the Uptake of Ammonia and Nitrate by Photosynthetic Organisms in the Sargasso Sea. Linmology and Oceanography, 9:448-451. Goldman, J.C., McCarthy, J.J. and Peavey, D., 1979. Growth Rate Influence on the Chemical Composition of Phytoplankton in Oceanic Water. Nature, 279:ZlO-215. Grice, G.D., Harris, R.P., Reeve, M.R., Heinbokel, J.F. and Davis, C.O., 1980. Large Scale Enclosed Water Column Ecosystems: An Overview of Food Web 1, The Final CEPEX Experiment. J. Marine Biological Association, U.K., 60:391-399. Ikeda, T., 1970. Relationship Between Respiration Rate and Body Size in Marine Plankton Animals as a Function of the Temperature of Habitat. Bull.Fac.Fish. Hokkaido Univ., 21:91-112. Jackson, G.A., 1980. Phytoplankton Growth and Zooplankton Grazing in Oligotrophic Oceans. Nature, 284:439-441. McCarthy, J.J., and Goldman, J.C., 1979. Nitrogenous Nutrition o f Marine Phytoplankton in Nutrient Depleted Water. Science, 203:670-672. MacIsaac, J . G . , and Dugdale, R.C., 1969. The Kinetics of Nitrate and Ammonia Uptake by Natural Populations of Marine Phytoplankton. Deep-sea, 16:45-57. Parsons, T.R., Takahashi, M., and Hargrave, B., 1977. Biological Oceanographic ' Processes. 2nd Edition, Permagon Press, London. Pasiac, W.J., and Gavis, J., 1974. Transport Limitation of Nutrient Uptake in Phytoplankton. Limnology and Oceanography, 19:881-888. Steele, J.H. and Yentsch, C., 1960. The Vertical Distribution of Chlorophyll. J. Marine Biological Association, U.K., 39:217-266.

219

THE RESIDUAL CIRCULATION IN THE NORTH SEA

Jacques C.J. NIHOUL

1

and Yves RUNFOLA

Geophysical Fluid Dynamics, LiPge University, Belgium 'Also at the Institut d'Astronomie et de Ggophysique, Louvain University (Belgium)

INTRODUCTION

Hydrodynamic models of the North Sea are primarily concerned with tides and storm surges and the associated currents which can have velocities as high as several meters per second. However the period of the dominant tide is only about a half day and the characteristic life time of a synoptic weather pattern is of the order of a few days. The very strong currents which are produced by the tides and the atmospheric forcing are thus relatively transitory and a Marine Biologist will argue that over time scales of biological interest, they change and reverse so many times that they more or less cancel out, leaving only a small residual contribution to the net water circulation. The importance of tidal and wind induced currents for the generation of turbulence and the mixing

0.f

water properties is of course not denied but many biologists would

be content with some rough parameterization of the efficiency of turbulent mixing and, for the rest, some general description of the long term transport of "water masses". Although the concept of "moving water masses", and its train of pseudo-lagrangian misdoings, appeal to chemists and biologists who would like to find, in the field, near-laboratory conditions, it is impossible to define it in any scientific way and charts of the North Sea's waters like the one shown in figure 1 and reproduced from Laevastu (1963) are easily misinterpreted and often confuse the situation by superposing a flow pattern on an apparently permanent "geography" of water masses. The notion of "residual" circulation - which, at least, has an Eulerian foundation

- has long remained almost as vague.

Some people have defined it as the observed flow

minus the computed tidal flow. Such a definition is understandable from a physical point of view but one must realize that the residual flow so-defined contains all wind-induced currents, including small scale fluctuations. It is definitely not a steady or quasi-steady flow and some attempts to visualize it by means of streadlines are questionable. What it represents, in terms of marine chemistry or marine ecology is not at all clear.

Actually, if one wants to take the point of view of the marine ecologist, one should really look at the mean flow over some appropriate period of time of biological interest. It is customary for experimentalists to compute, from long series of observations, daily, weekly and monthly averages. What such averages actually represent is debatable. No doubt that tidal currents are essentially removed in this process. However with tidal velocities, one or two orders of magnitude higher than residual velocities and the latter of the order of traditional current-meters'errors, one may fear that, as a result of the non-linearities of the equipment, the error remains the same order of magnitude after averaging and leads to a 100

%

inaccuracy in the calculated mean re-

sidual. (e.g. Nihoul, 1980). Moreover the choice of the periods of time over which the averages are made is not obviois as it seems to rely more on the calendar than on physical processes. One must be quite clear of what one gets from such averages. With tides reversing four times daily and changes in the synoptic weather pattern taking several days, one may expect daily averages to remove tidal motions while still catching most of the residual currents responding to the evolving meteorological conditions. Monthly averages, on the other hand, will have a more "climatic" sense and will presumably represent the residual circulation which is induced by macroscale oceanic currents (such as the North-Atlantic current in the case of the North Sea) and the mean effect of non-linear interactions of mesoscale motions (tides, storm surges

...) .

Here, the terms "macroscale", "mesoscale" (and later on "microscale") are used in reference with the time scales of motion. In general time scales and length scales are related but it doesn't have to be so and no such assumption is made here at this stage. The role of residual currents and residual structures (fronts

...)

in the dynamics

of marine populations, the long term transport of sediments or the ultimate disposal of pollutants, for example, is universally recognized but different schools of theoreticians and experimentalists still favour different definitions which, in the case

of the North Sea, may have little in common,apartfrom the fact that the strong tidal oscillations have been removed. Obviously each definition addresses a particular kind of problem and if, as it is now universally agreed, the residual circulation is defined as the mean motion over a period of time sufficiently large to cancel tidal oscillations and transient windinduced currents, there is still the problem of choosing the time interval of averaging, taking into account the objectives of the study. In any case, it is not demonstrated that such a time average may be obtained with sufficient accuracy from experimental records. As pointed out before, the averaging takes away more than 90 the instrumental error.

%

of the signal and the final result is of the same order as

221

F i g . 1. Water types i n t h e North Sea according t o Laevastu ( 1 9 6 3 ) . [Adapted from F o l i o 4 of S e r i a l A t l a s of t h e Marine Environment with t h e permission of t h e American Geographical S o c i e t y . ]

222

In the following, one examines how the problem can be approached through mathematical modelling.

THE GOVERNING EQUATIONS

The three-dimensional hydrodynamic equations applicable to a well-mixed continental sea, like the North Sea, can be written (e.g. Nihoul, 1975)

0.v

0

=

av +

0 . (VV)

at

where

n

+

2

n

A

V

=

- Vq

+ Q.R

is the Earth's rotation vector, q =

P

+ gx, , p is the pressure,

p

the speci-

fic mass of sea water, x3 the vertical coordinate and R the turbulent Reynolds stress tensor (the stress is here per unit mass of sea water) resulting from the non-linear interactions of three-dimensional microscale turbulent fluctuations. The turbulent Reynolds stress tensor can be parameterized in terms of eddy viscosity coefficients. In microscale three-dimensional turbulence, these coefficients are of the same order of magnitude in the horizontal and vertical directions. Then, horizontal length scales being much larger than the depth, the last term in the righthand side of eq.(2) can be written simply, with a very good approximation

where C is the vertical eddy viscosity and K the turbulent Reynolds stress (vector). The residual flow is defined as the mean flow over a time T sufficiently large to cover at least one or two tidal periods. If the subscript

"o"

denotes such an average,

one may write

v

=

vo + v,

(4)

with (V), =

vo

(5)

What Vo and V, respectively include depends on the time of integration T. If T is of the order of one day (exactly two or three periods of the dominant Mp tide), T

- lo5

,

the averaging eliminates the tidal currents and smoothes out all

current fluctuations, - generated by variations of the wind field, for instance which have a characteristic time smaller than T.

,

223 However, as mentioned before, changes in the synoptic weather pattern often have time scales comparable with T

-

gible meteorological forcing, T

10'.

Then, unless one considers periods of negli-

- lo5

does not correspond to a valley in the energy

spectrum of the currents. In that case, one cannot derive an equation for V, by averaging eq.(2) and assuming that, as for an ensemble average, the averaging commutes with the time derivative. Furthermore, V, defined in this way, depends very much on time and doesn't correspond to the quasi-steady drift flow the biologists have in mind when they talk about residuals. One might argue that such a time dependent daily mean is still worth calculating to follow the response of the sea to the evolving w e a t h e r p a t t e r n , e s p e c i a l l y in storm conditions. 5

This however would be equivalent to modelling a storm surge with a time step of 10 and the results cannot be very accurate. It is much wiser, in that case, to solve equations (I) and ( 2 ) , without averaging for tides and storm surges simultaneously. Actually, "daily" residuals (i.e. mean currents over exactly two or three tidal periods) are meaningful only when the atmospheric forcing is negligible or exceptionally persistent. In the first case, they represent the so-called "tidal residuals" which result from in - and out-flowing macroscale oceanic currents and from the residual effect of non-linear tidal interactions. Tidal residuals represent a major contribution to the total residual circulation and, with very much less computer work needed, they already give a good idea of the long term residual circulation, such as the climatic circulation described below, where asubstantial part of the atmospheric contribution is actually removed by averaging over a variety of different weather conditions. If one takes, for instance, the averaging time T between l o 6 (- two weeks) and lo7 (-four months), one may expect, over such a long time, a diversity of meteorological conditions resulting in an almost random atmospheric forcing on the sea. The current patterns will reflect the atmospheric variability and, on the average, there will be only a small residue. The mean flow over a time T

- l o 6 , lo7

may be regarded as the "climatic residual"

flow which affects the dynamics of biological populations, the long term transport of sediments and the slow removal of pollutants. As

pointed out before, one may conceive a third kind of residuals obtained by ave-

raging over two or three tidal periods

(T 2 lo5

s)

in conditions of exceptionnally

persistent atmospheric forcing. The persistence of the meteorological conditions drives off the atmospheric energy input to small frequencies and a time of the order of

lo5 is acceptable for averaging

as it corresponds again to a valley in the energy spectrum. This kind of residuals may be called in brief "wind residuals". One must be aware, however, that they give a rather limited view of wind-induced currents in the sea.

224 If a typical weather pattern has a characteristic time of a few days, one must either determine the time dependent wind-induced and tidal flow described by equations ( l ) and ( 2 ) or the climatic residual flow which contains only the macroscale residue of changing weather patterns. Still, with moderate computer work needed, wind residuals may perhaps provide a first idea of various wind effects on the residual flow pattern which would not be apparent in the climatic or tidal residual pattern but which might occasionally be spotted by instruments in the field. In the following "residual circulation" will refer to the climatic residual circulation

(T

2 lo6

s)

or the tidal and wind residual circulations

(T 2 lo5 s ) with

the restrictions made above. The equations for the residual flow may be obtained by taking the average of equations (1) and ( 2 ) over the chosen time T. The time derivative in the left-hand side of equation ( 2 ) gives a contribution

One may argue that, since the time T is always a multiple of the main tidal period, the numerator of ( 7 ) is of the same order as the residual velocity V,. Then, for T 2 105

,

The average of the Coriolis acceleration is

One may thus neglect the contribution of the time derivative in the equation for v,. The residual circulation is then given by the steady state equations

v.v,

where

= 0

Since V,

is one or two orders of magnitude smaller than V, which contains in

particular the tidal currents, the first term in the left-hand side of eq.(12) is completely negligible. The tensor N

in the right-hand side plays, for mesoscale

motions, a role similar to that of the turbulent Reynolds stress tensor R

in eq.(2)

and may be called the "mesoscale Reynolds stress tensor". The last term in the righthand side of eq.(11) represents an additional force acting on the residual flow and resulting from the non-linear interactions of mesoscale motions (tides, storm surges

... ) .

The importance of this force was discovered, first, by depth-integrated numerical models of the residual circulation in the North Sea (Nihoul 1974, Nihoul and Ronday 1975) and the associated stress was initially referred to as the "tidal stress" to emphasize the omnipresent contribution of tidal motions.

THE MESOSCALE REYNOLDS STRESS TENSOR

The tensor N

can be computed explicitly by solving eqs.(I) and (2) for mesoscale

motions and taking the average of the dyadic V,V,

.

In fact the solution of eqs.(l) and (2) with appropriate wind forcing and open sea boundary conditions yields

v

=

v, + v,

and one may reasonably ask the question why one must go through the process puting N

and solving eqs. (10) and ( 1 1 ) to obtain the residual velocity V,

why one cannot solve (1) and ( 2 ) for the total velocity V from V

d i r e c t l y , by averaging the solution of eqs.(1) and 6V

on V

of, say, 10

%,

1.e.

and simply derive V, (2).

The problem here, again, is that, in the North Sea, V, represents 90 If one allows for an error

of com-

%

of V

.

resulting from the imprecision

of open-sea boundary conditions and from the approximations of the numerical method,

.

the error is of the same order of magnitude as the residual flow V, Because of non-linearities, one may fear that, in the averaging process, this error does not, for the essential, cancel out as V, does. Thus averaging the solution V

of eqs. (1) and (2), one gets V,

an error which may be as large as

100

%

+

(6V),

i.e. the residual velocity with

(Nihoul and Ronday, 1976a).

The procedure is conceivable when modelling a very limited area (near a coast, for instance) where the mesh size of the numerical grid can be reduced and where the open-sea boundary conditions can be determined with greater accuracy by direct measurements. Then

6V can be made small enough for the average V,

a satisfactory evaluation of the residual flow V,

.

+

(6V),

to provide

226 In the case of the North Sea or, even, the Southern Bight or the English Channel,

models of such a high accuracy are prohibitively expensive and cannot be considered for routine forecasting.

v, to compute the mesoscale stress tensor N However, the classical models give

with a fair accuracy and they can be used

.

The latter can be substitutdd in eq.(11) and the system of eqs.(10) and (11) can be solved very quickly to obtain V,

.

One can show that, in this way, one can determine V,

with good accuracy.

Typical values for the North Sea show that, in general, the two terms and

8 . (- V,V,),

If

2

n

A V,

are of the same order of magnitude.

6V, is the error on V,

This error induces an error

, one

has

6Vo on V,

given by

i.e.

Hence the r e l a t i v e error is the same on error as before. Thus if

v,

and on

v, and not the absoZute

v, can be computed with, say, a

90 % precision, the solu-

tion of the averaged eqs.(10) and (11) will give the residual circulation with the same 90

8

precision.

THE EQUATION FOR THE HORIZONTAL TRANSPORT

If one writes

u

v = u + w e 3

=

u, +

emphasizing the horizontal velocity vector u transport as

uo -

u, dx, -h

=

-

H, u,

(131 i (13')

U(

,

one defines the residual horizontal

227

co

where

is the depth-averaged velocity, H, = h

the residual surface elevation. (H,

h

because

+ 5,

,

L o ,

n e a r t h e end o f t h e dyke o f " l e R a t i e r " . The seaward boundary c o n d i t i o n s f o r t u r b i d i t y a r e a l s o d e t e r m i n e d f r o m measurements i n s i t u o r from s i m u l a t i o n r u n s . S u r f a c e and bottom b o u n d a r i e s A t t h e s u r f a c e , t h e boundary c o n d i t i o n a p p l i c a b l e t.o t h e s t r e a m i s d i c t a t e d by

t h e s h e a r i n g s t r e s s o f t h e wind (more o f t e n t h a n n o t s e t t o z e r o ) . T h i s t e r m i s e a s i l y introduced

:

293 V a r i o u s e x p r e s s i o n s f o r t h e f u n c t i o n f a r e a v a i l a b l e from l i t e r a t u r e ( f o r examp l e Wilson,

1966).

W e assume t h a t t h e r e i s no f l u x o f s a l t from w a t e r t o a i r o r v i c e v e r s a

:

F o r t h e suspended s e d i m e n t , t h e v e r t i c a l f l u x due t o s e t t l e m e n t i s b a l a n c e d by the v e r t i c a l dispersion a t the surface

:

A t t h e b o t t o m , t h e f r i c t i o n a l stress on t h e b e d ,

T~

i s g i v e n by :

I n f o r t u n a t e l y , owing t o t h e d i f f e r e n c e i n magnitude between t h e v e r t i c a l g r i d s t e p and t h e t h i c k n e s s of t h e l a m i n a r s u b - l a y e r ,

it i s very d i f f i c u l t t o obtain

a n u m e r i c a l v a l u e f o r t h e v e l o c i t y g r a d i e n t n e a r t h e bottom. V a r i o u s a t t e m p t s t o u s e t h i s f u n c t i o n w e r e made, w h i c h , a l t h o u g h n o t c a u s i n g d i v e r g e n c e i n t h e c a l c u l a t i o n s , n e v e r t h e l e s s d i d n o t prove s a t i s f a c t o r y . W e t h e r e f o r e p r e f e r r e d t o use a f u n c t i o n o f t h e s p e e d i t s e l f , r a t h e r t h a n of i t s d e r i v a t i v e , of t h e u s u a l form :

The c o e f f i c i e n t k ( o r d e r of magnitude 2 t o 3 ) i s a c o e f f i c i e n t of f r i c t i o n anal o g o u s t o t h o s e of Chezy and of S t r i c k l e r f o r a v e r t i c a l l y - i n t e g r a t e d model

The v e r t i c a l component of v e l o c i t y a t t h e bottom i s z e r o :

w-h

= 0

T h e r e i s no f l u x of s a l t t h r o u g h t h e bed

:

:

294 The v e r t i c a l f l u x of s e d i m e n t i s e q u a l t o t h e d i f f e r e n c e " e r o s i o n - d e p o s i t i o n "

K'z

acs az

_ I _

- ws cs =

(5) erosion

deposition

The e r o s i o n f u n c t i o n i s g i v e n i n t h e form o f P a r t h e n i a d e s r e l a t i o n

:

=M(+-I)

erosion

ce

and t h e d e p o s i t i o n f u n c t i o n i s t h a t g i v e n by E i n s t e i n - K r o n e

=

w s cs

(1961) :

(1 - %)

deposition The c o n s t a n t of e r o s i o n M , d e t e r m i n e d i n t h e l a b o r a t o r y f o r v a r i o u s t y p e s o f sediments (Harrison e t a l . ,

1971

;

C o r m a u l t , 1971) i s o f t h e o r d e r o f 0.001 S . I .

and f o r d e p o s i t i o n T~~ may b e ce o b t a i n e d e i t h e r by measurement i n t h e f i e l d ( o r by d e f a u l t i n t h e l a b o r a t o r y ) , o r u n i t s . The c r i t i c a l bottom stress f o r e r o s i o n

T

from P o s t m a ' s d i a g r a m .

If If

T

T~~

I f T

ce

(1

+

Ri)-7/4)

Kuo et al. (1978) used Pritchard's formua, but took account of wind effects

:

where H is the height of the waves, L is the wavelength of the swell,

and T is the period of the swell.

Blumberg (19751, however, used a formula slightly different from the above, based on the theory of Montgomery and the numerical results of Kent and Pritchard

Nz =

Kz (1

+

Ri)

:

296 Nz

=

Kz = 0 i f R i > R i c

He t h u s i n t r o d u c e d a c r i t i c a l R i c h a r d s o n number, n u m e r i c a l v a l u e 10, above which a l l v e r t i c a l exchanges c e a s e d t o e x i s t . I n t h e a p p l i c a t i o n o f t h i s model t o t h e S e i n e e s t u a r y , we have s u c c e s s i v e l y u s e d r e l a t i o n s h i p s c l o s e t o t h o s e q u o t e d by Hamilton, and a l r e a d y e s t a b l i s h e d f o r t h e Gironde (De Grandpri., Nz = No

Kz =

+

KO +

1978).

U

(N1~

f(z)

+ N2)

(1 + 7 R i ) - 0 . 2 5

H U F

(K1

f(z)

+ Kz)

(1

H

+

Ri)-1-75

with : f ( z ) =

t h e n s i m p l a r e m p i r i c a l f u n c t i o n s , s u c h t h a t t h e v e r t i c a l exchange c o e f f i c i e n t s i n c r e a s e d t o w a r d s t h e s u r f a c e , o f t h e form

:

I n f a c t t h e n u m e r i c a l r e s u l t s o b t a i n e d d i d n o t d i f f e r much, and t h e a v a i l a b l e o b s e r v a t i o n s a r e t o o few t o a l l o w one t o d e t e r m i n e which r e l a t i o n s h i p i s b e t t e r . I n o u r p r e s e n t s t a t e of knowledge o f n a t u r a l phenomena, it seems t h a t one c a n a r r i v e a t s u f f i c i e n t l y a p p r o x i m a t e r e s u l t s whichever o f t h e d i f f e r e n t f o r m u l a e i s u s e d f o r t h e exchange c o e f f i c i e n t s : p r o v i d e d t h a t t h e c o e f f i c i e n t s i n c r e a s e i n v a l u e w i t h d i s t a n c e o f f t h e bottom i n t h e l o w e r p a r t o f t h e f l o w . Even l e s s i s known a b o u t t h e c o e f f i c i e n t of d i s p e r s i o n f o r t h e s e d i m e n t

e t al.

;

Kuo

(1978) a d o p t e d t h e same e x p r e s s i o n a s f o r t h e d i s p e r s i o n of s a l t .

During s u c c e s s i v e r u n s it a p p e a r e d t h a t t o o s m a l l v a l u e s o f t h i s c o e f f i c i e n t

K ' z n e a r t h e bottom c o u l d l e a d t o n u m e r i c a l i n s t a b i l i t y erosion -h

+

deposition

+

:

WsCs

K'z

In t h i s case, t h e c o n c e n t r a t i o n g r a d i e n t computed a t c e r t a i n t i m e s l e d t o spur i o u s v a l u e s a t t h e b o t t o m , b e c a u s e o f t h e e x t r a p o l a t i o n u s e d i n a p p l y i n g t h e bound a r y c o n d i t i o n s . The e x p r e s s i o n f o r K ' z w a s t h e r e f o r e s i m p l i f i e d t o t h e form

:

297 NUMERICAL SCHEME To date, the number of numerical models of this kind is small, because one has

not only all the difficulties associated with two-dimensional models (such as the outer estuary model), but a l s o that of integrating within a domain with continuously variable geometry (at the free surface), and the problem of representing the river-bed. Among the models of this type, several schematize the bed geometry to coincide with the mesh boundaries, and consider the case of a tide of small amplitude, which does not require any modification of the computation procedure as simulation proceeds (Blumberg, 1975

;

Elliott, 1976

;

Wilson, 1977

;

Kuo et al., 1978).

The resulting staircase-like appearance of the bed (fig. 4) is certainly inadequate to represent the phenomena of sedimentation

;

and the simplified schematiza-

tion employed is totally inapplicable to the Seine, where the tidal range is of the same order of magnitude as the depth.

(I,-V Variables _M_-

;th

Variables

_vu__

( i+ l P Variables

-

(i?2)"d Variables __h_-

Fig. 4. An example of a grid pattern for a multilayered model.

The inconveniences can be greatly reduced by introducing a transformation of co-ordinates whereby the computational grid becomes rectangular. Of course, this

298 c a u s e s new t e r m s t o a p p e a r i n t h e e q u a t i o n s o f hydrodynamics, which c o n s i d e r a b l y lengthen t h e calculations. T h i s t y p e of " l a y e r e d " hydrodynamic model w a s t h e r e f o r e shunned i n f a v o u r of a model u s i n g l o c a l v a l u e s , e s s e n t i a l l y si m i l a r t o t h a t p u b l i s h e d by Hamilton ( 1 9 7 5 ) . i n F i g . 5. The c o m p u t a t i o n p o i n t s f o r t h e

The c o m p u t a t i o n a l g r i d i s shown

s t r e a m components and t h e c o n c e n t r a t i o n a r e h e r e s e p a r a t e d t o a l l o w f o r a b e t t e r a p p r o x i m a t i o n of d e r i v a t i v e s by f i n i t e d i f f e r e n c e s .

Computatlon points

1:

:

F i g . 5. The f i n i t e d i f f e r e n c e g r i d .

s cs

ws

299 The method of integration is explicit, and uses centred approximations of the spatial derivatives, except for the advection term for the concentration, which is offset upstream. Unfortunately, this first-order "upstream" discretization introduces a spurious numerical dispersion, but nevertheless it is the most suitable, and the most economical in terms of computation time, for stabilizing the scheme. However, to try to reduce this effect, the dispersion term has been expressed in terms of a centred second-order scheme. The finite-difference form of the equations finally used was as follows

AS

t

= S . i+1, j

=

s t.

.

1,i

-

t

+

U2) < 0

- 'i, j

si ( U 1

t s.

s1 (U1 + U2) > 0

1-1,j

:

300

The equation of conservation of mass for the sediment has been rendered in a finite-difference form in exactly the same way as the equation of advectiondispersion for a solute, having taken into account the terminal velocity Ws, calculated at t.he same point as the concentration.

Modifications of the scheme near the boundaries The particularly interesting aspect of this numerical scheme is that it allows the relevant equations to be solved right up to the upper and lower limits of the domain, whatever their position. To do this, the computation requires values at nine grid-points surrounding the current calculation point. Near the boundaries, some of these points will lie outside the domain of integration. Accordingly, at each time-step, values of U,

S

and Cs are extrapolated to points above the surface,

and under the river-bed, using polynomial functions. For example, in fig. 6, the value So is obtained by parabolic extrapolation from the adjacent values

S1

and S 2 , and the condition of zero derivative at the

surface

~

Similary, SN+l is computed from SN-l and S using the condition of zero deriN vative at the bottom. Nevertheless, this second-order extrapolation proved insufficient to evaluate the dispersion terms near the boundaries, which correspond in fact to a second derivative

a

:

3

(

Kz az

We therefore use an extrapolation based on a polynomial of the third degree, passing through the points S

S 2 and S 3 and satisfying the condition of zero first

301 derivative at the surface.

Z

5-

\

\

\

-h-

Fig. 6. Salinity profile near the boundaries.

The calculation is identical for the salinity at the bottom, also for the stream velocity and the sediment concentration, but only at the surface. To compute the stream velocity near the bottom, Hamilton used a similar parabolic extrapolation based on the points

U

N-2'

U

N-1

and U N , whence he obtained U N + l

and

UIIllThis procedure, which is perfectly satisfactory numerically, is in practice in-

convenient, because it leads to a non-zero stream on the bottom. T h i s in turn leads to doubtful values for the stream rate one metre off the bottom, and for the total discharge in the water column (by integration of the function U ( z ) defined by interpolation).

A different technique has been introduced here, by assuming between the bed and the point suffixed N (fig. 7) a power law of the form

:

The coefficient A and a in this function are determined by keeping at point N the value of the function U ( z ) and its first derivative (obtained by the parabola UN-2,

u

~ and - ~ u,)

.

302

Fig. 7. Velocity p r o f i l e near t h e bottom.

C a l c u l a t i o n o f t h e t u r b i d i t y and i t s d e r i v a t i v e s near t h e bottom p r e s e n t s d i f f i c u l t i e s analogous t o t h o s e j u s t explained f o r t h e stream. I t i s even more important t o reproduce a c c u r a t e l y ( a s f a r a s p o s s i b l e ) t h e c o n c e n t r a t i o n c l o s e t o t h e bottom, because t h e d e p o s i t i o n f u n c t i o n uses t h i s value

:

In an o r i g i n a l v e r s i o n of t h e model a p p l i e d t o t h e Gironde (Du Penhoat and Salomon, 1 9 7 9 ) , a p a r a b o l i c e x t r a p o l a t i o n was used, and was open t o c r i t i c i s m a s f a r a s t h e accuracy of t h e r e s u l t s w a s concerned. I n o r d e r t o s i m u l a t e more c l o s e l y phenomena on a smaller s c a l e than t h e mesh s i z e , w e have here come c l o s e r ( a s f o r t h e v e r t i c a l stream p r o f i l e s ) t o t h e anal y t i c a l s o l u t i o n . We know t h a t i n a s t e a d y s t a t e , when t h e f a l l speed i s balanced by t h e v e r t i c a l d i s p e r s i o n , t h e c o n c e n t r a t i o n v a r i e s w i t h h e i g h t according t o :

We have t h e r e f o r e r e t a i n e d t h e q e n e r a l form of t h i s f u n c t i o n t o d e s c r i b e t h e

303 c o n c e n t r a t i o n n e a r t h e bottom : - B (z+h) C s ( z ) = Cs(-h) e

A f t e r f i n d i n g t h e c o n c e n t r a t i o n C s a t t h e p o i n t s s u f f i x e d N-2, N-1 and N , a par a b o l i c interpolation allows u s t o f i n d t h e derivative

& at az

the point N (fig. 8 ) .

z

-h

m

F i g . 8. T u r b i d i t y p r o f i l e n e a r t h e b o t t o m .

W e t h e n s e e k a n e x p o n e n t i a l e x p r e s s i o n which s a t i s f i e s e q u a t i o n ( l o ) and u s e s

t h e known v a l u e s CsN and __ az

.

T h i s e x p r e s s i o n t h e n g i v e s t h e v a l u e o f C s on t h e

b o t t o m , and a l s o t h e e x t r a p o l a t e d v a l u e C s

N+1T h i s p r o c e d u r e , a l t h o u g h numerically v e r y dangerous ( a t i n y e r r o r i n t h e t u r -

b i d i t y g r a d i e n t l e a d i n g t o c o n s i d e r a b l e d i f f e r e n c e s i n Cs on t h e b o t t o m , or i n i t s second d e r i v a t i v e ) , o n l y r a r e l y c a u s e d n u m e r i c a l i n s t a b i l i t y ; and w e were always a b l e t o e l i m i n a t e i t by a n a d e q u a t e p a r a m e t e r i z a t i o n o f t h e t u r b u l e n t exchange

t e r m s (principally K ' z ) .

S t a b i l i t y o f t h e scheme A s t a b i l i t y a n a l y s i s r e f e r i n g t o Von Neumann r e q u i r e m e n t s h a s been c a r r i e d o u t

by Hamilton (1975) f o r t h e cases o f a l i n e a r i z e d s y s t e m , and w i t h o u t t a k i n g i n t o a c c o u n t t h e p e c u l i a r t r e a t m e n t o f p o i n t s a t t h e b o u n d a r i e s . The c h a n g e s made h e r e t o t h e o r i g i n a l scheme a r e i n s u f f i c i e n t t o modify t h e c o n c l u s i o n s o f t h e s t a b i l i t y s t u d y , which g a v e

:

304

(+,

At < minimum

Ax

u

2gH

For the sub-critical flow dealt with in this study, the second criterion turns out to be less stringent than the third. The first and the third criteria therefore allow us to fix limits to two of the three integration steps (At, Ax, A z ) , the third being fixed by the density of results required. But of course, that the scheme is stable does not automatically imply that the solution is good, notably owing to the numerical dispersion introduced by the offsetting of certain derivatives. So, in the absence of a complete study of numerical perturbations, a very careful1 analysis of the results will have to be done.

Choice of steps for the integration A maximum depth of water of some 14 m suggests for the third criterion

:

At < 0.06 Ax It is awkward to calculate the limitation imposed by the vertical integration step, since the vertical speed is not well known a priori. We can deduce an order of magnitude for W by using the maximum rise rate (4 metres per hour) 35 W( 6 cm)

To unify the mesh-size and time-step of all three models, so that they might run simultaneously, the value of Ax

=

1000 m was used in this model. Accordingly,

the time-step is one minute, which has the advantage of being a simple fraction of the time-step in the vertically-integrated models, and facilitates their running in tandem. For the mesh-size Az, a value of 1.5 rn was chosen as a compromise between the desire for precision and the need to economise on computation time. It could have been very much reduced had the need been manifest.

RESULTS

Figures 9 to 12 give a picture of the circulation throughout a tidal cycle for a mean range of tide and low fresh-water flow. Particularly notable is the large area occupied by slack water at the end of the flood (fig. 9a), compared with the more abrupt reversal of the ebb (fig. llb or llc), and accompanied by a slight difference in phase between the bottom and the surface. This phenomenon is well-known in estuaries, but it appears here even

t

-5

-7

-9

1

-11

rnrn/s

i 360 350

f

* 1 m/s

340

I

330

320

310

ABSC155

KM

*

-9 -11

”

1

a

1 rn/s

360

350

330

340

320

310 KM

ABSCISS

9t

r)

1 rn/s 41

360

350

340

330

320

1

310 ABSCISS

Fig. 9. Instantaneous velocity field in the middle estuary (hour by hour)

KM

306

-7.

b

1

mm15

t +

-9 -

-7 -9

1 m/s

c

*

1m / s

11

Fig.

1

rnm/sf

10. I n s t a n t a n e o u s v e l o c i t y f i e l d in t h e m i d d l e e s t u a r y ( h o u r by h o u r , continued).

307

I l1 9

5u 7 iil5 = 3 1 -1 -3

-5

a

-7

*

-9

1m / s

-11

, _ _ J

360

350

340

330

-5

320

310 ABSCISS KM

-

-9

1 m/s

-11

Fig.

360

350

340

330

360

350

340

330

320

310 ABSCISS KM

320

310 ABSCISS KM

11. I n s t a n t a n e o u s v e l o c i t y f i e l d i n t h e m i d d l e e s t u a r y (hour by h o u r , continued).

308

11

= 9

*

-9 -11

1m / s

360

350

340

330

320

310 AB5CIS5

KM

310 ABSCISS

KM

11

' 9 1 I-

I

P Ly

I

-11 L-

Fig.

360

350

340

330

320

12. I n s t a n t a n e o u s v e l o c i t y f i e l d i n t h e m i d d l e e s t u a r y ( h o u r by h o u r , continued).

though the estuary is well mixed, under the conditions stated above. Furthermore, it is remarkable that this phase-lag at Commencement of Flood (surface lagging bottom) exists only in the lower reaches of the model, where there is a horizontal salinity gradient. It disappears further up-river, where the water is completely slack. Note also the intensity of the early flood compared with that of the ebb. The following diagram (fig. 13) represents the vectors obtained by integrating the stream over the same tidal cycle. We are well aware of the caution required in interpreting these integrated values as the residual current ; nevertheless, in this particular case the rate of the averaged stream (about 1 knot for low freshwater flow) is exceptional, and so clear that its essential character is undeniable. We may add that these results have been confirmed by measurements in the field (Avoine, 1980). This (Eulerian) residual sea-going current can be at once explained by the peculiar form of the tide in the Seine, and by the artificial works (dykes and training-banks) which have been carried out in this portion of the estuary. The very rapid rise in water level, followed by a near stand at high tide, accentuate the difference in mean water level between the flood and the ebb which one generally observes in estuaries. This difference in level, of the order of 2 metres in the region of the dykes, implies a difference in the flow cross-sections which has its repercussions on the streams, since the volume which comes in on the flood differs only slightly from that expelled on the ebb. The more the flow cross sections increase rapidly with height, the more important this effect becomes reinforcing the flood rates, and thus opposing the penetration of marine sediments into the estuary.

The submarine training-banks are very efficient in doing this, as far as sand is concerned (Salomon, 1976). As far as the fine sediment isconcerned, the dynamics are more obscure, but the

model herein described can throw some light on the problem. Simulation of the turbidity maximum It appears that, on examining measurements in the field (Avoine, 1980) that turbid accumulations exist in a quasi-permanent state in the reach between kilometres 320 and 360 from Paris, a sediment plug which is only occasionally and partially expelled from the channel. Since the Eulerian residual current is seaward, as we have just described, it does not seem that the classical explanation linked to the nodal point of density, is valid. We therefore decided to investigate, with the aid of the model, another interpretation. For this, we considered that the bed of the estuary was initially inerodable, and we imposed a turbidity of 1 g/1 everywhere. After running the model for a few tidal cycles, supposing that there had been no input of sediment at the landward and seaward boundaries, we obtained the results presented in figures 15 to 17. The fine sediments collect in a sort of nucleus, and oscillate with the tide, practi-

311

. 02

03

04

_ 0.5 a6

~

0.7

0.8

~

0.919/1)

360

350

0.2

0.3

0.4

0.5

a6

0.7

0.8

340

330

320

310 UPSTREAM

DOWNSTREAM

-1OKmd

0.9 (9, I I

360 DOWNSTREAM

350

340 k l O K m

330

4

320

310 UPSTREAM

Fig. 15. Computed instantaneous distribution of sediment concentrations (two hours between e a c h ) .

312

360

350

DOWNSTREAM

340 (--lo

330 Km

~

320

310 UPSTREAM

-!

H,

a 7 6

0.2

0.3

04

0.5

0.6

0.7

0.8

0.9(9/1)

2

1 0 -1

-2

-3 -4

-5 360 DOWNSTREAM

Fig.

350

340

330

320

310 UPSTREAM

klOKm-(

16. Computed i n s t a n t a n e o u s d i s t r i b u r i o n o f s e d i m e n t c o n c e n t r a t i o n s ( t w o hours between e a c h , c o n t i n u e d ) .

31 3

-1

5c

41

360

350

DOWNSTREAM

340

330

i1OKm

320

-4

310 UPSTREAM

?

0.2

03

04

05

a6

0.7

360 DDWNSTRFAM

350

340

330

-10 K m -

320

310 UPSiREAM

Fig. 17. Computed i n s t a n t a n e o u s d i s t r h u t i o n ot sediment concentrations (two h o u r s between each, continued).

314 c a l l y without being e x p e l l e d from t h e e s t u a r y . Figure 18 summarises t h e process ; seaward t r a n s p o r t during t h e ebb, a weak s e t t l i n g i n t h e lower reaches before being completely re-suspended,

then t r a n s p o r t up-river,

with a more g e n e r a l s e t t l i n g

owing t o t h e downward v e r t i c a l v e l o c i t i e s , t o t h e more p r o t r a c t e d s l a c k water and t h e g r e a t e r volume of water (and t h e r e f o r e of s e d i m e n t ) , and t h e p r o g r e s s i v e r e suspension by t h e ebb. I t t h e r e f o r e follows t h a t t h e Lagrangian r e s u l t a n t f o r f i n e sediment i s more o r l e s s n i l i n t h i s p a r t of t h e e s t u a r y : t h e p a r t i c l e s a r e recycled. I t can a l s o be seen t h a t t h e i r r e g u l a r i t i e s of t h e bottom a c t a s sediment traps.

CONCLUSION

The numerical model described above appears t o reproduce favourably v e l o c i t y f i e l d s and t u r b i d i t y p r o c e s s e s . Because it o p e r a t e s on instantaneous v a l u e s , it

i s p a r t i c u l a r l y s u i t e d t o reproduce u l t r a - t i d a l dynamic p r o c e s s e s , b u t not long term t r e n d s . In t h e p r e s e n t a p p l i c a t i o n t o t h e Seine e s t u a r y , examination of t h e r e s u l t s y i e l d s a p o s s i b l e i n t e r p r e t a t i o n of e s t u a r i n e sediment behaviour. According t o t h e c h a r a c t e r of t h e t i d e , and i t s importance r e l a t i v e t o t h e f l u v i a l d i s c h a r g e , a t l e a s t two mechanisms can e x p l a i n t h e formation of an e s t u a r i n e t u r b i d i t y maximum :

- d e n s i t y phenomena, which have been c l a r i f i e d many t i m e s , and which a r e cert a i n l y dominant i n s t r a t i f i e d e s t u a r i e s (small t i d e , important f l u v i a l discharge, deep) ; -

dynamic t i d a l phenomena, which we have evidenced i n t h e s p e c i f i c case of t h e

Seine, and d o u b t l e s s r e l a t i v e l y more important f o r t h e t i d e t h e r e i s b i g (and even favourably d i s t o r t e d ) , t h e f l u v i a l discharge i s small and t h e water i s shallow. Probably t h e s e two t y p e s of causes e x i s t simultaneously, with v a r i a b l e i n t e n s i t y , i n t h e Seine it seems t h a t t h e dynamic phenomenon i s v e r y important i n t h e dyked r e a c h e s , b u t it would not be impossible f o r a nodal p o i n t t o e x i s t seaward o t t h e dykes, mainly during high r i v e r flow, and t h a t t h e dynamics of accumulation t h e r e be q u i t e d i f f e r e n t , t h e more so s i n c e t h e l a t e r a l dimension would have t o be taken i n t o account.

Svmbols used B : width of t h e e s t u a r y

g

:

a c c e l e r a t i o n of g r a v i t y

h : depth

(below maximum low t i d e )

H : t o t a l depth

k

:

(from s u r f a c e t o bottom)

friction coefficient

K x , Kz : d i s p e r s i o n c o e f f i c i e n t s f o r mass ( s o l u t e ) , b e f o r e width averaging

Ka : Karman's c o n s t a n t K'x, K'z : d i s p e r s i o n c o e f f i c i e n t s f o r sediment, b e f o r e width averaging

31 5

..

h

LOW TIDE

! m '

Concentration

5

- 5O

I

h ~FlDOD(L,T.+Zh30)

(1 0

. .

-5

Fig.

18. Computed sediment behaviour d u r i n g a t i d a l c y c l e .

I-.-.I

0.5 04

,

-

03 0.2

316 I<x, Kz

:

dispersion coefficients for mass (solute), after width averaging

K'x, K ' z

:

Nx, Nz

dispersion coefficients for momentum, before width averaging

Nx,

:

dispersion coefficients for sediment, after width averaging

Nz : dispersion coefficients for momentum, after width averaging

1'

Q =

Udz

-h Ri

:

Richardson number

S

:

salinity

t

:

time

U , W : horizontal and vertical components of velocity

V*

:

friction velocity

Ws

:

settling velocity

x, z

:

z,

bed roughness

5

:

:

horizontal and vertical axis

surface elevation

P : density

p

: p

T

:

averaged over H

shear stress

REFERENCES Avoine, J . , 1980. S.A.U.M. de l'estuaire de la Seine. Etudes hydroskdimentaires. Internal report, university of Caen (France). Bowden, K.F. and Hamilton, P., 1975. Some experiments with a numerical model of circulation and mixing in a tidal estuary. Estuarine and coastal marine science, 3

:

281-301.

Blumberg, A.F., 1975. A numerical investigation into the dynamics of estuarine circulation. Chesopeake bay institute, technical report 91. Blumberg, A.F., 1978. The influence of density variations on estuarine tides and circulations. Estuarine and coastal marine science, 6

:

209-215.

Cormault, P., 1971. Determination experimentale du debit solide d'krosion de s6diments fins cohesifs. Fourteenth congress of I.A.H.R., 4

:

D2.

De Grandpr6, C., 1979. ModBle bidimensionnel en temps reel de la circulation verticale estuarienne. Application Du Penhoat, Y . and Salomon, J . C . ,

a

la Gironde. Oceanologica acta, 2

:

61-68.

1979. Simulation numerique du bouchon vaseux en

estuaire. Application 2 la Gironde. Oceanologica acta, 2 Dyer, K., 1973. Estuaries

:

:

253-260.

a physical introduction. John Wiley, New York.

Elliott, A.J., 1976. A numerical model of the internal circulation in a branching tidal estuary. Chesapeake bay institute, special report 54. Festa, J.F. and Hansen, D.V., 1976. A two-dimensional numerical model of estuarine circulation

:

the effects of alternating depth and river discharge. Estuarine

and coastal marine science, 4

:

309-323.

317 Hamilton, P., 1975. A numerical model of the vertical circulation of tidal estuaries and its application to the Rotterdam waterway. Geophysical journal of the royal astronomical society, 40

:

1-21.

Harrison, A.J.M. and Owen, M.W., 1971. Siltation of fine sediments in estuaries. Fourteenth congress of I.A.H.R., 4

:

D1.

K u o , A., Nichols, M. and Lewis, J., 1978. Modeling sediment movement in the turbi-

dity maximum of an estuary. Virginia institute of marine science, bulletin 111. Munk, W.H. and Anderson, E.R., 1948. Note on the theory of the thermocline. Journal of marine research, 7

:

276-295.

Pritchard, D.W., 1960. The mixing and movement of contaminants in tidal estuaries. In proceedings of the first international conference on waste disposal in the marine environment, university of California at Berkeley, Perganion press. Salomon, J.C., 1976. Modele mathematique de la propagation de la maree en estuaire et des transports sableux associes. Application aux estuaires de la Loire et de la Seine. Thesis, university of Brest (France). Wilson, B.W., 1966. Note on surface wind stress over water at low and high wind speed. Journal of geophysical research, 65

:

3377-3382.

Wilson, R.E., 1977. A model of dynamics in the lower potomac river estuary. Chesapeake science, 18

:

177-187.


319

NUMERICAL SIMULATIONS OF SALINITY, TURBIDITY AND SEDIMENT ACCUMULATION IN THE SCHELDT ESTUARY

W. BAEYENS’, Y. ADAM2, J.P. MOMMAERTS2 and G. PICHOT’

’Dienst Analytische Scheikunde, Vrije Universiteit Brussel, Brussels (Belgium) 2Beheerseenheid Model Noordzee en Schelde, Ministerie van Volksgezondheid en Leefmilieu, Brussels (Belqium)

ABSTRACT In order to simulate the physical behaviour of the Scheldt estuary, a hydrodynamic and a dispersion model have been devised. Both models are two dimensional, vertically integrated, and are solved numerically with a multioperational finite difference scheme, using a grid of 300 x 300 meters. The hydrodynamic model, which allows the simulation of instantaneous water levels and mean velocities over depth is controlled at the downstream boundary by time-varying water levels and at the upstream boundary by the river flow. The dispersion model, which predicts the evolution of salinity and turbidity in the water column and the sedimentary budget at the bottom, is controlled at the upstream and the downstream boundary by timevarying salinity values dependent on the river flow and by time-varying turbidity values averaged over the river flow. An increase of the river flow causes a downstream shift of the brackish water zone. Due to the influence of the salinity on flocculation and therefore on sedimentation of suspended material, the sedimentation zone is also shifted downstream. This results in higher turbidities and a lower sedimentary budget at the bottom in the upstream part of the estuary. Under average hydrodynamic conditions the computed sedimentary budget integrated over a tidal cycle at the different grid points agrees well with observations of mud accumulation in the same area.

INTRODUCTION The physical behaviour of the Scheldt estuary i.e. the flow of water, salts and particulate matter, has a great influence on the dynamics of the ecosystem (growth of living organisms, transport of heavy metals, etc.). For instance, the heterotrophic bacterial activity is very high in the upstream part of the Scheldt estuary but drops dramatically at about 60 km from the river mouth

(G.

Billen et

320 al., 1977). This drop has been explained by the effect of increased salinity which causes (1) flocculation of suspended matter and organic matter and subsequent sedimentation, (2) inhibition of the activity of the fresh water bacteria. Considering the dynamics of phytoplankton, primary production is controlled by the incident light and the transparency of the water which can be inferred from the turbidity. As soon as the intensity of the incident light is sufficient to ensure photosynthesis, the development of diatoms starts at the mouth of the estuary where the turbidity is minimum

(0.

Beckers and R. Wollast, 1977). During summer

the area of development progressively moves upstream as a result of an increasing light intensity and an exhaustion of silica in the downstream part of the estuary. It is obvious from the few examples mentioned above, that a sound understanding of estuarine physics is a prerequisite for all concerned with the dynamics of estuarine ecosystems. Unfortunately, the complex geometry of the estuary (ebb and flood channels, tidal flats, meanders) as well as non-tidal fluctuations of the hydrodynamic boundaries (river flow and tidal amplitude range from 10 m3/s to

400 m3/s and from 2.96 m to 4.42 m respectively) make the description and prediction of the velocity field and hence of the dispersion of salinity and turbidity very difficult. Moreover, the behaviour of the turbidity is strongly depending on direct and indirect interactions with the other physical variables. Flocculation of the fine grained material supplied by the river starts as soon as the salinity exceeds

1

This flocculation zone has no fixed position but moves to and fro during

a tidal cycle. In periods of high (low) river flow and decreasing (increasing) tidal amplitude at the mouth, the tidal flocculation zone is shifted downstream (upstream). Local hydrodynamic conditions govern the settlinq down of the flocculated material. Considering the annual amount of material accumulating at tlfe bottom in various areas of the Scheldt estuary (Wollast, 1977), two distinct sedimentation zones can be defined. In the area Rupelmonde (km 90) - Doel (km 60) the accumulation amounts to 2000

lo3 tons/year

Hansweert (km 35) it amounts to 220

lo3

and in the area Doel (km 60) -

tons/year (these values only reflect the

balance of sedimentation and erosion). In order to gain better insight in processes such as flocculation, sedimentation and erosion and consequently in the interactions between the physical variables, we decided to construct a mathematical model which should enable us to simulate these phenomena and to predict the evolution in space and time of the selected variables. It should also allow to calculate local sedimentary budgets.

MATHEMATICAL EQUATIONS

:

HYDRODYNAMICS

In shallow seas as well as in well-mixed estuaries it is generally sufficient to consider depth-averaged variables. The momentum and continuity equations governing the dynamics of the fluid after integration over the depth become

:

321

3H

*

R . VH

- - t

at

. v

-

=

H

with :

''

-h

=

0

v dz

-

v e l o c i t y vector V -

mean v e l o c i t y v e c t o r over depth

Vh

gradient i n horizontal directions

f

Coriolis factor

e

u n i t vector i n t h e v e r t i c a l d i r e c t i o n

Ll

gravitational acceleration

5

s u r f a c e water l e v e l r e l a t i v e t o t h e r e f e r e n c e plane

h

d i s t a n c e from t h e r e f e r e n c e p l a n e t o t h e bottom

H

t o t a l depth

V

viscosity coefficient

Ts, Tb s u r f a c e and bottom stresses P

f l u i d density

D E F I N I T I O N OF THE CONTROL PARAMETERS

The t h r e e c o n t r o l parameters V,

T

'rb i n equation

and

A s t h e v i s c o s i t y term i n c l u d e s i n f a c t two e f f e c t s

:

( 1 ) need t o be s p e c i f i e d .

on t h e one hand eddy

v i s c o s i t y caused by e r r a t i c s m a l l s c a l e motions and on t h e o t h e r hand shear t u r b u l e n c e due t o t h e inhomogeneous v e r t i c a l v e l o c i t y f i e l d , t h e o v e r a l l v i s c o s i t y c o e f f i c i e n t ( V ) i s t h e sum of t h e eddy (V

V V

1 . According t o Kolmogorov's t h e o r y ,

(V )

e

V

and t h e s h e a r v i s c o s i t y c o e f f i c i e n t equals 5 m 2 / s ,

while an e s t i m a t i o n of

on t h e b a s i s of Nihoul's work (Nihoul, 1975) gave a value of 20 m 2 / s .

Hence

e q u a l s about 2 5 rn2/s. The s h e a r s t r e s s a t t h e s u r f a c e ( T

can become s i g n i f i c a n t i n p e r i o d s of very

s t r o n g winds, b u t i s g e n e r a l l y very small i n e s t u a r i e s compared with t h e shear s t r e s s a t t h e bed ( 7 ) . Therefore T i s n o t included i n t h e model. b By d e f i n i t i o n , bottom stress and s h e a r v e l o c i t y (V a r e r e l a t e d a s follows k

:

However, i n two dimensional, v e r t i c a l l y i n t e g r a t e d models, t h e s h e a r stress must be i n f e r r e d from t h e mean v e l o c i t y over depth. Often t h e following expression

i s used Tb

=

:

P D V ' I

1 1 1

(5)

where D i s a drag c o e f f i c i e n t , dependent on t h e roughness of t h e channel bed. I n

322 h y d r a u l i c engineering e x t e n s i v e use i s made of Chezy's formulation :

.D

=

(6)

g/C2

with C t h e Chezy c o e f f i c i e n t . From v e r t i c a l v e l o c i t y p r o f i l e s and corresponding s h e a r v e l o c i t i e s ( s e e SOURCES AND S I N K S ) , w e deduced f o r t h e bottom of t h e Scheldt e s t u a r y a t y p i c a l f r i c t i o n c o e f f i c i e n t (Manning's n) of 3.3

lo-*.

NUMERICAL METHOD AND BOUNDARY C O N D I T I O N S

The p a r t i a l d i f f e r e n t i a l e q u a t i o n s (1) and ( 2 ) a r e approximated by t w o f i n i t e d i f f e r e n c e e q u a t i o n s , one e x p l i c i t t h e o t h e r i m p l i c i t , used a l t e r n a t i v e l y f o r a s t e p by s t e p s o l u t i o n i n time. The advantage of such a procedure i s t h a t over a whole time s t e p t h e d i f f e r e n t t e r m s i n e q u a t i o n s (1) and ( 2 ) are e i t h e r c e n t r a l i n time o r averaged over t h a t time i n t e r v a l , allowing less s e v e r e s t a b i l i t y c o n d i t i o n s concerning t h e time s t e p . This scheme i s v e r y c l o s e t o L e e n d e r t s e ' s (Leendertse e t a l . ,

1971a) multi-

o p e r a t i o n method. Only t h e advection t e r m s are c a l c u l a t e d on a h i g h e r time l e v e l by an i t e r a t i v e procedure, and t h e v i s c o s i t y term, which i s added t o t h e momentum equation i s c a l c u l a t e d e x p l i c i t l y . The c a l c u l a t i o n s a r e c a r r i e d o u t with a 300 x 300 m mesh-size

g r i d (Figure 1 ) .

The downstream boundary i s s i t u a t e d a t 45 km f r o m t h e mouth, t h e upstream boundary

a t 1 2 0 km from t h e mouth. From km 65 on, t h e S c h e l d t becomes s o narrow (about

500 t o 600 m e t e r s ) , t h a t we have " s t r a i g h t e n e d " t h e r i v e r , l e a v i n g i t s crosss e c t i o n a l geometry (width, depth, t i d a l f l a t ) unchanged. The g l o b a l t i m e s t e p e q u a l s 2 minutes. AS one of our o b j e c t i v e s r e q u i r e s a mean hydrodynamic s i t u a t i o n , t h e following

boundary c o n d i t i o n s a r e used :

- Downstream

:

- Upstream

a mean (Q

:

a mean i n p u t t i d e =

80 m 3 / s ) ,

a high ( Q = 350 m 3 / s )

and a low (Q = 1 m 3 / s )

r i v e r flow The i n i t i a l c o n d i t i o n s ( v e l o c i t i e s a r e z e r o and t h e water l e v e l e q u a l s t h e low water l e v e l a t t h e downstream boundary) do n o t have any i n f l u e n c e on t h e f i n a l r e s u l t s , because s i m u l a t i o n s a r e c a r r i e d o u t u n t i l a c y c l i c p a t t e r n ( g e n e r a l l y a f t e r t h r e e t i d e s ) i s obtained.

RESULTS

In o r d e r t o s i m u l a t e f l o o d i n g of t i d a l f l a t s d u r i n g r i s i n g t i d e and subsequent r e t r e a t i n g of t h e land-water boundary d u r i n g ebb, an adapted numerical procedure was used. To i l l u s t r a t e t h i s procedure, t h e v a r i o u s d r y ( c i r c l e s ) and wet g r i d p o i n t s ( i n t e r s e c t i o n s ) a t low w a t e r a r e r e p r e s e n t e d on F i g u r e 1.

323

Fig. 1 : The numerical g r i d a t high water (on t h e l e f t ) and a t low water (on t h e r i g h t ) . The d r y g r i d p o i n t s a t low water a r e i n d i c a t e d by c i r c l e s . The agreement between measured and computed t i d e l e v e l s i s very qood. But achieving a good agreement between measured and computed v e l o c i t i e s , and p o s s i b l y a d j u s t i n g t h e model a c c o r d i n g l y , i s of course more important f o r c o n s t i t u e n t t r a n s p o r t s i m u l a t i o n s . This i s , however, a very d i f f i c u l t t a s k , because one needs r e l i a b l e d a t a on i n s t a n t a n e o u s mean v e l o c i t i e s over depth, f o r t h e hydrodynamic boundary c o n d i t i o n s used i n t h i s model (mean i n p u t t i d e , mean r i v e r f l o w ) . Although

w e were n o t able t o compare t h e c a l c u l a t e d v e l o c i t i e s with f i e l d d a t a , two f a c t s suggested t h e c a l c u l a t e d v e l o c i t y f i e l d was r e a l i s t i c : ( 1 ) with a comparable hydrodynamic model of Jamaica Bay, Leendertse e t a l .

(1971b) observed a f a i r l y

good agreement between t h e i r c a l c u l a t e d and measured d a t a ; (2) w e c a l c u l a t e d t h e water m a s s t r a n s p o r t through f o u r c r o s s s e c t i o n s and found t h a t agreement with observed d a t a was good (Ministere des Travaux P u b l i c s , personal communication) and t h a t t h e law of conservation of t o t a l f l u i d mass was s a t i s f i e d . From t h e computed v e l o c i t y p a t t e r n s a t d i f f e r e n t moments of t h e t i d e , it i s c l e a r t h a t most of t h e time very high v e l o c i t i e s occur i n t h e channels, whereas i n t h e shallow p a r t s , t h e v e l o c i t i e s a r e much lower, causing l a r g e v e l o c i t y g r a d i e n t s on a l o c a l s c a l e . Small v e l o c i t i e s a r e only observed h a l f an hour before and a f t e r t h e t u r n of t h e c u r r e n t . The c a l c u l a t e d v e l o c i t y p a t t e r n one hour before

324 high water and a t t h e moment of c u r r e n t i n v e r s i o n i s shown on Figure 2 .

.Fig. 2 : The c a l c u l a t e d v e l o c i t y p a t t e r n one hour b e f o r e high water (on t h e l e f t ) and a t t h e t u r n of t h e c u r r e n t (on the r i g h t ) . F i n a l l y , v e l o c i t y p a t t e r n s were c a l c u l a t e d f o r t h e t h r e e d i f f e r e n t r i v e r flows Very small d i f f e r e n c e s i n l o c a l v e l o c i t i e s were observed, confirming t h a t t h e instantaneous v e l o c i t i e s a r e almost e n t i r e l y due t o t h e t i d a l a c t i o n .

MATHEMATICAL EQUATIONS : DISPERSION

The e v o l u t i o n of suspended s o l i d m a t t e r and s a l i n i t y can be described by t h e i r mass conservation equation. This equation i s i n t e g r a t e d over depth.

. __ am at with

t

: P

R

vh .

HIP

=

D c1

+

HR

t

(7)

HS

c o n c e n t r a t i o n of c o n s t i t u e n t P i n t e r a c t i o n term (production-destruction

r a t e o f P by i n t e r a c t i o n s

with o t h e r c o n s t i t u e n t s ) S

source - s i n k term ( i n p u t - o u t p u t r a t e of P)

D c1

diffusion t e r m

325 As the velocity field is known, only the terms in the right hand side of equation ( 7 ) must be specified

:

DIFFUSION (Da) The global diffusion takes into account eddy diffusion and shear diffusion. The eddy diffusion coefficient ( A ) can be calculated in a way analogous to the eddy viscosity coefficient and equals 5 m2/s. It appears from the studies of Elder (1959) and Nihoul et al. (1975) that the magnitude of shear diffusion is proportional to the velocity and depth and that it acts in the same direction as the velocity vector. Hence, we expressed the shear diffusion coefficient (1 ) as

.

As

Q

:

VH G / C

The global diffusion coefficient ( A ) is then the sum of A and As,

(8)

which is isotropic,

which is anisotropic.

INTERACTIONS (HR) While the salinity is a passive constituent (other constituents have no influence on its evolution), biological and chemical reactions could produce or eliminate certain specific compounds of the suspended matter. This would result in a substantial modification of the solid matter composition in time and space. Such a modification, however, was not observed by Wollast (1973). His results, on the contrary, indicate a remarkably constant composition in the major elements. As the concentration of suspended matter is not affected by such interactions, these terms were not considered in the model.

SOURCES AND SINKS (HS)

This term includes sewage and industrial outfalls as well as interactions with the bottom sediments. The outfalls are actually spread over a large part of the upstream estuary. As the simulation model cannot represent channels with a dimension smaller than

the mesh-size, the lateral inputs are grouped at four locations. At each discharge point the flux of suspended matter, based on regular surveys, equals 250 kg particulate matter/minute. The interaction between the water column and the bottom involves erosion and sedimentation. The sedimentation flux depends on the sedimentation velocity of the particles and the turbulence or shear stress at the bottom. When a viscous bottom layer is maintained on the estuarine floor, the flux of material is simply due to the slow sedimentation of particles. To allow for the periodic disruption of the viscous layer and ejection of sediments, a correcting factor, which is

326 related to the degree of sublayer instability, is introduced

with

:

S

sedimentation flux

U

sedimentation velocity

P

suspended matter concentration or turbidity

:

H

total depth

Tb

bottom shear stress

T

limiting shear stress above which no deposition takes place

Studies on flocculation processes, particle size distribution and sedimentation velocities (Wartel, 1971b

;

Migniot, 1968) allowed us to derive the following

relation between 0 (meters/minute) and salinity (m S )

. .

U

=

1.6 10

-*

U

=

1.6 10

-2

-

1.1 10

-' (10 -

Sa1.)/8

:

Sal. >

10 m S

(10)

Sal.
m a y t h u s h e l p i n e x p l a i n i n g t h e p a t t e r n of mud accumulation o r sand bank s t a b i l i z a t i o n . I f t h e d i s t r i b u t i o n o f < z > i s such t h a t

a l l v e c t o r s a r e d i r e c t e d outwards a region

of maximum energy, t h i s could mean t h a t a c o n s t a n t e r o s i o n o c c u r s t h e r e ; i f t h e v e c t o r s a r e d i r e c t e d inwards, t h i s might induce a high t u r b i d i t y l e v e l i n t h e water column, and a s t a b l e bed.

T h e < r > v e c t o r f i e l d may a l s o e x p l a i n t h e o r i g i n of t h e

deposited sediments and t h e f a t e of eroded m a t e r i a l .

W e s h a l l thus t r y t o correlate

t h e d i s t r i b u t i o n of energy and s t r e s s with t h e map of s u p e r f i c i a l sediments of t h e c o a s t a l a r e a under study.

DISCUSSION OF THE RESULTS

The d i s t r i b u t i o n of energy i s p l o t t e d on Figure 3 and t h e v e c t o r d i s t r i b u t i o n of s t r e s s on Figure 4 . From t h e f i r s t 'of

Units a r e a r b i t r a r y . t h e s e f i g u r e s , one can see t h a t sand banks a r e c h a r a c t e r i z e d

by l o c a l maxima of t h e energy i n Region I (Flemish Banks), b u t t h a t

o t h e r maxima

appear, e i t h e r c l o s e t o t h e banks o r even n o t t i g h t e n with t h e g e n e r a l bank s t r u c ture.

For i n s t a n c e , j u s t SW of t h e Oost Dijk Bank, t h e r e i s alocalmaximum t h a t

does n o t coincide with any bank.

The same phenomenon appears i n t h e region of t h e

Akkaert Bank and Goote Bank. On t h e c o n t r a r y , t h e Wandelaar Bank, which i s a f l a t bank of d i f f e r e n t n a t u r e than t h e o t h e r s (more mud i n t h e s e d i m e n t s ) , i s c h a r a c t e r i z e d by a f l a t minimum of t h e energy. On t h e o t h e r , deeper channels l i k e t h e Westdiep, t h e Scheur and t h e Oostgat a r e p l a c e s where t h e energy i s higher. From t h e viewpoint of e r o s i o n s t r e s s , w e s t e r n b a n k s show a d i s t r i b u t i o n of small s t r e s s v e c t o r s t h a t g e n e r a l l y t u r n around t h e heads of t h e banks inducing t h a t m a t e r i a l eroded from t h e banks tend t o r o t a t e around them.

Whereas t h e stress i s

markedly s t r o n g and d i r e c t e d along t h e d i r e c t i o n of t h e main t i d a l c u r r e n t s near t h e Akkaert and Goote Bank, t h e r e g i o n of t h e Wandelaar shows a t y p i c a l s t r e s s pattern. In t h e r e g i o n westwards of t h i s bank, t h e stress i s d i r e c t e d eastwards, i n t h e d i r e c t i o n of t h e r e s i d u a l t i d a l c i r c u l a t i o n i n t h e Southern Bight.

figure 4

Oistribution

of e r o s i o n

stress

343

344 I n t h e region eastwards, t h e stress i s d i r e c t e d northeastwards, a probable e f f e c t of t h e d i s c h a r g e of t h e S c h e l d t e s t u a r y . The c e n t e r of t h e Wandelaar i s t h e v e r y p l a c e where t h e s t r e s s e s converge. This means t h a t suspended m a t t e r o r i g i n a t i n g from t h e surroundings of t h e bank w i l l converge towards t h e bank.

A s a l o c a l energy minimum e x i s t s t h e r e , i t follows t h a t

t h e bank i s a p l a c e where accumulation of sediments t a k e s p l a c e . Since t h e major source of suspended sediment i n t h i s region i s t h e Scheur channel. (higher energy, h i g h e r s t r e s s , e s t u a r i n e d i s c h a r g e ) , where f i n e sands and mud domin a t e t h e sedimental c o n t e n t , t h i s i n d i c a t e s t h a t t h e f a t e of t h e upper l a y e r of t h e Wandelaar Bank i s t o become even more muddy. A l a s t i n t e r e s t i n g f e a t u r e of t h e s t r e s s f i e l d i s t h e g e n t l e t u r n i n g of t h e

s t r e s s v e c t o r s around t h e

W a l v i s c h s t a a r t Bank.

A t f i r s t s i g h t , it seems t h a t t h e r e a r e more than random f e a t u r e s i n t h e energy and s t r e s s f i e l d s computed from t h e hydrodynamical numerical model.

However, up

t o now, one could argue t h a t one has no experimental evidence of t h e v a l i d i t y of t h i s approach. D i r e c t experimental evkdence i s of course impossible, b u t t h e r e i s an i n d i r e c t proof showing t h a t t h e model r e s u l t s r e p r e s e n t a t l e a s t some a s p e c t s of t h e geophysical r e a l i t y . Figure 2 i s a map of t h e d i s t r i b u t i o n of f i n e sands i n t h e region of i n t e r e s t . BY f i n e sands, we mean p a r t i c l e s with a mean diameter of l e s s t h a n 74 microm.

The map shows t h e d i s t r i b u t i o n of t h e r a t i o of f i n e sand t o t h e t o t a l mass of sandy sediments.

One s e e s a t f i r s t s i g h t a s t r o n g n e g a t i v e c o r r e l a t i o n between t h i s r a t i o

and t h e energy l e v e l :

t h e h i g h e s t t h e energy, t h e lowest t h e r a t i o .

In g e n e r a l , r e g i o n s c l o s e t o t h e c o a s t , where t h e energy i s low, a r e p l a c e s of high f i n e sand c o n t e n t , t h e only exceptions being t h e Scheur channel, which t r a n s p o r t s t h e f i n e sands and muds from t h e e s t u a r y . Typical c o r r e l a t i o n s a r e :

- t h e presence of high f i n e sand r a t i o i n a region responding t o a l o c a l minimum of energy

NW of t h e Oost Dijk Bank, cor-

;

- a b l o t of f i n e sands between t h e Buiten Rate1 Bank and t h e Oost Dijk Bank : - two tongues of f i n e sands extending, on one and another s i d e of an energy maximum l o c a t e d on t h e Oostende Bank, up t o both ends of t h e Kwinte Bank ;

- t h e f i n e sand region of t h e Steendiep, a l s o a s s o c i a t e d w i t h an energy minimum l o c a t e d i n a deep channel. A l l t h e s e c o r r e l a t i o n s show t h a t t h e r e

i s a good

correspondance between energy

and stress d i s t r i b u t i o n s o n t h e one h a n d , a n d t h e sedimentological f e a t u r e s of t h e seabed i n t h e c o a s t a l zone on t h e o t h e r hand. The d e f i n e d energy and stress, which a r e parameters computed from a hydrodynamica1 numerical mode1,are much more e a s i l y a v a i l a b l e than sediment samplings and

345 can be used, with some confidence, t o study and f o r e c a s t t h e e v o l u t i o n of t h e upper sediment l a y e r of t h e c o a s t a l s h e l f . However, t h i s s u r p r i z i n g l y good agreement between experimental survey and model f e a t u r e s , has been o b t a i n e d without t a k i n g i n t o account such important p h y s i c a l phenomena as t h e e f f e c t of s u r f a c e waves and t h e s p a t i a l v a r i a t i o n of bottom f r i c t i o n . The r e l a t i v e s m a l l impact of t h e s e f e a t u r e s may however been explained.

E f f e c t of s u r f a c e waves

T h e c o n s i d e r e d a r e a i s a g i t a t e d by very s t r o n g t i d a l c u r r e n t s . t h e mean depth i s g r e a t e r than 10 m , they are

I n regions where

more e n e r g e t i c than s u r f a c e waves.

I n more shallow r e g i o n s , t h e t o t a l i n f l u e n c e by waves i s s i g n i f i c a n t , from an energ e t i c p o i n t of view.

However, it is w e l l known ( e . g . Gullentops & a l , 1976) t h a t

s u r f a c e waves i n t h e Flemish Banks are n o t as high n e i t h e r a s s t r o n g a s elsewhere, because t h i s region l i e s i n t h e shadow o f o f f s h o r e banks, which

break t h e most

e n e r g e t i c long p e r i o d waves (mainly t h o s e coming from NW, which have t h e l o n g e s t fetch).

From t h e mean annual p o i n t of view, one can assume t h a t t h e s t r e s s induced

by waves i s p e r i o d i c , with a s h o r t time s c a l e , and with random d i r e c t i o n :

the

resulting s t r e s s is therefore negligible.

E f f e c t of t h e n a t u r e of t h e bottom on f r i c t i o n

Most experiences with hydrodynamicalnumericalmodels ( e . g . Ronday, 1976) show t h a t parameterized bottom f r i c t i o n i s almost c o n s t a n t , and t h a t t h e v a r i a t i o n s of t h e f r i c t i o n c o e f f i c i e n t s l i g h t l y change t h e r e s u l t s .

One can assume t h a t t h e bottom

f r i c t i o n i s o n l y s t r o n g l y i n c r e a s e d i n p l a c e s where sand r i p p l e s a r e observed, but such l o c a t i o n s have a very l i m i t e d s u r f a c e a s compared t o t h e t o t a l a r e a under study

.

FORECASTING THE EVOLUTION OF THE SEABED UNDER SAND W I N N I N G

I t i s n o t claimed t h a t t h i s simple model e x p l a i n s a l l t h e mechanisms and f e a t u r e s

of e r o s i o n and sedimentation i n t h e c o a s t a l zone.

However, t h e c o r r e l a t i o n s s t r e s s e d

formerly allow u s t o have some confidence i n a p o s s i b l e use of t h i s model t o f o r e c a s t t h e e v o l u t i o n of t h e r e c e n t sediments i n t h e c o a s t a l zone under t h e e f f e c t of sand winning. The technique i s t h e following :

- compute t h e energy and s t r e s s from t h e v e l o c i t i e s provided by t h e hydrodynamical numerical model, run using t h e a c t u a l depth d i s t r i b u t i o n ;

- compute a new d e p t h d i s t r i b u t i o n i n t h e winning a r e a s , using t h e aforementioned

346 assumptions, and assuming moreover t h a t during t h e l i m i t e d time span of 3 y e a r s , the p e r t u r b a t i o n s caused by t h e winning have no feedback e f f e c t . (In o t h e r words, t h i s means t h a t t h e time s c a l e necessary f o r an e f f e c t i v e i n f l u e n c e of t h e p e r t u r b a t i o n s on t h e system is much longer t h a t t h e time s c a l e of t h e o p e r a t i o n s t h a t cause the perturbation.

This assumption may not be t r u e f o r l a r g e l o c a l p e r t u r b a t i o n s and i s

only a f i r s t approximation f o r small d i s t u r b a n c e s .

However, t h i s approach i s the

only one p o s s i b l e i f one t r i e s t o deduce long term changes from t h e r e s u l t s of s h o r t term models and experiments.

A more a c c u r a t e study would indeed r e q u i r e t h e design

of a long term e v o l u t i o n model o r measurement s t r a t e g y , t h e l a t t e r i s s u e allowing p r a c t i c a l l y no f o r e c a s t ) .

- With new topography run t h e hydrodynamical numerical model t o compute new space and time d i s t r i b u t i o n of v e l o c i t i e s ;

- perform f i r s t s t e p again with p e r t u r b a t e d v e l o c i t i e s

;

- compute d i f f e r e n c e s i n energy and stress f i e l d s and p l o t t h e maps

;

- deduce from t h e d i f f e r e n c e f i e l d t h e p o s s i b l e e v o l u t i o n of t h e system. This i s what we u s u a l l y c a l l a d i f f e r e n t i a l study.

Provided t h a t t h e mathematical

model reasonably reproduces t h e p h y s i c a l r e a l i t y , such an approach i s r a t h e r r e l i able. I t i s t o be noted t h a t a l l feedback e f f e c t s a r e h e r e n e g l e c t e d , which may cause

over- o r underestimation of t h e e f f e c t s .

This f a c t must be taken i n t o account

during t h e i n t e r p r e t a t i o n phase.

RESULTS OF THE DIFFERENTIAL STUDY

Figures 5 and 6 show r e s p e c t i v e l y t h e d i f f e r e n c e s i n energy and stress a s s o c i a t e d with sand winning a c t i v i t y .

Energy d i s t r i b u t i o n

(full lines :

increase; dotted

lines

:

The i n f l u e n c e v a r i e s from bank t o bank.

decrease) On t h e Kwinte Bank, t h e energy i n c r e a s e s

s l i g h t l y ( 1 % ) around t h e n o r t h e a s t e r n and s o u t h w e s t e r n ends.

A s l i g h t increase

of t h e same magnitude o r a b i t l a r g e r appears on both s i d e s of t h e Buiten Rate1 Bank and on t h e e a s t e r n s i d e of t h e Oost Dijk Bank, whereas a s l i g h t d e c r e a s e may be observed on t h e western s i d e of t h e Oost Dijk Bank. decrease i s much more pronounced (up t o 4 % ) .

o f t h i s l a t t e r bank, one observes i n c r e a s e s of about

Scheur

.

On t h e Wandelaar Bank, t h e

On t h e Southern and Western s i d e s

3

%,

and of about 1

%

i n the

I Figure 5

Energy

dilferences

347

w

rp -3

348 Stress distribution

V a r i a t i o n s i n t h e s t r e s s f i e l d a l s o c h a n g e from p l a c e t o p l a c e ; t h e d i f f e r e n c e vectors a r e generally opposite t o t h e o r i g i n a l vectors. d i f f e r e n c e i s about 10 %.

The maximum m a g n i t u d e o f t h e

L e t u s n o t i c e t h a t t h e s c a l e of d i f f e r e n c e v e c t o r s on

Figure 6 i s 2 0 times t h e s c a l e of s t r e s s v e c t o r s on Figure 4.

Combining t h e r e s -

p e c t i v e r o l e of energy and stress, one can deduce w i t h a l o t of c a u t i o n , a p o s s i b l e e v o l u t i o n of t h e banks and t h e i r neighbourhood.

The i n c r e a s e of energy does n o t

seem t o be s u f f i c i e n t t o a c c e l e r a t e s i g n i f i c a n t l y t h e e r o s i o n of t h e sands t h a t form t h e banks, b u t may i n f l u e n c e t h e d e p o s i t i o n of f i n e r sands. A l l western banks show a s i m i l a r e v o l u t i o n p a t t e r n :

i n c r e a s e of energy on

both s i d e s , and a s l i g h t decrease of e r o s i o n s t r e s s ; t h e s e v a r i a t i o n s should not i n f l u e n c e t h e p o s i t i o n of t h e bank. The s i t u a t i o n seems t o b e c l e a r e r on t h e WandeLaar.

On t h e bank i t s e l f , t h e

energy d e c r e a s e s , and t h e d i f f e r e n c e s s t r e s s v e c t o r s p o i n t towards t h e c o a s t . The decrease of energy should induce t h e r e an i n c r e a s e of f i n e p a r t i c l e s c o n t e n t s i n t h e new sediment l a y e r .

Since, i n t h e r e g i o n s surrounding t h e bank, energy

i n c r e a s e s (except between t h e bank and t h e c o a s t ) , t h e p r o b a b i l i t y of p a r t i c l e s coming and s e t t l i n g on t h e bank i n c r e a s e s .

finer

The sand q u a l i t y on t h e

Wandelaar should s t i l l decrease. A s most of t h e suspended p a r t i c u l a t e m a t t e r i s t h i s r e g i o n comes from t h e Scheur,

t h i s can be i n t e r p r e t e d a s a displacement southwestwards of t h e S c h e l d t e s t u a r y . Let u s r e c a l l t h a t t h e hydrodynamical p e r t u r b a t i o n s have been computed under t h e assumption t h a t t h e r e i s no immediate r e s t o r i n g of t h e bank.

As this

assumption i s p a r t l y wrong ( a s i t can be deduced from t h e l a t t e r a n a l y s i s ) , t h e p e r t u r b a t i o n s should i n f a c t be l e s s important t h a t computed.

They a r e , however,

f a r from being n e g l i g i b l e on a long term b a s i s , mainly on t h e Wandelaar. BIBLIOGRAPHY

Adam Y . , W. Bayens, J . P . Mommaerts, G. P i c h o t , 1980. Ecological modelling a s a t o o l f o r t h e s c i e n t i f i c management of sand winning i n c o a s t a l w a t e r s , i n D. Dubois ( E d i t o r ) , Second I n t e r n a t i o n a l Conference on t h e S t a t e - o f - t h e - a r t i n Ecological Modelling Elsevier-Amsterdam. 1956. An approach t o t h e sediment t r a n s p o r t problem from g e n e r a l Bagnold R.A., physics. U . S . Geol. Surv. Prof. Papers 4221. Gullentops F . , M. Moens, A . Ringele, R. Sengier, 1976. Geologische kenmerken van de suspensies en sedimenten i n J. Nihoul & F . Gullentops ( E d i t o r s ) , Rapport F i n a l du P r o j e t Mer-S6dimentologie - E d i t i o n s d e s S e r v i c e s de l a Programmation de l a P o l i t i q u e S c i e n t i f i q u e . B r u x e l l e s . Hjiilstrom F . , 1939. Transport of sediment by moving w a t e r i n P.D. Track ( E d i t o r ) , Recent Marine Sediments 5-31, Am. ASSOC. P e t r o l . G e o l o g i s t s , T u l s a , Oklahoma. Ronday F . , 1976. ModSles Hydrodynamiques de l a c i r c u l a t i o n e n mer peu profonde, i n J . Nihoul & F. Ronday ( E d i t o r s ) , Rapport F i n a l du P r o j e t Mer-ModSles Hydrodynamiques, E d i t i o n d e s S e r v i c e s de l a Programmation d e l a P o l i t i q u e S c i e n t i f i q u e . Bruxelles.

Ronday F . , G. Belhomme, 1978. Modele Mathematique de l a Zone CBtiere Belge Rapport f i n a l - Unpublished manuscript.

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351

SUBJECT I N D E X

Abidjan,

147.

A b i o t i c environment, 192. Advection, 6,

60,

77,

104,

150,

165,

193, 201,

Africa - Southern A f r i c a , 18, 19, 40, 41. - Northern A f r i c a , 18. - Northwest A f r i c a , 19, 37, 40, 41. - West A f r i c a , 15, 151. Alaska, 13. A l e u t i a n chain, 38. Amazonia,

15,

Anchoveta,

19,

155,

22,

156,

23, 157,

30,

31,

158,

33,

39.

161.

A n t a r t i c , 36. Arcona Basin, 169. Antlantic - A t l a n t i c Ocean, 99, 287. - North A t l a n t i c , 220, 228, 270. Mid A t l a n t i c Bight, 2 0 , 24, 25, - South A t l a n t i c Bight, 28, 32. - A t l a n t i c c i t y , 26. - A t l a n t i c s h e l f , 81.

28.

Auke Bay, 197. B a l t i c Sea, 165,

169,

173,

174,

B a r o c l i n i t y , 76,

102,

178,

179.

175, 177.

Bay of GorBe, 143. Belgian Coast, 232, Bering Sea, 4,

7,

233.

15,

35,

36,

37,

39,

Boom, 330. Bothnia, 169. Boussinesq approximation, 101. B r a z i l , 41. B r i t i s h Isle, 33,

51,

52.

Bristol - B r i s t o l Bay, 38. - B r i s t o l Coast, 10. Brunt-Vaisala frequency, 174. Buoyancy, 51, 67, 174, 211, 217, 278. - Buoyancy f l u x , 52, 531 54, 56, 58. California,

13,

39,

Cape Canaveral, 80.

40,

41,

165.

40,

42.

281, 295,

322.

352 Cape Formoso, 104,

123.

Cape H a t t e r a s , 34, 81. Cape Lopez, 104. Cape Newenham, 38. Cape Palmas, 104,

119, 104,

Cape Three P o i n t s , Cap-Vert,

141,

123,

134.

123,

124,

125,

134.

143.

Casamance, 150. C e l t i c Sea, 197, 287. Chesapeake Bay, 25, Chile,

196.

16.

C i r c u l a t i o n , see a l s o c u r r e n t , 7, 143, 154, 239. - Residual c i r c u l a t i o n , 224, 225, 226, 228, 232, - F r o n t a l c i r c u l a t i o n , 11. - Oceanic c i r c u l a t i o n , 154, 155, 156.

234,

239,

245,

251.

Clausocalanus, 2 13. c h l o r o p h y l l , 15, 23, 28, 80, 197, 201, 202, 203, 209. C o r i o l i s parameter, 82,

141,

144,

145,

174, 224, 274,

321.

147,

149,

150,

151,

152,

153,

165,

193,

Crabs, 6. Current, see a l s o c i r c u l a t i o n , 3, 30, 31, 119, 197, - C u r r e n t d i s t r i b u t i o n , 1, 278. - C u r r e n t v e l o c i t y , speed, 3, 83, 94, 165, 179. - Current d i r e c t i o n , 83. - Residual c u r r e n t , 4, 220, 270, 310. - Boundary c u r r e n t , 29, 31, - Loop c u r r e n t , 31, 62. - Bottom c u r r e n t , 51. - T i d a l c u r r e n t , 52, 64, 86, 149, 222, 225, 251. - Surface c u r r e n t , 144, 148, 152. - C u r r e n t reversal, 123. - Macroscale c u r r e n t , 228. Dakar, south-Dakar,

219,

223,

236,

245,

251,

150.

Danish S t r a i t s , 169. Delaware, 25. Density, 7, 54, 76, 175, 176, 179, - S p e c t r a l d e n s i t y , 175, 176. Diagenesis,

39,

183,

193,

290.

40,

Diffusion, s e e a l s o d i s p e r s i o n , 3, 6, 35, 165, 166, 193, 199, 209, - Molecular d i f f u s i o n , 156, 209, 210, 212, 214, 217, 274. D i n o f l a g e l l a t e , 141,

143,

197,

Dispersion, see a l s o d i f f u s i o n , D i s s i p a t i o n , 209,

281, 325.

199, 202. 155,

156, 157, 159,

161, 201,

324.

210.

Eddy, s e e a l s o turbulence, 4, 26, - Cyclonic eddy, 10, 80. - Spin-off eddy, 28, 31. - Eddy v i s c o s i t y , 102, 239, 250. - Eddy d i f f u s i o n , 325. - Synoptic eddy, 165, 179.

150,

152,

154,

174,

185,

186, 270.

278,

282.

353 Ekman - Ekman s u c t i o n , 26. - Ekman t r a n s p o r t , 144, - Ekman upwelling, 146.

148,

153.

Energy - Energy d i s s i p a t i o n , 8, 9, 11, 174, 234, - Energy exchange, 238, 239. - Turbulent energy t r a n s f e r , 192. English Channel, 226, Erosion,

295,

297,

237,

270.

287.

325,

326,

330,

331.

E r t e l ' s r e l a t i o n , 179. Euphotic - Euphotic zone, 13, 14, 22, - Euphotic depth, 71, 72.

26,

35,

38,

70,

71,

73,

74.

Europe, 41. Eutrophic,

15, 36,

43.

Fauna, 4. Feeding ground, 2. F i n i t e element method, 276. Finland,

169.

F i s h , 3,

7,

158.'

Fladen Ground, 38. Flamborough Head, 10. F l o c u l a t i o n , 319,

320,

326,

329,

331.

F l o r i d a , 26, 28, 30, 31, 32, 41, 79, 80, 82, - West F l o r i d a , 21, 31, 32. - South F l o r i d a ' s A t l a n t i c Coast, 79, 96. F o r t P i e r c e , 82. F r i c t i o n , 7, 270, 293. - F r i c t i o n v e l o c i t y , 54, 55. - F r i c t i o n c o e f f i c i e n t , 322. - F r i c t i o n stress, 227, 239, 294. - Residual f r i c t i o n , 232. - F r i c t i o n a l drag, 31. - F r i c t i o n a l r e t a r d a t i o n , 82. Front, 10, - Frontal - Frontal - Frontal

134, 141, 152, 166, c i r c u l a t i o n , 11. movement, 196. d i s c o n t i n u i t y , 199.

George Bank, 25, Georgia, 29,

26,

33,

34,

30.

Geostrophic - Geostrophic f l o w , 76. - Geostrophic c u r r e n t , 182. - Geostrophic s h i f t , 187. German Bight, 10. Gironde, 285, Gulf of Benin,

297. 123.

191.

36.

83,

88,

93,

95,

96,

97.

3 54 Gulf of Guiana, 20, 30, 31, 99, 100, 104, 123, 134. Gulf o f Lion, 279. Gulf of Maine, 73, 74, 76. Gulf of Mexico, 15, 21, 22, 23, 29, 31, 42. Gulf Stream, 80. Gyre, 165, 232, 233, 245, 251, 270. - R e s i d u a l g y r e , 228. H a l o c l i n e , 169, 187. H e a t , 10, 176, 201. - H e a t flux, 53, 55, 274, 276, 278. H e a t exchange, 64.

-

H e r b i v o r e , 6. Honfleur,

286.

Hudson, 23, 25, 26. - Hudson Canyon, 24. H u r r i c a n e David, 95. Indian Arm,

196.

I s o b a t h , 23, 38, 148, 151, 185. I s o p l e t h , 31, 159, 160. I s o t h e r m , 59, 71, 86, 88, 151, 281. Jamaica Bay, 323. J e l l y f i s h , 7. K a t t e g a t t , 169. Kolmogorov s c a l e , 174. Lake Tahoe, 165. L e n i n g r a d , 169. Le R a t i e r ,

293.

L i g h t , 72, 74, 165, 320. - L i q h t q u a l i t y , 98. - L i g h t i n t e n s i t y , 98, 158. - L i g h t e f f e c t , 71. - L i g h t l i m i t a t i o n , 74, 75, 76, 204. - ' S h o r t a g e o f l i g h t , 199. Long I s l a n d Sound, 192, 193. L o u i s i a n a , 22, 23, 28, 41. Manitounuk I s l a n d s , 197. M a u r i t a n i a , 147. Mesoscale, 143, 150, 152, 154. - Mesoscale wind v o r t i c i t y , 152, 233. - Mesoscale Reynolds stress t e n s o r , 225, 227, 238, 239, 245. - Mesoscale flow, 237. Microzone, 209, 210,

212, 217.

M i g r a t i o n , 2. - M i g r a t i o n v e l o c i t y , 3 , 4.

Mississipi River, 19, 20, 22, 23.

355 Mixing, 5, 7, 33, 201, 203, 293. - Mixing r a t e , 63. - V e r t i c a l mixing, 67, 68, 71, 72, 74, 77, 193, 196, 202. - Mixing d e p t h , 68, 76. - Mixed layer, 75, 156, 158, 161, 175, 199. Montauk P o i n t , 26. N a n t u c k e t S h o a l s , 26. N e w J e r s e y , 25. New York, 13, 25, 32. - N e w York B i g h t , 23, 33.

N o r t h e r n England, 250. North-Hinder,

3.

N o r t h Sea, 2, 3, 4, 10, 11, 15, 38, 39, 52, 63, 64, 169, 219, 220, 2 2 2 , 225, 226, 228, 232, 239, 245, 250, 251. N o r w a y , 38. - Norwegian Deep, 38.

Nova S c o t i a , 34. N u t r i e n t , 1, 5, 7, 10, 13, 15, 16, 18, 19, 20, 23, 2 8 , 38, 42, 51, 52, 61, 63, 64, 67, 73, 74, 75, 76, 77, 8 0 , 143, 148, 150, 152, 153, 155, 156, 166, 173, 191, 192, 196, 198, 199, 200, 201, 204, 205, 209, 210, 2 1 1 , 282. - N u t r i e n t i s o p l e t h , 31. - N u t r i e n t c o n c e n t r a t i % n , 68. - N u t r i e n t d e n s i t y , 76. O i t h o n a , 213. O l i g o t r o p h i c , 15, 19, 26. Onslow Bay, 81. Oregon, 33, 41. Ozmidov buoyancy s c a l e , 174. P a c i f i c Ocean, 147, 156. papa ( o c e a n s t a t i o n ) , 54. P e r u , 13, 15, 16, 17, 18, 19, 20, 21, 2 2 , 36, 40, 41, 42, 155, 156, 159, 160. Photic layer,

193, 196, 197, 199, 201, 202.

Photosynthesis,

18, 34, 68, 69, 70, 71, 72, 74, 76, 156, 192, 201, 210, 320.

Phytophagous, 156. P h y t o p l a n k t o n , 6 , 10, 11, 13, 14, 1 5 , 16, 19, 20, 2 1 , 2 2 , 34, 36, 40, 42, 67, 68, 70, 71, 77, 80, 141, 143, 155, 157, 158, 160, 161, 165, 191, 192, 193, 196, 197, 198, 199, 200, 201, 202, 203, 204, 209, 210, 216, 217, 285, 320. P l a i c e , 2. P l a n k t o n , 23, 41, 155, 156, 165, 209, 210, 282. P o i n t e des Alrnadies,

141, 152.

Pose, 290. P u g e t Sound, 196. p y c n o c l i n e , 23, 53, 60, 61, 63, 124, 184. R e s i d u a l f l o w , 225, 239, 245, 250. R e s p i r a t i o n , 68, 69, 70, 71, 72, 74.

3 56 Rhine River, 38.

192,

Richardson number,

196.

R i j k s s t a t i o n voor Z e e v i s s e r i j Oostend, 3. River River - River - River - River

-

r u n o f f , 19, 23, i n f l u x , 169. flow, 324, 331. discharge, 19.

28,

33,

191,

196,

197,

Rossby - Rossby's p o t e n t i a l v o r t i c i t y theorem, 178, - Rossby wave, 105, 182, 187. - Rossby r a d i u s of deformation, 174, 187.

198,

201.

179.

Rupelmonde, 327. Saanich I n l e t , 197. Sahel, 99. S t . Lawrence, 191,

192,

196,

201.

S t . Louis, 147. S a l i n i t y , 170, 173, 175, 325, 327, 329, 331.

176,

274,

292,

293, 294,

297,

302,

310,

319,

320,

324,

Santa Barbara Basin, 40. Sargasso Sea, 68,

71,

73,

74,

Scale - T i m e scale, 1, 7, 11, 14, - Length s c a l e , 1, 3, 4, 7, S c h e l d t , 319,

322,

75,

76.

166, 192, 193, 203, 219, 220, 245. 8, 14, 124, 187, 192, 193, 209, 220,

222,

245.

330.

Sediment ( s e d i m e n t a t i o n ) , see a l s o t u r b i d i t y , 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 219, 220, 223, 233, 285, 294, 295, 297, 301, 302, 310, 315, 319, 320, 325, 329, 330. - Sedimentation v e l o c i t y , 292, 325, 326, 331. Seine, 285,

286,

Senegal, 143,

287,

298,

315.

150.

S h e l f , 52, 64, 147, 148. - Shelf break f r o n t , 4. - Shelf f r o n t , 5. - Middle s h e l f zone, 6. - Outer s h e l f zone, 7, 84. - European C o n t i n e n t a l s h e l f , 7, 9, 11. - Shelf bottom sediments, 15. - Shelf-slope, 41. - Inner s h e l f 79. - Shelf break, 83, 88, 89, 90, 91, 92, 93, - Shelf c i r c u l a t i o n , 150. Southern s h e l f , 141. - C o n t i n e n t a l s h e l f , 97, 143.

-

Shetland I s l a n d s , 38. Skagerrak, 169. Skeletomena costatum, 211. Solar - S o l a r r a d i a t i o n , 1. - S o l a r energy, 199.

95.

357 Southern Bight, 3, 226, 232. Spanish Sahara, 37. Spawning - Spawning ground, 2, 3. - Spawning p e r i o d , 3. s t a b i l i t y , 197, 200, 201. - V e r t i c a l s t a b i l i t y , 191, 192, 196, 202. - S t a b i l i t y spectrum, 192. - S t a b i l i z a t i o n , 197, 198, 199, 203. - l D e s t a b i l i z a t i o n , 198, 203. S t r a i t s o f Dover, 228. S t r a t i f i c a t i o n , 23, 33, 51, 64, 141, 143, 152, 165, 166, 169, 173, 191, 193, 196,

197, 199, 201, 202, 203, 204, 295.

-

-

D e s t r a t i f i c a t i o n , 192, 193, 196, 199, 201, 203, 204. Thermal s t r a t i f i c a t i o n , 52, 59, 67.

Stream, 299, 303, 310. - Stream f u n c t i o n , 227. - Streamline, 80, 96, 236, 245, 251, 270. - Stream v e l o c i t y , 292, 302. S t r e s s , s e e a l s o turbulence, f r i c t i o n . - Reynolds stress Turbulent Reynolds stress, 222, 225, 251. - Mesoscale Reynolds stress t e n s o r , 225, 227, 238, 239, 245. - Residual s t r e s s , 234. - Surface s t r e s s , 235. - Bottom stress, 235, 236, 237. - Turbulent stress, 235. - Mesoscale stress, 250. - Shear stress, 274, 321. Structure - F i n e s t r u c t u r e , 5, 174, 175, 176. - Microstructure, 174, 175. Synoptic - Synoptic - Synoptic - Synoptic - Synoptic

v a r i a b i l i t y , 177, p r o c e s s e s , 183. o r i g i n , 185.

78, 82.

scale,187.

Temperature, 1, 2, 11, 13, 51, 53, 54, 59, 61, 62, 79, 81, 83, 84, 86, 87, 88, 9 0 ,

91, 96, 97, 141, 147, 149, 152, 165, 170, 175, 176, 179, 191, 203, 204, 274, 276, 278, 279, 281. Texas, 21, 23, 29, 41. - W e s t Texas, 30. T h a l a s s i o s i r a , 211. Thermocline, 5, 13, 51, 52, 55, 56, 5 7 , 58, 60, 62, 63, 64, 77, 85, 88, 89, 90, 143,

148, 150, 156, 169, 175, 176, 187, 201, 202, 273, 278, 279, 281, 282. Vhermohaline, 174, 182. - Thermohaline mixing, 101. - Thermohaline c i r c u l a t i o n , 152. - Thermohaline f i e l d , 187. Thiaroye, 143, 148, 151. Tide, 7, 42, 101, 191, 193, 197, 219, 223, 250, 285, 287, 288, 298, 310, 322, 323,

329.

-

Red t i d e , 205.

358

- Tidal - Tidal - Tidal - Tidal - Tidal - Tidal -

Tidal

- Tidal - Tidal - Tidal - Tidal - Tidal - Tidal

-

Tidal

front, 7 v e l o c i t y , 3, 32, 33, 34, 52, 59, 220. motion, 32, 220, 225, 250. mixing, 8, 11, 15, 16, 26, 32, 33, 38, excursion, 11. energy, 33. resuspension, 37. d i s s i p a t i o n , 52. i n f l u e n c e , 57, 324. c y c l e 193, 305. stream, 201. p e r i o d , 250, 251, 331. prism, 293. o s c i l l a t i o n , 220.

T u r b i d i t y , see also sediment, 18, 21, 310, 315, 319, 326, 327, 329, 331.

39,

39,

191, 203,

42,

204,

Turbulence, see a l s o eddy, 4, 51, 52, 53, 55, 56, 58, 165, 175, 197, 219, 270, 273, 274, 275, 279, 281.

58,

60,

285,

141,

61,

290,

148,

63.

292, 296,

152,

155,

304,

156, 158,

Unalaska I s l a n d , 38. upwelling, 8, 13, 15, 16, 18, 19, 21, 23, 84, 86, 87, 89, 91, 92, 93, 94, 95, 96, 145, 146, 147, 148, 150, 152, 153, 154, 203, 204. - Eddy-induced ufiwelling, 26, 29, 30, 31,

26, 28, 30, 31, 33, 36, 79, 80, 81, 82, 83, 99, 104, 110, 118, 119, 123, 124, 141, 144, 156, 158, 160, 161, 166, 191, 197, 202, 42.

Vancouver I s l a n d , 215. Velocity, 33, 53, 54, 99, 106, 227, 236, 274, 293, - Velocity s c a l e , 3, 11. - Velocity p a t t e r n , 7. - Current v e l o c i t y , 3. - Entrainment v e l o c i t y , 55, 57, 60, 62, 63, 76. - Mean v e l o c i t y , 103. - V e r t i c a l v e l o c i t y , 145, 151, 152, 235. - Longitudinal v e l o c i t y , 157. - Velocity f i e l d , 175, 183, 250, 320, 321, 325. - Phase v e l o c i t y , 187. - Residual v e l o c i t y , 224, 225, 233, 285. - Shear v e l o c i t y , 326. V i s c o s i t y , 245, 293, 321. - Eddy v i s c o s i t y , 102, 222, 239, 250, - Kinematic v i s c o s i t y , 174, 274. Vorticity,

26,

Water column, 202, 203.

31,

151,

152,

19, 23, 29,

32,

154, 33,

301,

319,

323,

324.

193,

196,

197,

270.

178, 245, 34,

294,

39,

Wave - B a r o c l i n i c wave, 179. - Barotropic s h e l f wave, 151. - E q u a t o r i a l wave, 105. - Gravity wave, 107, 175. - Kelvin wave, 99, 100, 107, 118, 123. - I n t e r n a l wave, 176, 185. - Wave l e n g t h , 175, 187. - Wave number, 187, 192. - Rossby wave, 107, 118, 119, 134. - Wave speed, 106, 165. - Topographic wave, 179, 187.

250,

69,

251,

185,

270.

191,

192,

199, 201,

359

-

Trapped wave, 105, 182, Yanai wave, 107, 118.

187.

Wind, 7, 99, 151, 191, 193, 197, 201, 202, 219. Wind c u r l , 29, 30. Wind c u r r e n t , 11, 61. Wind energy, 32. Wind f i e l d , 251. Wind f o r c i n g , 33. Heating wind, 77. Local wind, 152. Wind r e s i d u a l , 223, 224, 251. Wind s t r e s s , 26, 81, 82, 83, 84, 92, 93, 97, 154, 197, 227, 228, 234, 237, 276. Trade wind, 19, 100, 143. Wind v e l o c i t y , 55, 144, 145, 197. Mesoscale wind v o r t i c i t y , 152, 233. Yoff,

148,

100,

101,

110,

118,

123,

144,

151.

York River, Yucatan,

99,

196.

31.

Zooplankton, 7, 28, 215, 216, 217.

36,

80,

155,

158,

159,

160, 201,

209,

210, 211, 212,

213, 214,

Acknowledgments The e d i t o r i s indebted t o h i s research s t u d e n t s P . J o r i s and M .

t h e index.

J o s s a f o r t h e i r h e l p i n preparing


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