Bottom Turbulence (Elsevier oceanography series ; 19)

BOWOM TURBULENCE

BOWOM TURBULENCE

FURTHER TITLES IN THIS SERIES 1 J.L. MERO THE MINERAL RESOURCES O F THE SEA

2

L.M. FOMIN

THE DYNAMIC METHOD IN OCEANOGRAPHY

3 E.J.F. WOOD MICROBIOLOGY OF OCEANS AND ESTUARIES

4

G.NEUMANN

OCEAN CURRENTS

5

N.G. JERLOV

OPTICAL OCEANOGRAPHY

6

V. VACQUIER

GEOMAGNETISM IN MARINE GEOLOGY

I W.J. WALLACE THE DEVELOPMENT O F THE CHLORINITY/SALINITY CONCEPT IN OCEANOGRAPHY

8

E. LISITZIN

SEA-LEVEL CHANGES

9

R.H.PARKER

THE STUDY O F BENTHIC COMMUNITIES

1 0 J.C.J. NIHOUL MODELLING O F MARINE SYSTEMS

11 0.1. MAMAYEV TEMPERATURE-SALINITY ANALYSIS O F WORLD OCEAN WATERS

1 2 E.J. FERGUSON WOOD and R.E. JOHANNES TROPICAL MARINE POLLUTION

13 E. STEEMANN NIELSEN MARINE PHOTOSYNTHESIS

1 4 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 IN OCEANOGRAPHY AND OCEAN ENGINEERING

18 J.W. CARUTHERS FUNDAMENTALS O F MARINE ACOUSTICS

Elsevier Oceanography Series, 19

BOTTOM TURBULENCE PROCEEDINGS OF THE 8th INTERNATIONAL LIEGE COLLOQUIUM ON OCEAN HYDRODYNAMICS Edited by VJAQUES C.J. NIHOUL Rofessor o f Ocean Hydrodynamics, University of Lihge, Likge, Belgium

ELSEVIER SCIENTIFIC PUBLISHING COMPANY Amsterdam - Oxford - New York 1977

ELSEVIER SCIENTIFIC PUBLISHING COMPANY 335 Jan van Galenstraat P.O.Box 211, Amsterdam, The Netherlands Distributors for the United States and Canada: ELSEVIER NORTH-HOLLAND INC. 52, Vanderbilt Avenue New York, N.Y. 10017

Library of Congress Cataloging in Publication Data

Liege Colloquium on Ocean Hydrodynamics, 8 t h , Bottom t u r b u l e n c e .

1976.

( E l s e v i e r oceanography s e r i e s ; 1 9 ) Bibliography: p. I n c l u d e s index. 1. Turbulence--Cmgresses. 2 . Turbulent boundary layer--Congresses.* 3. Ocean bottom--Congresses. I. Nihoul, Jacques, C. J. 11. T i t l e . GC203.L53 1976 551.4'7 77-3546 ISBN 0-444-41574-2

Elsevier Scientific Publishing Company, 1977. 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,Amsterdam, The Netherlands

0

Printed in The Netherlands

V FOREITORD

I'hile

the atmospheric boundary layer has been extensively

investigated, the marine boundary layer above the sea floor although very similar in character

-

-

was, until recently, much

less well k n o w n ; the difficulty of making measurements in the sea, near the bottom, and the cost in equipment and human effort of any single experiment, reflecting on the calibration and the quality of the models. Bottom turbulence is however a determinant factor in such important problems as bottom friction and energy dissipation in marine circulation, sedimentation, bottom erosion, recycling of nutrients, trapping and release of pollutants, etc.. Understanding bottom turbulence is prerequisite for the development of accurate forecasting models of the marine systems which, nowadays, the extensive exploitation of the sea requires. In the recent years, the perfection of advanced techniques and the extension of the research effort have brought n e w interesting results an1 a more comprehensive insight into the characteristics of marine turbulence in the bottom boundary layer. Furthermore, the detection, in the bottom layer of the sea, of semi-coherent structures and the simultaneous study of the effects of the suspended sediments load have contributed, beyond the simple investigation of marine turbulence, to a better understanding of the general features of turbulence and such phenomena

-

still much debated

-

as drag reduction by

additives. The International LiSge Colloquia o n 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 n e w subjects i n 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 o n to a survey of major recent discoveries, essential mechanisms, impelling question-marks

VI and valuable suggestions for future research. The Scientific Organizing Committee of the Eighth Colloquium saw the desirability of bringing together, on the important topic of bottom turbulence, specialists from different fields, experimentalists and modellers, hydrodynamicists and sedimentologists. T h e present book which m a y be regarded a s the outcome of the colloquium comprises the proceedings of the meeting and specially commissioned contributions o n observations, parameterization and modelling of turbulence in the bottom boundary layer of the sea.

Jacques C.J. N I F O U L

VII

The Scientific Organizing Committee

of

the Eighth International

LiSge Colloquium onocean Hydrodynamics and all t h e p a r t i c i p a n t s w i s h to e x p r e s s t h e i r g r a t i t u d e to the B e l g i a n V i n i s t e r o f E d u c a t i o n , the N a t i o n a l S c i e n c e F o u n -

dation

of B e l g i u m , t h e

University

of

L i a g e and t h e O f f i c e of N a v a l R e s e a r c h for their m o s t v a l u a h l e support.

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IX LIST OF PARTICIPANTS

.

Mr

Y. ADAM, Institut d e MathEmatique, UniversitE de LiPge, LiPge, BELGTUM.

Dr

.

L. ARMI, l!oods Hole Oceanographic Institution, \.roodsHole Massachusetts, U.S.A.

Mr

.

A. BAH, Institut d e MathEmatique, Universitd de LiPge, LiPge, BELGIUM.

Prof. J. BOWMAN, State University of New York, Stony Brook, New York, U.S.A. Prof. G. CHABERT D'HIERES, Institut d e MEcanique, UniversitE Scientifique et MEdicale de Grenoble, St. Martin d'Heres, FRANCE. G.S. COOK, Systems Oceanography Branch, Naval Underwater

Dr.

Systems Center, Newport, Rhode Island, U.S.A. Prof

I

W.O.

CRIMINALE, Department of Oceanography and Geophysics

Program, University of Washington, Seattle, Washington, U.S.A. Dr.

A.M. DAVIES, Institute of Oceanographic Sciences, Bidston Observatory, Birkenhead, Merseyside, ENGLAND.

Prof. A. DISTECHE, Institut d e Zoologie, Universit6 de Lisge, LiSge, BELGIUM. Dr.

A. EDVARDS, Scot. Marine Biological Association, SCOTLAND.

Dr.

R.D. FLOOD, Woods Hole Oceanographic Institution, Wood s Ho 1e , Mas sac hu s e t t s , U

Mr.

. S .A.

J. FONT, Instituto d e Investigaciones Pesqueras, Barcelona, SPAIN.

Dr.

C 1 . FRANKIGNOUL, Max-Planck Institut fsr Meteorologie,

Hamburg, GERMANY. Dr. nr

.

C.M. GORDON, Naval Research Laboratory, Washington,U.S.A. P.K. KUNDU, School of Oceanography, Oregon State University, Corvallis, Oregon, U.S.A.

Miss

H. LAVAL, Institut d e MathEmatique, UniversitE de LiPge, Lisge, BELGIUM.

X Dr.

G. LEBON, Institut d e MathQmatique, UniversitE de Liege, LiBge, BELGIUM.

Prof

C. LE PROVOST, Institut d e Mgcanique, Centre National d e Recherches Scientifiques, Grenoble, FRANCE.

Mr.

A. LOFFET, Tnstitut de MathEmatique, Universitg de Liege, Liege, BELGIUM.

Dr.

F. MADELAIN, Centre National pour 1'Exploitation des OcEans, Centre OcEanologique de Bretagne, P,rest, FRANCE

Prof. J.C.J.

NTHOUL, lnstitut d e MathEmatique, Universitg d e

Litge, LiSge, BELGIUM. Prof. J . J . PETERS, Waterbouwkundig Laboratorium. Borgerhout, BELGIUM. Mr.

G. PICHOT, Institut d e MathEmatique, Universit6 d e LiBge, LiPge, BELCIUM.

Dr.

R.D. PINGREE, T h e Laboratory, Plymouth, Devon., U . K .

Prof. RAMMING, Universitat Hamburg, Institut fiir Veereskunde, Hamburg, GrRMANY. Dr. Dr.

H.W. RIEPMA, K.N.M.I., J.

D e Bilt, THE NETHFRLANDS.

RODRF., Oceanografiska Institutionen, Universitv of

Got henhur g , G 6 t ebo rg , SWEDEN. Dr.

F. RONDAY, Institut de MathEmatique, Universitg de L i e g e , LiGge, BELGIUM.

Mr.

Y. RUNFOLA, Institut de MathEmatique, UniversitE de LiPEe, LiSge, BE1,GIUM.

Mr.

U.J.

SALAT, Instituto de Investigaciones Pesqueras,

Barcelona, SPAIN. Prof. J . I . . SARMIENTO, Lamont-Doherty Geological Observatory, Columbia University, Palisades, N.Y., U . S . A . Prof. J.D. SVITI1, Department of Oceanography, University of Washington, Seattle, U.S.A. Mr.

J. S M I T Z ,

Institut d e MathEmatique, Universit6 de Liege,

Liege, DELGIUM.

XI Mr.

R.L.

SOULSBY, Institute of Oceanographic Sciences,

Taunton Somerset, U . K . Dr.

J.S. TOCHKO, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, U.S.A.

Dr.

VANDEF.BORGHT, Laboratoire de Chimie Industrielle, Universitd Libre de Bruxelles, BELGIUM.

Prof. G.L. WEATHERLY, Florida State University, Department of Oceanography, Tallahassee, U.S.A. Dr.

B. WILLIAMS, N.A.T.O.

Saclant A.S.W.

Centre, La Spezia,

ITALY. Dr.

A.J. WILLIAMS 3rd. Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, U.S.A.

Prof. M. WIMBUSCH, Nova University, Oceanographic Laboratory, Dania. Florida, U.S.A. Prof. R. WOLLAST, Laboratoire de Chimie Industrielle, Universitd Litre de Bruxelles, Bruxelles, BELGIUM.

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CONTENTS

. . . . . . . . . . . . . . . . . . . . . . . ACKNOWLEDGMENTS. . . . . . . . . . . . . . . . . . . . LIST OF PARTICIPANTS . . . . . . . . . . . . . . . . . FOREWORD

V VII IX

A.M. DAVIES : The numerical solution of the threedimensional hydrodynamic equations, using a . B-spline representation of the vertical current profile

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

1

A.M. DAVIES : Three-dimensional model with depthvarying eddy viscosity I.D. LOZOVATSKY, R.V.

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

OZMIDOV, J.C.J.

27

NIHOUL :

. .

49

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

59

Bottom turbulence in stratified enclosed seas C.M. GORDON & J. WITTING : Turbulent structure in a benthic boundary layer A.J. WILLIAMS 3 r d & J . S . of

TOCHKO : An acoustic sensor

.

a3

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

99

velocity for benthic boundary layer studies

J.C.J. NIHOUL : Turbulent boundary layer bearing silt in suspension (abstract)

R.D. PINGREE & P.K. GRIFFITHS : The bottom mixed layer of the continental shelf (abstract)

. . . .

101

G.L. WEATHERLY & J.C. VAN LEER : O n the importance of stable stratification to the structure of the bottom boundary layer o n the Western Florida shelf. J.D.

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

103

SMITH & S.R. McLEAN : Boundary layer adjustments to bottom topography and suspended sediment

. . .

123

L. ARM1 : The dynamics of the bottom boundary layer of the deep ocean W.O.

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

153

CRIMINALE Jr. : Mass driven fluctuations within the Ekman boundary layer

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

165

P.K. KUNDU : On the importance o f friction in two typical continental waters : off OreRon and Spanish Sahara

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

187

XIV J.P. VANDERBORGHT & R. WOLLAST : Mass transfer properties in sediments near the benthic boundary layer..

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

J.J. PETERS

:

209

Sediment transport phenomena in the

Zaire River

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

22 I

G.L. WEATHERLY : Bottom boundary layer observations in the Florida current M.J.

BOWMAN & W . E .

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

237

ESAIAS : Coastal j e t s , fronts,

and phytoplankton patchiness

. . . . . . . . .

255

J. SALAT & J. FONT : Internal waves in the N.-W. Africa upwelling G.S.

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

COOK, R.W. MORTON & A.T.

269

MASSEY : A report on

environmental studies of dredge spoil disposal sites

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

275

Part I : An investigation of a dredge spoil disposal site. Part 11: Development and u s e of a bottom boundary layer probe. SUBJECT INDEX

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

30 I

1 THE NUMERICAL SOLIJTION OF THE THREE-9IMENSIONAT. HYDRODYNAMIC EQUATIONS, USING A B-SPLINE REPRESELlTATION OF THE VERTICAL C IIRRENT

PROF IL E

A.M. DAVIES Institute of Oceanographic Sciences, Bidston Observatory, Birkenhead, Merseyside L 4 3 7 R A , England. ABSTRACT A numerical model

is described in which vertical current

structure may be determined using a n e w method involving expansion through the depth in terms of B-splines.

By way of a first

test, wind induced motion in a simple rectangular basin is computed, yielding surface elevations and vertical current profiles in good agreement with those obtained by Heaps ( 1 9 7 1 ) using an integral transform method,

The effect of varying eddy viscosi-

ty is investigated, considering the changes thereby produced in the wind induced vertical and horizontal circulations and in the surface and bottom currents. INTRODUCTION Two-dimensional finite difference models, based on the vertically-integrated equations of continuity and motion, have been used extensively in recent years to calculate tides and storm surges.

This approach is satisfactory for problems where

the primary aim is to calculate changes in sea surface elevation, but for problems involving water circulation, and particularly in engineering the calculation of the forces exerted by the sea on off-shore structures, a knowledge of vertical current profile

is required.

The use of a Laplace transform method to recover

the vertical current structure from a two-dimensional vertically integrated model has been proposed by Jelesnianski ( 1 9 7 0 ) and applied by Forristall ( 1 9 7 4 ) to the calculation of current profiles generated by a hurricane in the Gulf of Mexico.

This me-

thod is particularly suitable for determining the depth distribution of currents at a specific position for a given moment in

2

time, but for circulation studies the size of the computations would make i t less convenient. Finite difference models with grid boxes in both the horizontal and the vertical have been used recently in circulation studies (e.g. Leendertse 1 9 7 3 ) .

This model involves vertical

integration over each layer, and the use of a coefficient of interfacial friction.

The bottom stress, however, is expressed

in terms of the current in the bottom layer, a physically more realistic assumption than that employed in many two-dimensional models where the bottom stress is related to the depth mean current.

However, solutions in the vertical are only available

at discrete points, and the determination of a continuous velocity profile is not possible. Heaps ( 1 9 7 1 ,

1976)

has overcome this latter problem for

both the linear and non-linear hydrodynamic equations by expanding the two components of horizontal current in terms of depthdependent eigenfunctions with time-dependent, horizontallydependent coefficients.

Both surface and bottom boundary condi-

tions are satisfied in the limit as the number of terms in the

In practice, Heaps shows that the expansion tend to infinity. expansion converges very rapidly, yielding a technique which is particularly economic in computer time. In this paper a method is proposed in which the two components of horizontal current are expanded in terms of the product of depth dependent functions (B-splines), vary with time and horizontal position.

and coefficients which The determination of

the coefficients is accomplished by substituting these expan

-

sions into the two equations of motion and minimizing the resulting residual with respect to each coefficient in a least squares sense.

The surface and bottom boundary conditions are sa-

tisfied exactly by using linear combinations of B-splines. The application of the present method to the solution of the linear three-dimensional hydrodynamic equations, assuming a rectangular basin of constant depth with a constant eddy viscosity and a constant bottom friction coefficient, yield nearly identical solutions for wind induced motion to those obtained by Heaps ( 1 9 7 1 ) ,

providing an initial confirmation of the

3

accuracy and stability of the method.

The time variation of

both horizontal and vertical circulation induced by the wind is calculated for a number of cases having different eddy viscosi.ty, and the influence of eddy viscosity u p o n surface and bottom currents together with the induced circulation is examined. SOLUTIO'J

OF THE BASIC EQUATIOhTS U S I Y G AM EXPAMSIPN OF R-SPLINES

For a homogeneous fluid, neglecting shear stress i n the horizontal, the advcctive terms, and the equilibrium tide, the equations of continuity and motion may be written

where denotes time,

t

x,y,z C a r t e s i a m co-ordinates, form

2ft han :d set,

with x and y in the horizontal plane of the undistorbed sea surface, and z measuring depth below that surface, h

undisturbed depth of water,

E;

elevation of the sea surface ahove the undisturbed level,

u,v

components of the current at depth z

,

in the direc-

tions of increasing x,y respectively, P

the density of the water,

Y

the geostrophic coefficient, uniform and constant,

g

the acceleration due to gravity.

Also,

F,G denote internal shear stresses at depth z

,

in the

4

x,y directions respectively, given by au

-,

F = - p N - - az

av G = - P N - az

(4)

where N is a coefficient of eddy viscosity,-i general varying

,

with x,y and z lysis.

av at

but taken as a constant in the following ana-

Substituting ( 4 ) into ( 2 )

+ yu =

-

g

ac + a aY

(N

and ( 3 ) gives

av z )

(6)

To solve these equations i t is necessary to specify both

surface and bottom boundary conditions.

At the surface,

where F s , Gs denote the components of wind stress over the water surface in the x and y directions, suffix o denoting evaluation at z = 0. Similarly at the sea bed, z = h

,

where G B, F B denote the components of bottom friction in the x and y directions. Assuming a slip condition at the sea bcd :

where k is

a

constant coefficient, ( E )

gives

,

A n o slip bottom boundary condition, namely uh = vh = 0 , when employed with a coefficient of eddy viscosity which varies near the sea bed, is used in an extension of the present paper (Davies 137Ga).

However, for constant eddy viscosity, the rela-

tionships given by ( 1 0 ) are appropriate. Expanding the two components of velocity in terms of depth dependent functions Mr(z)

(4'th order B-splines) gives

The B-splines have a number of particularly useful features which make them a good choice as a set of basis functions.

They

have been used extensively for the accurate fitting of numerical data (Powell 1970), and yield very accurate solutions when used in solving linear hydrodynamic equations (Davies 1976b) and n o n linear partial differential equations (Davies 1 9 7 6 ~ ) . The incorporation of boundary conditions is particularly easy due to the piecewise nature of the functions. Points along the z a x i s , at which the E-spline changes from a z e r o - t o a non-zero function are termed k n o t s , Xr.

A fourth

CX

order B-spline Mr being non-zero over the interval X though at the points Xr-4

and X r

,

< z r-4 provided these knots are

single, Mr and its derivatives vanish. shows the region 0

F o r example, Fig. I

z < h divided into ten interior k n o t segand ( 1 2 ) , with

ments, corresponding to m = 1 3 i n equations ( 1 1 ) knots at 0 = X


9 0 m flowed in a direction ranging from 30° to 90' counter clockwise looking down to the interior flow. Although the transition f r o m westward to southward flow in the interior occurred at time = 7 2 hours a comparable change below z = 90m

120

occurred approximately 1 0 hours l a t e r . p e r i o d t h e c u r r e n t s were weak.

During t h i s t r a n s i t i o n

Bottom boundary l a y e r t h i c k n e s s . We i n f e r t h a t t h e BBL t h i c k n e s s w a s a b o u t 6m f o r t h e p e r i o d s o f n o r t h w a r d a n d westward i n t e r i o r f l o w s and a b o u t l l m f o r t h e p e r i o d o f s o u t h w a r d i n t e r i o r f l o w . These t h i c k n e s s e s a r e s i g n i f i c a n t l y l e s s t h a n t h a t e x p e c t e d i f t h e BBL were a n e u t r a l l y or n e a r l y n e u t r a l l y s t r a t i f i e d t u r b u l e n t Ekman l a y e r . The l a t t e r t h i c k n e s s s h o u l d be a b o u t ku,/f = k (.03) V / f ( W e a t h e r l y ( 1 9 7 2 ) ) which w i t h Vg = 1 0 - 2 0 c m / s , r e p r e s e n t a f i v e v a l u e s f o r t h e g e o s t r o p h i c c u r r e n t a t o u r s i t e , i s about 20-40m. Ekman v e e r i n g . L a r g e , p e r s i s t e n t c u r r e n t d i r e c t i o n c h a n g e s , i n a s e n s e c o n s i s t e n t w i t h Ekman v e e r i n g , were o b s e r v e d d u r i n g t h e p e r i o d s of northward and southward i n t e r i o r flow i n t h e BBL. D u r i n g n o r t h w a r d f l o w t h e a v e r a g e Ekman v e e r i n g w a s % 30' a n d f o r s o u t h w a r d f l o w it was % 7 5 0 . The v e e r i n g o c c u r r e d i n t h a t p a r t o f t h e BBL which w a s t h e r m a l l y s t r a t i f i e d and t h e amount o f v e e r i n g w a s d i r e c t l y p r o p o r t i o n a l t o t h e temperature g r a d i e n t . D u r i n g t h e p e r i o d o f westward f l o w when t h e i n t e r i o r f l o w w a s weaker a n d more v a r i a b l e t h e a v e r a g e Ekman v e e r i n g was s m a l l , % 3.5'. For c o m p a r i s o n t h e e x p e c t e d Ekman v e e r i n g f o r a n e u t r a l l y s t r a t i f i e d t u r b u l e n t Ekman l a y e r w i t h V g = 10-20cm/s and a g e o s t r o p h i c d r a g c o e f f i c i e n t .03 i s about l o o ( M I . u*/V g Was t h e BBL a v e r y s t a b l y s t r a t i f i e d t u r b u l e n t Ekman l a y e r ? S e v e r a l f e a t u r e s common t o s u c h boundary l a y e r s s u g g e s t it was. I t s i n f e r r e d d e p t h was l e s s t h a n t h a t f o r a n e u t r a l l y s t r a t i f i e d t u r b u l e n t Ekman l a y e r . The Ekman v e e r i n g s f o r n o r t h w a r d and s o u t h w a r d i n t e r i o r f l o w s w a s a p p r e c i a b l y g r e a t e r t h a n t h a t f o r a n e u t r a l l y s t r a t i f i e d t u r b u l e n t Ekman l a y e r . The Ekman v e e r i n g i n c r e a s e d when t h e s t r a t i f i c a t i o n i n c r e a s e d , i . e . , t h e veering w a s g r e a t e r f o r southward flow t h a n f o r n o r t h w a r d f l o w . The t o t a l v e e r i n g i n p e r i o d s o f s t r o n g e s t s t r a t i f i c a t i o n , e n c o u n t e r e d when t h e i n t e r i o r f l o w was n o r t h ward, r a r e l y e x c e e d e d 90°, t h e l i m i t i n g v a l u e f o r a v e r y s t a b l y s t r a t i f i e d t u r b u l e n t Ekman l a y e r . A I ' j e t - l i k e ' ' s t r u c t u r e w a s o f t e n observed i n v e r t i c a l p r o f i l e s of h o r i z o n t a l s p e e d and d i r e c t i o n .

-

Upwelling ( d o w n w e l l i n g ) i n t h e BBL. We have p r e s e n t e d arguments t h a t i f t h e i n t e r i o r , geostx>ophicflow i s along i s o b a t h s w i t h d e e p water t o t h e r i g h t ( l e f t ) l o o k i n g downstream u p w e l l i n g ( d o w n w e l l i n g ) o f c o l d e r ( w a r m e r ) w a t e r may o c c u r i f t h e isotherms are n o n - p a r a l l e l t o a bottom with p o s i t i v e s l o p e . P r o v i d e d t h e r e i s n o t a c o m p l e t e b a l a n c e between h o r i z o n t a l a d v e c t i o n a n d v e r t i c a l d i f f u s i o n of h e a t , t h e BBL t e m p e r a t u r e s h o u l d d e c r e a s e ( i n c r e a s e ) w i t h t i m e . Our d a t a a p p e a r s c o n s i s t e n t with such a p r o c e s s occuring. F u r t h e r , w e have suggested t h a t s i n c e t h e bottom s l o p e a n g l e f o r southward flow i s about t e n t i m e s l a r g e r t h a n t h a t f o r northward flow l a 9 / 3 t l f o r t h e f o r m e r s h o u l d be a b o u t t e n s t i m e s l a r g e r t h a n f o r t h e l a t t e r . Our d a t a i s a l s o c o n s i s t e n t w i t h t h i s i d e a . I t i s i n t e r e s t i n g t o n o t e t h a t u p w e l l i n g i n t h e BBL c a n c a u s e t h e BBL t o become more s t a b l y s t r a t i f i e d t h a n t h e f l u i d a b o v e

121

the boundary layer. Bottom homogeneous layers. Such layers were the exception rather than the rule. They were seen in about 40% of the profiles and 80% of these layers had depths < 7m. Several features are inconsistent with their formation being due solely to turbulent mixing: (a) generally the BHL layer temperatures remained constant or cooled as they thickened and (b) whether these layers were capped hy sharp 'elbos' or smooth curves was not indicative of whether they were thickening or decaying. Horizontal advective processes seem essential to their formation. Finally this is a preliminary report. Possible complicating features (tiltle-dependence, baroclinicity, insulated bottom, internal gravity waves, implications of the site being at a shelf break) need to be considered further. It is encouraging that the relatively simple arguments presented here account for many of the observed features. ACKNOWLEDGEMENTS This research was sponsored by the Office of Naval Research under contract N000-14-75-C201 and by the National Sciance Foundation, Continental Shelf Dynamics Program, under grant GA-34009. REFERENCES Armi, L. and R.C. Millard, Jr., 1976. The bottom boundary layer of the deep ocean. J. Geophys. E . ,81, 49834990. Businger, J.A. and S.P.S. Arya, 1974. Height of the mixed layer in the stably stratified planetary boundary layer. Advances & Geophysics, H.E. Landsberg and J. Van Mieghem, ed., Academic Press, New York, pp. 73-92. Deardoff, J.W., 1970. A three-dimensional numerical investigation of the idealized planetary boundary layer. 1,377-410. Geophys. Fluid I)+., Kundu, P.K., 1976. E man veering - observed near the ocean bottom. J. Ph s. Oceanogr., 6, 238-242. Mercado, A. ana n*J Leer, 1976.- Near bottom velocity and temperature profiles observed by cyclosonde. Submitted to Geophys. Res. Letters. Niiler, P.P., 1976. Observations of low-frequency currents on the Western Florida coritinental shelf. Memoires de la Societe Royale des Sciences de Liege, Tome X, pp. 331-358. Pedlosky, J., 1974. Long shore currents, u m n g and bottom topography. J. Phys. Oceano r., 4, 217-226. Smith, J.D. and C.F. Long, h e zffect of turning in the bottom boundary layer on continental shelf sediment transport, Memoires de la Societe Royale des Sciences de Liege, Tome X , 369-396. Van Leer, J., W. Duing, R. Erath, E. Kennelly, and A. Speidel, 1974. The cyclosonde: an unattended vertical profile

122

for s c a l a r a n d v e c t o r q u a n t i t i e s i n t h e u p p e r o c e a n . Deep-sea R e s . , 2 1 ( 5 ) : 385-400. W e a t h e r l v . G . L T 1 9 7 r A s t u d v of t h e b o t t o m b o u n d a r y l a y e r of t h e F l o r i d a C u r r e n t . Phys. Oceano r . , 2 , i4-13. Weatherly, G . L . , 1975. A numei?icGtu&me-aependent t u r b u l e n t Ekman l a y e r s o v e r h o r i z o n t a l a n d s l o p i n g J. Oceano r . , 5 , 2 8 8 - 2 9 9 . bottoms. W e a t h e r l y , G.L.-and P . P . Niile:, 1 9 7 4 . Bottom homogeneous l a y e r s i n t h e F l o r i d a C u r r e n t . Geophys. %. L e t t e r s , 1, 316-319. Winbuzh, M . and W . Munk, 1 9 7 0 . The b e n t h i c b o u n d a r y l a y e r . The S e a , Vol. 4 , P a r t 1, New York, W i l e y , p p . 731-758. Wuns~h,C.,1970. On o c e a n i c boundary m i x i n g . Deep-sea Res., 293-301. -

2.

-.

c,

123 BOUNDARY LAYER ADJUSTMENTS TO BOTTOM TOPOGRAPHY AND SUSPENDED SEDIMENT

J. Dungan Smith and S . R. McLean Department of Oceanography, University of Washington Seattle, Washington

ABSTRACT An accurate knowledge of flow in the immediate vicinity of the sea bed is important in marine geological, benthic ecological, geochemical, and sediment transport studies. However in many cases, the velocity field is complicated by the presence of ripples and dunes on the sea bed and suspended sediment-induced stratification in the flow.

Recently techniques

for handling these factors were developed by the authors, but they were applied only to a situation where the sea bed was comprised of a single size and specific gravity class.

In this paper these techniques are

extended to the case wi-?re the suspended material is characterized by an ensemble of settling velocities and critical shear velocities.

The results

are applied first to a flat sea bed and then to spatially averaged flow over a wavy boundary such as might be produced by natural bed forms. These calculations indicate that the sediment transport process can have a significant effect on flow near the sea bed and that proper account must be taken of the settling velocity distribution comprising the suspended sediment concentration field. INTRODUCTION In marine and fluvial systems, near-bottom velocity fields capable of eroding and transporting sediment can be modified relative to those in non-sediment bearing flods in three jmportant ways.

First, near-bed

particle motions substantially increase the apparent roughness of the bottom.

Second, when such flows carry suspended sediment, the vertical

eddy diffusive transfer of mass and momentum is inhibited by the maintenance of a stable density field and third, such flows inevitably produce This is contribution 931 from the University of Washington. The work described herein was supported by NSF Grant GA-14178 and DES-75-15154.

bed forms causing the near-bottom velocity to vary as a function of downstream position and the stress on the bottom to be supported, in part, by form drag on the topographic features.

In order to permit accurate mean

velocity and sediment transport computations, each of these effects must be accounted for.

In a recent paper, Smith and McLean (in press) have

presented a method by which the spatially averaged velocity profile in a sediment-bearing flow over two-dimensional topographic features can be computed. A s part of this theory, means of determining the apparent bed roughness, the suspended sediment concentration profile and the effect that the suspended sediment has on the mean velocity field

are provided.

For computational simplicity this was done using a single size class deemed representative of the entire sample.

In the paper at hand the

problem is generalized so that the bed sediment sample can be divided into any number of size and specific gravity classes, thus avoiding the somewhat arbitrary choice of an effective sediment size and specific gravity.

In applying the generalized theory, size distributions obtained from the crest and trough of a large sand wave in the Columbia River are used. Both samples were procured in 1969 as part of a comprehensive examination of sand wave dynamics carried out over a field of 2 to 3 meter high, 70 to 100 meter long dunes during a period of maximum, but nearly steady river flow.

These particular samples have been chosen for use here because data

from five Columbia River experiments were employed by Smith and McLean to set several coefficients in their spatially averaged flow theory, and subsequently in this paper, velocity and sediment concentration profiles computed using the proper size distributions will be compared to those obtained previously by Smith and McLean.

Bed sediment analyses indicate that the

river bottom was comprised of material with the same size and specific gravity composition from year to year.

However, the trough sample is more

representative of the bed composition under conditions of zero or near zero sediment transport because, under the high boundary shear stress part of a non-uniform flow, an erodible bed sample comprised of a wide variety of sediment particles always appears to be deficient in the lighter and finer classes.

This effect can be seen by comparing the two size distributions

shown in Fig. 1.

125

30

-

20

-

% 10

-

01

1

0.5

1

1.0

1

1

1.5

1

1

1

2.0

1

I

2.5

3.0

J

Fig. 1. Sediment size distrihution from the trough (A) and crest (B) of a 2.7 m high, 74 m long sand wave in the Columbia River. Size data for ten specific classes along with the settling velocity and critical boundary shear stress for each size class are given in Table 1. TABLE 1 Sediment Parameters for Each Size Class of Two Bed Samples xS(cm/sec)

D 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00

.595 -500 .420 .354 .297 .250 .210 .177 .149 .125

7.14 6.04 5.01 4.04 3.28 2.62 2.07 1.65 1.28 0.99

2

‘ I(dynes/cm ~

3.12 2.71 2.40 2.18 7.00 1.86 1.72 1.58 1.45 1.32

% )

%

(Sample A)

-

2.5 4.5 8.5 13.0 21.0 19.5 15.0 9.5 5.0 1.5

(Sample B) 5.0 8.5 19.0 24.0 24.0 11.0

5.0 2.5

1.0

--

Included are sediment size, settling velocity, critical boundary shear stress, and percent of material in ten categories for each distribution. Sample A is from the trough of a 2.7 m high, 74 m long sand wave in the Columbia River and Sample B is from its crest.

126 Apparent Bed Roughness

In flow over a geometrically smooth, fixed boundary, the apparent roughness of the bed (2,) can be computed using the work of Nikuradse (1933);

however, once the transport of bed material has been instigated,

the characteristic sand grain diameter and the viscous sublayer thickness no longer provide the relevant length scales.

The presence of a solid

phase in the lower part of the flow tends to equalize the momentum distribution in this region making the velocity profile, when plotted with the logarithm of the distance from the boundary denoted

on

the ordinate, appear

concave from the right hand side, thus increasing the apparent boundary roughness for the flow in thenon4ediment transporting region.

Physically,

this tendency to equalize the momentum distribution in the near-bottom layer arises because the sediment comprising the river or sea bed is ejected in a near-vertical direction with zero horizontal velocity and extracts momentum from the flow until

1) it lands o n the bottom again or

2) it reaches the horizontal velocity of the fluid.

In the former

situation (the bed load case) the maximum velocity difference between the sedimentary particles and the transporting fluid occurs in the neighborhood of the top of the trajectory causing the maximum momentum defect to lie just below this level.

The sediment grains put a stress on the flow

and cause the velocity profile in the multicomponent fluid to increase less rapidly with distance from the boundary than would be the case in an otherwise analogous non-sediment transporting flow.

The characteristic

length scale in this situation is the thickness of the bed load layer. In the suspended sediment transport case, the particles attain the horizontal velocity of the fluid well before reaching their maximum elevation and under these circumstances maximum momentum loss to the transporting fluid occurs in the region of the maximum velocity difference so the appropriate length scale is the height of this zone.

In an examination of the bed load transport by wind, Owen (1964) recognized that the effective boundary roughness z should be proportional to the thickness of the bed load layer and argued that the bed load layer should be of order ~ , ~ / 2 g . Owen's expression is obtained by balancing potential energy at the top of the trajectory with the kinetic energy of the particle just after the flight has been initiated and assuming that the particle's vertical velocity at this point is proportional to u,. Using aeolian velocity profile data for the bed load transport situations studied by Bagnold (1941), Chepil (1945a,b,c) and Zingg (1953), Owen determined the constant of proportionality between zo and ~ , ~ / 2 g to be

127 2.07 x

Even when t h e d e n s i t i e s that c a n c e l f o r t h e a e o l i a n s i t u a t i o n

are r e t u r n e d so t h a t z

-

= psu,'/2(p

p)g, a quick c a l c u l a t i o n using

t y p i c a l v a l u e s f o r t h e r e l e v a n t p a r a m e t e r s i n d i c a t e s t h a t Owen's e x p r e s s i o n

i s n o t v a l i d under f l u v i a l and m a r i n e c o n d i t i o n s .

However, i t i s l i k e l y

t h a t t h e i n i t i a l k i n e t i c e n e r g y p e r u n i t volume of t h e sediment p a r t i c l e (psuo2)

i s n o t p r o p o r t i o n a l t o psu,2

b u t r a t h e r t h a t i t depends upon t h e

work done p e r u n i t p a r t i c l e volume i n l i f t i n g t h e sediment g r a i n from t h e bed.

-

T~

2 A s t h e f o r c e on a sediment g r a i n i s of t h e o r d e r ( T -~ T )D where . c T~ i s t h e e x c e s s boundary s h e a r stress averaged o v e r a few t e n s of

g r a i n d i a m e t e r s and D i s t h e p a r t i c l e d i a m e t e r , and as t h e d i s p l a c e m e n t i s of 3 t h e o r d e r D , t h e work done i s s c a l e d by ( T -~ rc)D . T h e r e f o r e t h i s approach y i e l d s a n e x p r e s s i o n of t h e form

z

=

zN

for

'b

-

'Ic

+

T

b

< -

T

c

and

z

0

=

(Ps

zN

for

P)g

T

b

T

where zN i s t h e v a l u e o b t a i n e d from t h e e x p e r i m e n t s of Nikuradse. Good agreement between Owen's r e s u l t s and t h o s e from a s e t of f i e l d measurements made by Smith and McLean i n t h e Columbia R i v e r i s o b t a i n e d when Owen's method i s s o m o d i f i e d .

The c o e f f i c i e n t a

a v a l u e of 2 6 . 3 i n rhe Columbia R i v e r d a t a .

w a s found t o have

In c o n t r a s t , i f t h e c r i t i c a l

boundary s h e a r stress f o r t h e i n i t i a t i o n of sediment motion were t a k e n t o b e z e r o and p case, a

were t a k e n t o b e much g r e a t e r t h a n p a s i n t h e a e o l i a n

= 2 2 . 4 p u t s ( l b ) i n q u a n t i t a t i v e agreement w i t h t h e e x p r e s s i o n

Here T = P U , ~ is t h e s h e a r stress on t h e sediment b bed averaged o v e r a r e g i o n of o n l y a few t e n s of g r a i n d i a m e t e r s i n s c a l e

o b t a i n e i by Owen.

and denoted s u b s e q u e n t l y i n t h i s paper a s t h e l o c a l boundary s h e a r stress, whereas motion.

T

i s t h e v a l u e of t h i s p a r a m e t e r a t t h e i n i t i a t i o n of sediment I t should be n o t e d t h a t T

depends upon t h e s i z e and s p e c i f i c

g r a v i t y of t h e sediment p a r t i c l e s c o m p r i s i n g t h e bed and i s denoted by T

when r e f e r r i n g t o a p a r t i c u l a r component of t h e sediment sample. Smith and McLean ( i n p r e s s ) d i d n o t a d d r e s s t h e problem of what t o

do w i t h ( l b ) when t h e bed i s comprised of more t h a n a s i n g l e s i z e and specific gravity class.

However t h e model p r e s e n t e d above i s based on

s i n g l e p a r t i c l e mechanics and i t i s c l e a r t h a t t h e n e t momentum d e f e c t due to

a d i s t r i b u t i o n of sediment s i z e s i n t h e bed l o a d l a y e r must be made up

128 of the sum of the individual defects. Moreover, if the sediment distribution is monomodal and if the sample is reasonably well-sorted, the height of the maximum momentum defect cannot differ significantly from that given by multiplying the height to which the grains in each size class rise times the number of grains in that size class and averaging over all size classes, that is, taking the concentration weighted average of a

(‘cb

-

T~)”

For greater accuracy or for use with more complicated sediment (p, - p)g. size and specific gravity distributions, a complete model of the bed load transport process must be used to evaluate the momentum defect; however, no such model is yet available and in most practical situations, the

procedure that has just been outlined here is sufficient.

In the suspended sediment case the situation is somewhat more complicated because the grains no longer return directly to the river or sea bed, and the region over which momentum exchange occurs between the sediment and fluid components is more broad.

Nevertheless, order of magnitude cal-

culations using the coupled particle-fluid equations of motion indicate that the finer bed load grains would attain the horizontal velocity of the fluid by the end of one flight and that particles destined to be transported as suspended load also attain the horizontal velocity of the fluid at a height of the order of magnitude given by (lb). ments permit the constant of proportionality between

Although these argu(ib

-

iC)/(pS

- p)g

and z o to vary between the bed load and suspended load cases and probably between situations characterized by well and poorly sorted sediment distributions, no evidence of a systematic variation is available to date and it is suggested that the value a

=

2 6 . 3 determined for a well-sorted

bed material being transported as bed load can be employed in all problems. Two factors assist in permitting more general use of (lb) with the abovementioned coefficient. First, in most suspended sediment transport cases T

is small relative to

ib

and does not vary widely, making (lb) relatively

insensitive to particle size, thus to the nature of the sediment distribution.

Second, the velocity field varies logarithmically with zo so

small errors in the latter parameter are not of great importance.

Perhaps

experimental and theoretical work to be carried out in the future will provide a more accurate means of finding z but for the present the use of (lb) with a coefficient of 26.3 should suffice in most practical sediment transport problems.

129 The E f f e c t s o f Suspended Sediment-Induced S t r a t i f i c a t i o n on Near Boundary Flow

Theore t i c a 1 Cons i d e r a t i o n s Smith and McLean ( i n p r e s s ) do n o t p r o v i d e a means of d e t e r m i n i n g what happens i n a suspended sediment problem when t h e bed sediment is comprised of a d i s t r i b u t i o n of p a r t i c l e s i z e s and s p e c i f i c g r a v i t i e s , n o r do t h e y account f o r t h e d i f f e r i n g d i f f u s i v i t i e s between sediment and momentum. I n t h i s s e c t i o n t h e s e d e f i c i e n c i e s a r e r e c t i f i e d t h u s p r o v i d i n g a complete t h e o r y f o r d e t e r m i n i n g v e l o c i t y and sediment c o n c e n t r a t i o n d i s t r i b u t i o n s i n h o r i z o n t a l l y uniform flow. Following Hunt (1969) o r Smith (1976, p. 5 6 0 ) , t h e e q u a t i o n s f o r cons e r v a t i o n of sediment and f l u i d mass i n a h o r i z o n t a l l y

uniform, m u l t i -

component f l o w can be w r i t t e n as

and

Here, €

is

e

i s t h e average. sediment c o n c e n t r a t i o n of component c l a s s n , and

tie

total

c o n c e n t r a t i o n of suspended m a t e r i a l , w

v e l o c i t y of component n , K nent n, K

W

is the s e t t l i n g

i s t h e mass d i f f u s i o n c o e f f i c i e n t f o r compo-

i s t h e mass d i f f u s i o n c o e f f i c i e n t f o r t h e water, and w

W

is the

For s t e a d y f l o w t h e s e two e x p r e s s i o n s can

v e r t i c a l v e l o c i t y of t h e water. be combined t o g i v e

A s t h e K ' s and K

W

a r e a l l d i f f u s i o n c o e f f i c i e n t s f o r mass, t h e y must b e

s e t e q u a l f o r r e a s o n s g i v e n by Smith and Hopkins (1972):

however, t h e y

need n o t b e e q u i v a l e n t t o t h e d i f f u s i o n c o e f f i c i e n t f o r momentum, Km. R e s u l t s from suspended sediment t r a n s p o r t s t u d i e s a s w e l l as from i n v e s t i g a t i o n s of s t a b l e a t m o s p h e r i c boundary l a y e r s i n d i c a t e t h a t t h e y may d i f f e r

.

Both s u g g e s t t h a t K = K = a K Suspended sediment s t u d i e s (Hunt, 1969) n w m s u g g e s t t h a t a i s a c o n s t a n t and i n d i c a t e t h a t i t l i e s between 1 . 2 and 1 . 5 .

130 The atmospheric investigations are concerned with the diffusion of heat rather than sediment particles, but heat is carried by the fluid and should diffuse with the mass diffusion coefficient thereof, so it is likely that the effects are the same.

In the latter case, a is found to depend upon

the degree of stratification parameterized by the distance from the boundary divided by the Obukhov length.

a =

Thus

1

+

cl

+ B5

55

where

and 3 L =

pu*

Here, p is the fluid density, u* is shear velocity, g is the acceleration due to gravity, k is von Karman’s constant, and flux into the fluid from the boundary.

(PX’)~ is the buoyancy

Businger, et a1 (1971) show that

5 is related to the gradient Richardson number at the boundary in the

following manner,

In general the gradient Richardson humber depends upon the density given in the sediment transport situation by the concentration field through

In sediment transporting problems, the values of a obtained from (4a) vary from 1.2 to 1.35.

The agreement between results from suspended sediment

studies and calculations based on meterological formulae appears not to be fortuitous and suggests that the use of (4a) and (5), which are derived from comprehensive atmospheric boundary layer experiments, is likely to be fruitful in sediment transport problems.

In addition to the concentration dependence of the coefficient a, the momentum diffusion coefficient K also varies with flow stratification, m

131 t h u s depends on € ( z ) .

Smith and McLean show t h a t n e a r t h e boundary

where

t h e n a r g u e t h a t ( 7 ) p r o b a b l y i s v a l i d t h r o u g h o u t t h e e n t i r e boundary l a y e r . Here

5

=

z / h i s t h e n o n d i m e n s i o n a l d i s t a n c e from t h e boundary and f 2 ( C ) i s

t h e n o r m a l i z e d d i s t r i b u t i o n o f eddy v i s c o s i t y w i t h h e i g h t under n e u t r a l conNear t h e boundary f (5) 2 5 i n agreement w i t h s i m i l a r i t y t h e o r y . 2 Above 0 . 1 h t h e eddy v i s c o s i t y i n c r e a s e s a t a d e c r e a s i n g r a t e and e v e n t u a l l y

ditions.

f a l l s o f f w i t h h e i g h t , a p p r o a c h i n g z e r o a t t h e t o p of t h e boundary l a y e r .

I n a r i d e r t h e boundary l a y e r t h i c k n e s s i s e q u i v a l e n t t o t h e f l u i d d e p t h ( h ) whereas on t h e c o n t i n e n t a l s h e l f i t i s t h e Ekman d e p t h g i v e n a p p r o x i m a t e l y by u,/2f

that l i m i t s it.

*

The form of f 2 g i v e n i n (7b) w a s o b t a i n e d by f i t t i n g a two-part polynomial t o t h e d a t a o f Klebanoff

(1954) and Townsend (1951), as shown by

Although t h e s e d a t a are f o r a growing boundary l a y e r

Hinze (1959, p. 493).

on a f l a t p l a t e r a t h e r t h a n f o r a f l o w o f f i n i t e d e p t h , t h e s h a p e o f (7b) i s i n r e a s o n a b l e agr,eement w i t h less a c c u r a t e d a t a from c h a n n e l f l o w s , f o r

example, see Vanoni (1946).

U s e of ( h a ) ,

( 5 ) . and ( 7 a ) f o r R

i

defined

w i t h i n t h e f l o w r a t h e r t h a n a t t h e boundary rests on a n unconfirmed postulate a t t h i s point.

However, t h e s e e x p r e s s i o n s must b e s a t i s f i e d asymptot-

i c a l l y and c a n n o t b e v e r y f a r i n e r r o r i f a t a l l .

With t h e a s s i s t a n c e o f

t h i s a s s u m p t i o n , a g e n e r a l i z e d v e r s i o n o f 5 c a n b e d e f i n e d and u s i n g ( 5 ) , (6),

( 7 ) and a u / a z = r / p K

m

i t becomes

112

c=--"

20

(8)

T h i s new p a r a m e t e r i s no l o n g e r d e f i n e d by (4b) and i s no l o n g e r d i r e c t l y r e l a t e d t o L as d e f i n e d i n ( 4 c ) . c a n b e r e p l a c e d by r b ( l

-

For a steady, uniform channel flow

~(5)

5).

*See Smith and Long (1976) f o r a d i s c u s s i o n o f t h e bottom boundary l a y e r on c o n t i n e n t a l s h e l v e s and i t s e f f e c t on s e d i m e n t t r a n s p o r t .

132 In order to solve ( 3 ) , a boundary condition must be applied at the top of the momentum defect layer.

To a first approximation this ought to be

proportional to the level of maximum momentum defect which in turn ought to be proportional to the value of z

taken above.

Moreover, an apparent value

of sediment concentration at level zo can be used just as w e l l as the actual value at level mzo, where m is a constant of proportionality, as long as the expression for the suspended sediment concentration profile remains fixed in Indeed, this is the case in all'problems

form for a given value of zo.

except those involving extremely small scale boundary topography. The use of a fictitious rather than a real reference concentration has the advantage of permitting the boundary conditions on the flow and sediment transport problems to be applied at the same level, a result that is most useful in complicated situations. The solution to ( 3 ) using (4a),

(7) and Kn

=

K w

=

aK is m

where w n Pn = ku*

and solving T

= T

b

(1

- 5)

= pK ( a u / a z ) where Km is given by (7) yields

m

When z

0, i n s u r i n g t h a t t h e f l u c t u a t i o n s are a m p l i f i e d .

An e q u i v a l e n t set of d a t a f o r a f o r c e d problem are shown in F i g u r e s 4 ,

5, and 6.

The v a l u e s o f t h e p a r a m e t e r s remain t h e same as f o r t h e p a s s i v e

boundary case s o t h a t a r e a s o n a b l e comparison can b e made.

The e x a c t form

of t h e f o r c i n g a t t h e boundary was chosen t o b e Gaussian i n t h e p l a n a r varia b l e s z and y as w e l l as i n t i m e .

As a r e s u l t ,

come new p a r a m e t e r s t h a t must be s p e c i f i e d .

t h e s t a n d a r d d e v i a t i o n s be-

F o r t h e n u m e r i c a l example de-

p i c t e d , t h e c h o i c e s c o r r e s p o n d to a l e n g t h scale of 8.5 cms w i t h t h e z and

182

-R e s 350

-

K = .35 110.

4-.

I

Cr .-.05716417

ci =

L

I

-1.0 -.B

1

I

1

-.6 -.4 - 2

0

.01801811

= 49074

J

I

1

1

I

2

.4

.6

.B

I

1.0

F i g u r e 3. K i n e t i c energy by components f o r s e l f - e x c i t e d system. is l o c a t e d a t n = 4.5.

Pycnocline

y v a r i a t i o l i s e q u a l and a t i m e s c a l e c o r r e s p o n d i n g t o 20 seconds.

Field data

(Martin, p r i v a t e communication) i n d i c a t e t h a t t h e s p a c e s c a l e i s t y p i c a l of what i s o b s e r v e d whereas t h e t i m e s c a l e i s n o t a s w e l l knorm and depends on a g r e a t many f a c t o r s .

Adjustment of t h e t i m e s c a l e can b e made i f t h e an-

p l i t u d e of t h e d r i v i n g d u e t o t h e mass f l u x is allowed t o vary.

For exam-

w

p l e , by l e t t i n g t h e f o r c e d and t h e f r e e o s c i l l a t i o n a m p l i t u d e s f o r t h e

component of t h e v e l o c i t y b e e q u a l ,

ae'/az

= .30

x

second p e r i o d ; i n c r e a s i n g t h e p e r i o d t o 2 h o u r s r e q u i r e s cn-l under t h e same c i r c u m s t a n c e s . able.

cm-l f o r t h e 20

a B ' / a z = .30

x

The l a t t e r i s p r o b a b l y more reason-

I f i t i s r e c a l l e d t h a t o n l y t h e l a m i n a r problem i s b e i n g i n v c s t i -

g a t e d , t h e n t h e s e a m p l i t u d e s are small indeed. Three major f e a t u r e s are r e v e a l e d when t h e s t r u c t u r e of t h e f o r c e d prob-

l e m i s examined.

F i r s t , t h e Reynolds stress c o r r e l a t i o n s of F i g u r e 4 have

s i g n i f i c a n t v a l u e s closer t o t h e s o l i d boundary t h a n t h o s e of t h e f r e e problem.

Second, t h e buoyancy f l u x ( F i g u r e 5) now c a u s e s a t r a n s f e r of energy

t o the fluctuations. f e r i o r t o its

-

-z)w

Third, t h e counterpart.

c; orrelation -

( F i g u r e 4 ) i s now in-

The r e l a t i v e v a l u e s of k i n e t i c e n e r g y of

t h e components ( F i g u r e 6 ) , on tne o t h e r hand, f o l l o w t h e p a t t e r n of t h e self-excited oscillations.

Some u n d e r s t a n d i n g of t h e r e s u l t s can b e found

by n o t i n g t h a t t h e r e i s a profound d i f f e r e n c e i n t h e two probleiis.

The

183

- - - -1nflpxion point

-1.0 -.B

- 6 -.4

Figure 4.

-.2

0

I

1

1

1

1

.2

.4

.6

8

1.0

Reynolds stresses f o r f o r c e d o s c i l l a t i o n s .

c

Re = 350 K = .35 4 = lloo Cr =-.05716417 Ci 0.0

I

I

I

I

I

I

1

1

'

1

1

-1.0 -.8-.6-.4 -.2 0 .2 4 .6 .8 1.0

F i g u r e 5.

Buoyancy f l u x f o r f o r c e d o s c i l l a t i o n s .

184

I

R e = 350 K * .35 110.

4

-

Cr =-.05716417

ci

I

l

l

1

1

-1.0 -.8 -.6 -.4 -.2

F i g u r e 6.

= 0.0

0

.2

.4

.6

.8

1.0

Forced o s c i l l a t i o n k i n e t i c energy.

homogeneous problem i s one t h a t i s u n s t a b l e and t h e r e f o r e t h e energy produced by t h e working t h e t h e Reynolds s t r e s s e s on t h e mean g r a d i e n t s must exceed t h e d r a i n by t h e buoyancy f l u x and t h e v i s c o u s d i s s i p a t i o n .

The

f o r c e d problem i s one t h a t i s n e u t r a l , t h a t i s , t h e r e i s a s o u r c e of cnergy a t t h c boundary s o l o n g a s t h e i c e d i s c h a r g e s b r i n e , and t h i s i n p u t must be e x a c t l y b a l a n c e d by t h e l o s s - g a i n

from t h e same s o u r c e s - s i n k s t h a t a r e

common t o t h e a c c o u n t i n g i n t h e p a s s i v e boundary s i t u a t i o n . r e a s o n t h a t t h e phase i n t h e buoyancy f l u x i s r e a d j u s t e d .

It is for t h i s

Secondly, t h e r e

i s one more p r o d u c t term i n t h e t o t a l energy c o n s e r v a t i o n e q u a t i o n f o r t h e f o r c e d problem t h a t c a n n o t a p p e a r when cbe boundary c o n d i t i o n s a r c iiono-

__

geneous.

Specifically, t h e pressure-velocity

correlation

v a n i s h a t t h e boundary b e c a u s e t h e r e i s a f i n i t e negative;

w

p'w'

cannot

(either positive or

i t is p o s i t i v e f o r t h e case i l l u s t r a t e d ) a t t h e i c c cover.

This

a c t i o n a l s o c o n t r i b u t e s t o t h e phase a l t e r a t i o n .

Although o n l y two examples arc q u a n t i t a t i v e l y p r e s e n t e d , i t s h o u l d be n o t e d t h a t t h e s t r u c t u r e can b e a l t e r e d even more i f one i s w i l l i n g t o al-

low n complete v a r i a t i o n of a l l t h e v a r i a b l e s , even though t h e b a s i s f o r t h e c a l c u l a t i o n s i s l i n e a r mathematics.

The i l l u s t r a t i o n s p r o v i d e d s e r v e

t o emphasize t h a t any s t r u c t u r e i n t h e s e c i r c u m s t a n c e s can be v e r y compli-

185 c a t e d a n d a r e s u l t a n t must i n some way b e a c o m b i n a t i o n o f a l l t h e i n g r e d i ents.

Besides t h e physical requirements, t h i s i s p r a c t i c a l l y guaranteed

f o r , a t t h e v e r y minimum, t h e r e a l s p a c e e q u i v a l e n t o f a n y c o r r e l a t i o n must b e a sum ( o r a n i n t e g r a t i o n ) o v e r a l l wave numbers a n d f r e q u e n c i e s .

The

d a t a o f F i c u r e s 1 t o 6 a r e f o r b u t o n e F o u r i e r component f r o m t i i t ! p o s s i b l e band of u n s t a b l e o s c i l l a t i o n s t h a t c a n o c c u r b e t w e e n

O.d35 2

K

5 0.707.

I n a d d i t i o n L h e r e a r e numerous n e u t r a l and damped s o l u t i o n s t h a t must b e t a k e n i n t o a c c o u n t i n a c o m p l e t e summation. One l a s t comment i s i n o r d e r .

The t u r b u l e n t g e o p h y s i c a l b o u n d a r y l a y e r

t h a t h a s b e e n o b s e r v e d u n d e r t h e i c e c o v e r o f t h e A r c t i c p r e s e n t s o n e more c r i t i c a l l e n g t h s c a l e beyond t h a t o f t h e r e l a t i v e l o c a t i o n o f t h e mixed l a y e r w i t h r e s p e c t t o t h e s o l i d boundary and t h e r e g i o n of s h e a r .

This

length is t h e depth of t h e non-spiraling

o r l o g a r i t h m i c p o r t i o n of t h e mean

v e l o c i t y t h a t is c l o s e t o t h e boundary.

I f t h i s r e g i o n e x t e n d s f a r enough,

t h e dynamics o f t h e t u r b u l e n t b a l a n c e can be compl et el y a l t e r e d , j u s t a s happens i n a c o n v e n t i o n a l f l a t p l a t e boundary l a y e r t h a t i s f u l l y t u r b u l e n t .

I n o t h e r w o r d s , as i s a l r e a d v known f o r t h e f l a t p l a t e b o u n d a r y l a y e r ( B e t c h o v and C r i m i n a l e , 1 9 6 4 ) , i t i s c o n c e i v a b l e t h a t a s t a b i l i t y a n a l y s i s

of t h e t u r b u l e n t p r o b l e m w i l l r e v e a l t h a t a l l o s c i l l a t i o n s w i l l b e c o m p l e t e l y stabilized.

i f t h i s is t r u e , t h e s y s t e m assumes a n e q u a l l o o t i n g w i t h

nore conventional turbulence,

t h a t i s , t h e r e is a s t a b l e l i m i t c y c l e .

I'he

f o r c i n g d u e t o t h e mass f l u x b o u n d a r y c o n d i t i o n s i s a mechanism t h a t must b e i n c l u d e d o v e r a n d beyond t h o s e t e r m s t h a t n o r m a l l y l e a d t o a m a i n t e n a n c e of t h e t u r b u l e n c e . be d u e t o

The l a m i n a r c a l c u l a t i o n s r e v e a l t h a t new s t r u c t u r e can

lie phenomenon.

A c o m p l e t e t r e a t m e n t i s t h e t o p i c o f work t h a t

is i n progress. ACKIlOWLEDGEi IEiJTS I s h o u l d l i k e t o t h a n k t h e d i l i g e n t a s s i s t a n c e i n t h e n u m e r i c a l conipu-

t a t i o n s by G.

S p o o n e r and t h e s u p p o r t o f t h e A e r o m e c h a n i c s D i v i s i o n o f t h e

A i r F o r c e O f f i c e o f S c i e n t i f i c R e s e a r c h f o r t h e i r s u p p o r t u n d e r AFOSR G r a n t

74-2579.

REFERENCES B e t c h o v , R.

a n d W.0. C r i m i n a l e ,

B e t c h o v , R. a n d W.O. P r e s s (1967).

P h y s i c s o f F l u i d s , S ( 1 9 6 4 ) 920.

C r i m i n a l e , S t a b i l i t y of P a r a l l e l Flows

Academic

186 Brown, R.A.,

J. A t m s .

Sci.,

27(1970)742.

Brown, R.A.,

J. A t m s .

Sci.,

29(1972)850.

G r e e n s p a n , H.P., (1968). Howard, L.N.,

T h e - T h e o r y of R o t a t i n g F l u i d s , Cambridge U n i v e r s i t y P r e s s ,

J. F l u i d Mech.,

10(1961)509.

K a y l o r , R. a n d A.J. F a l l e r , J. A t m s . L a n d a h l , M.T.,

J. F l u i d Mech.,

Sci.,

L i l l y , D.K.,

J. A t m s .

Miles, J.W.,

J. F l u i d Mech.,

S m i t h , J.D.,

Rapp. P. -v.

Sci.,

29(1972)497.

29(1967)441.

23(1966)481. 10(1961)496.

R6um. Cons. i n t . E x p l o r . Mer., 1 6 7 ( 1 9 7 4 ) 5 3 .

187 ON THE IETPORTANCE OF FRICTION IN T\JO TYPICAL COP!TTNENTAL WATERS : OFF OREGON AND SPANISH SAHARA PIJI!SH

K. KUNDU

School of Oceanography, Oregon State University, Corvallis, Oregon 97231 ABSTRACT The current meter data at various depths near the coasts of Oregon (water depth 100 m) and northwest Africa (water

-

depth < 6 7 m) have been analyzed. raged over about seven day periods,

The results have been aveso

that stationary Ekman

layer-like characteristics could be detected.

It has been

concluded that the entire water column off Africa is frictional, whereas the Oregon coastal dynamics are not s o .

This is due to

the lower Coriolis parameter, larger friction velocity u* the much lower stratification off Africa.

,

and

The horizontal den-

sity gradients can explain the observed vertical velocity shears off Oregon, but not off Africa.

A typical

U~

near

Africa is about 0 . 8 cm/s, whereas that near Oregon is about

0.3 cm/s.

The thickness of the bottom Ekman layer is estimated

to be about 60 m off Africa and 1 2 m off Oregon, whereas the thickness of the logarithmic layer is estimated to be about 9 m off Africa and 2 m o f f Oregon. been observed off Africa.

Ekman turnings of 2 5 ' - 4 0 "

have

The upper surface layer data near

Oregon display hodographs resembling the classical Ekman spiral, rather than the "slab" type mixed layer. INTRODUCTION The objective of the present note is to examine the current meter data from two typical coastal upwelling regions off Oregon and Spanish Sahara, in order to ascertain whether the entire water column is frictionally dominated for time scales long compared to the inertial period, of the order a week or more.

An idealized coastal upwelling problem in the northern

188

hemisphere is the following (Fig.1)

: A southward wind stress

acts parallel to the coast, driving an offshore Ekman flux at the ocean surface-, which therefore needs a compensating onshore return flow.

The question that we want to answer is : Is the

return flow through a bottom Ekman layer ?

Or is it through a

frictionless geostrophic interior generated by a northsouth pressure gradient ?

Nonlinear forces will be neglected in this

study, since the Rossby number for the Oregon region has been found to be less than 0 . 1 5 (Kundu et al., 1 9 7 5 ) and our calculation shows that it is also small off Africa. Some of the various possible situations are listed in Fig. 1 by means of profiles in the u-z, v-z and u-v planes, where u,

v,

w are the velocity components in the

northward),

upward) directions respectively.

eastward), The geostro-

phic interior in Case 1 can be of negligible thickness, so that the top and bottom Ekman layers may be almost adjacent to each other, in which case the profiles in Case I

(ii), say, may look

very similar to those in Case 2 (iii) or 2 (iv).

It is, there-

fore, not a trivial task to determine whether the return flow is frictional or geostrophic. The analytical model of Garvine ( 1 9 7 1 )

for upwelling re-

gions assumed that the bottom Ekman layer is dynamically unimportant, and that the return flow is accomplished geostrophically by means a northsouth pressure gradient.

Because of the

absence of such a pressure gradient, on the other hand, the theory of Allen ( 1 9 7 3 )

predicted that for large times the re-

turn flow is through a bottom Ekman layer, assumed thin compared to the water depth. (1976).

The recent vork of Smith and Long

however, suggested that the entire water depth on the

Oregon-Washington shelf is frictionally dominated, that is, the flow field is simply two Ekman layers one on top of the other, the bottom layer balancing the offshore mass flux of the top layer. Some

hodograph profiles calculated by Smith and Long are

reproducedlin Fig. 2 .

The pressure gradient was taken to be

'Smith and Long had a northward wind stress. Their solutions have been replotted here with signs changed, so as to correspond to our southward wind stress.

189

r, = o 7y= than in the latter part of the experiment (mean speed ~ 4 0 cm/s). For the first part uR typi al=.45 cm/s and for the latter part uR tyRic 1z.80 cm/s. As in Weatherly (1972) persistent veering tge correct sense for Ekman veering was observed in the logarithmic layer which for the first part of the experiment had mean value of ~7~ and f o r the latter part ~ 2 7 ~ Since . the mean current direction at the top of the logarithmic layer was aligned approximately in direction of isobaths it is inferred that, as in Weatherly (19721, most of the Ekman veering occurred in the lower part of the boundary layer. INTRODUCTION In Weatherly (1972) (hereafter referred to as W) are reported some observations of the bottom boundary layer (BBL) of the Florida Current at one location in the Florida Straits. Not unexpectedly this study indicated that the BBL had many features of a stationary turbulent Ekman layer. Specifically, these observations indicated a BBL of thickness h = .4u / f = 25m, where uR = the friction velocity and f = the Coriofis parameter; a total average Ekman veering a o = sin-l (Cu /Vg) = loo, where C = an emperical constant = 4.5 and V = *he geostrophic velocity outside the BBL; and a geostr%phic drag u,/V = 04. The surface Rossby number Ro = coefficient cf V /fz where z o = th!? bottom roughness parameter, was x and the above values of .a and cf are not inconsistent with the BBL being a turbulent Ekman layer characterized by such a value of Ro (Deardorff (1970)). Certain features, however, of the study of W were inconsistent with the BBL being a quasi-stationary turbulent Ekman layer. The observed Ekman veering was strongly and directly proportional to Ro rather than being a weak function of R0-l. In addition all the mean veering occurred in the lower part of the BBL rather than in the upper part. Fig. 1 shows the location where W made his observations (hereafter referred to as Site A). In order to test whether the above, unexpected features about the observed Ekman veering could be due to the location of the observations a similar Q!

?66

238

experiment w a s r e p e a t e d a t a n o t h e r s i t e a l s o i n d i c a t e d i n F i g . 1. A t t h e s e c o n d s i t e ( h e r e a f t e r r e f e r r e d t o as S i t e B) t h e b o t t o m t o p o g r a p h y , as i n d i c a t e d i n F i g . 1, b o t h u p s t r e a m ( s o u t h ) and downstream ( n o r t h ) as w e l l a s c r o s s - s t r e a m i s

F i g . 1. S i t e of e x p e r i m e n t o f W e a t h e r l y ( 1 9 7 2 ) ( A ) and o f e x p e r i m e n t r e p o r t e d h e r e (B) i n t h e S t r a i t s of F l o r i d a . Depths a r e i n f a t h o m s .

239

more regular. Site A is in the Miami-Bimini transect of the Florida Straits, a region characterized by a horizontal constriction in the Straits, a shoaling up of the bottom in the middle of the Straits, and a deep trench in the western region of the Straits. The purpose of this paper is to report the BBL observations made at Site B and to compare them with those made at Site A by W. REVIEW In the preceeding section some of the results. of W were discussed as background for the present study. In this section the results of this study are summarized in more detail. Bottom currents. The mean (over a 64 day period) current 14m a b o v e h e bottom had a magnitude of ~ 1 cm/s 0 and direction ~ 3 4 3 ~ This . direction is aligned approximately along the direction of isobaths which in vicinity of Site A, looking . of the low frequency, large downstream, is ~ 3 4 0 ~ Much amplitude fluctuations in the speeds were due to the K1 and O1 constituents of the tidal currents as predicted using the amplitudes and phases given by Smith et a1 1969. The highest 0 speeds were ~ 3 cm/s. Friction velocit A typical value of u* was ~ 0 . 4 cm/s; this v a l d z i h t to be representative for the Florida Current at this site. Peak values around 1.0 cm/s were observed. The above u* values were computed using a value of 0 . 4 0 for von Karman's constant, as were the values for Site B given later. If one takes von Karman's constant 20.35 (cf. Businger et a1 1971) then these u* values should be scaled by the faczra.875. The bottom roughness parameter Rou hness ammeter z z w a k o h d ? variable. However, for periods o? comparatively strong, steady flow a value zo = .03 cm was found. Such a zb value suggests that the bottom roughness elements had sizes Q 1 cm (cf. W Eq. (6)) which was consistent with bottom photographs. Geostro hic drag coefficient 9. With u*=.4cm/s and Vg=lO&average current speed at 14 cm above the bottom, cf I u /Vg = .04. This value is consistent with a steady, neutraf ly stratified planetary boundary layer characterized by a surface Rossby number Ro = V /fzo = 5x106 (Dearg dorff (1970)). Lo arithmic la er thickness. A logarithmic layer of thickw h s e r v e d . This is consistent with the relation 61 given in W for a neutrally srratified turbulent Eknan layer. However, as pointed out by M. Wimbush (personal communication) the theoretical justification for the expression (cf. Monin and Yaglom 1970 Eg. (6.61)) is incorrect. Emperically the logarithmic layer thickness is 10%-15% the thickness of a neutrally strati,ied planetary boundary layer (cf. Businger and Arya (1974) p. 79). The observed 6in is also consistent with this relation (see BBL thickness below). BBL thickness. Speed profile data indicated that a representative thickness of the BBL was 25m. This is consistent with the relation for the thickness of a neutrally stratified planetary boundary layer h = .4u*/f.

.

Q

240

The mean v e e r i n g f o r t h e e x p e r i m e n t w a s Ekman v e e r i n g . 100 i n t h e c o r r e c t s e n s e f o r Ekman v e e r i n g ( c o u n t e r c l o c k w i s e l o o k i n g down). T h i s v a l u e i s c o n s i s t e n t w i t h t h a t p r e d i c t e d by s i m i l a r i t x t h e o r y , u s i n g t h e c o n s t a n t of D e a r d o r f f (19701, f o r Roz5xlO However, i n c o n t r a s t t o s i m i l a r i t y t h e o r y , t h e v e e r i n g o c c u r r e d i n t h e l o w e s t p a r t of t h e BBL ( t h e l o g a r i t h m i c l a y e r ) r a t h e r t h a n above i t , and w a s d i r e c t l y p r o p o r t i o n a l t o Ro r a t h e r t h a n i n v e r s e l y p r o p o r t i o n a l .

.

EXPERIMENT The o b s e r v a t i o n s r e p o r t e d h e r e were made i n a r e g i o n a b o u t 26O30'N, 79O4O'W where t h e bottom t o p o g r a p h y i s r e g u l a r b o t h i n t h e l o n g - i s o b a t h and c r o s s - i s o b a t h d i r e c t i o n ( c f . F i g . 1). I n t h e c r o s s - i s o b a t h d i r e c t i o n s t h e bottom s l o p e s downward toward t h e east w i t h a s l o p e % - 1 . 5 ~ 1 0 ' ~ . The n e a r b y u n i f o r m l y spaced and s t r a i g h t i s o b a t h s a r e a l i g n e d %go e a s t of n o r t h which i s assumed t o be t h e a p p r o x i m a t e d i r e c t i o n of f l o w o f t h e mean bottom c u r r e n t s j u s t above t h e BBL. According t o H o l l i s t e r (1973) t h e bottom i n t h i s r e g i o n i s a s i l t y sand o f c o m p o s i t i o n 60%-80% c a r b o n a t e sand o f d i m e n s i o n s .062mm 2.0mm and t h e r e m a i n d e r s i l t of d i m e n s i o n s .004mm .062mm. The w a t e r d e p t h a t S i t e B i s a b o u t 640 m . The two moorings d e s c r i b e d i n W were s e t a t S i t e B. They a r e b r i e f l y d e s c r i b e d h e r e , f o r more d e t a i l see W. One mooring, d e s i g n a t e d C I I , c o n s i s t e d o f n i n e Savonius r o t o r s l o c a t e d a t t h e h e i g h t s above bottom g i v e n i n T a b l e 1. The o t h e r mooring, d e s i g n a t e d CM, c o n s i s t e d of four Geodyne f i l m c u r r e n t meters; t h e h e i g h t above bottom o f t h e Savonius r o t o r and vane of e a c h c u r r e n t m e t e r i s g i v e n i n T a b l e 1. The f u n c t i o n of t h e C I I mooring w a s t o make d e t a i l e d s p e e d p r o f i l e neasurements from which t h e h e i g h t o f t h e l o g a r i t h m i c l a y e r (and hence u* and zo from Eq. (1)) and t h e h e i g h t o f t h e BBL c o u l d be i n f e r r e d . The CM mooring w a s deployed t o i n f e r Ekman veering.

-

-

T a b l e 1. H e i g h t s above t h e bottom o f t h e mid-point o f t h e c u r r e n t s e n s o r s on e a c h mooring. The u n c e r t a i n t i e s of t h e s e h e i g h t s i n c l u d e t h e a c c u r a c y w i t h which t h e y were measured and e s t i m a t e d s e t t l i n g of e a c h mooring - i n t o t h e bottom. CII Savonious Rotor

1 2 3 4 5 6 7 8 9

Mooring

CM Mooring

Height (m)

1.07 1.43 1.79 2.21 3.24 4.28 6.31 10.38 20.40

f .03 f .03 f .03 f .01, fi . 0 4 f .04 f

.04

f .05 f .06

Current Meter CM1 CM3 CM18 CM34

Rotor Height

(m> 1.12 2.93 16.49 32.78

f .03

-+ .03 f .10 f .15

Vane H e i g h t (m)

1.34 3.16 17.81, 34.18

f f f f

.03 .03 .10 .15

241

The speeds measured by the CII rotors were recorded every 178 seconds ( % 3 minutes). The current meters were set on the continuous mode which in this case resulted in the current direction being recorded every 5 seconds and the rotor revolutions being recorded continuously. The film record from the CII mooring was read by eye. The current meter film records were read by an automated film reader by the manufacturer1. From this data one-minute averaged current speeds and directions were formed, and it is these one-minute averaged current meter values that were used as input data in this study. In order to obtain information on the temporal variability of temperature in the BBL two thermistors were placed on the CM mooring, at 5 m and 19 m above the bottom, and aqthird thermistor was placed on the CII mooring at 20 m above the bottom. The thermistor packages, made by C. Wilkins at Nova University, Dania, Florida, were self-contained units in their own pressure housings and recorded continuously on a Rustrack recorder with an absolute accuracy of s.l°C and a The sensors were Yellow Spring relative accuracy of s.02'C. model 44-00-33 thermistors. The three thermistor instruments returned with full temperature records; their temperature data was digitized every 15 minutes. A freefall STD (see W p. 58) was to have been used to provide data on the density distribution in the BBL as well as to calibrate the drift in the thermistor instruments. However, the STD developed major problems at the beginning of the experiment and no STD profiles were obtained. Five bottom color pictures were taken with a freely dropped camera near Site B after the experiment. A l l were taken within several hours of each other and indicated a silty sand bottom somewhat smoother than that seen at Site A by W. Fig. 2 is a black and white reproduction of one of the photographs. The moorins were set on 20 July 1972 and recovered on 27 July 1972. The CM moor'ing was set 4.2 km from the CII mooring in a direction 22O west of north. Approximately 164 hours (6.8 days) of speed data was obtained from the CII mooring. No data was obtained from the lowest rotor because a wire was damaged during launch. The second rotor from the bottom failed to give data between hours 42 and 85 of the experiment. It is not known whether this was due to something obstructing the rotor or to an intermittent, unknown electrical problem. Current meters CM1, CM3, CM18, and CM34 (at heights above the bottom, respectively, 'L 1, 3, 18, and 34m) returned, respectively, 162, 158, 49, and 0 hours of current speed and direction data.

Geodyne Division, EGEG International, Waltham, Massachusetts.

242

P i g . 2. R e p r o d u c t i o n o f c o l o r p h o t o g r a p h made 1. 1 . 8 m above Note c l o u d o f s i l t a b o u t t h e b a l l a s t t h e b o t t o m a t S i t e B. weight.

RESULTS AND C O N C L U S I O N S

Bottom c u r r e n t s . S i m i l a r t o t h e observations a t S i t e A by W , t h e o t t o m c u r r e n t s a t S i t e B d u r i n g t h e p e r i o d o f t h e e x p e r i m e n t c a n be c h a r a c t e r i z e d by a mean n o r t h w a r d f l o w o r i e n t e d a p p r o x i m a t e l y a l o n g i s o b a t h s . However, u n l i k e t h e s t u d y o f W , t h e mean f l o w , which i s a s s o c i a t e d w i t h t h e F l o r i d a C u r r e n t , changed d u r i n g t h e e x p e r i m e n t . The a v e r a g e s p e e d a t 20 m above t h e bottom f o r t h e f i r s t 72 h o u r s o f t h e e x p e r i m e n t w a s 1 5 . 4 c m / s , and f o r t h e remaind e r of t h e e x p e r i m e n t t h e a v e r a g e s p e e d a t t h i s h e i g h t w a s F i g . 3 shows 4-hour a v e r a g e d s p e e d s a t z = 2 0 m p l o t 3 8 . 5 cm/s. t e d as a f u n c t i o n o f t i m e . A l s o shown a r e t h e p r e d i c t e d t i d a l c u r r e n t s u s i n g t h e a m p l i t u d e s and p h a s e s g i v e n i n Smith et a 1 (1969) p l u s , r e s p e c t i v e l y , a mean s p e e d o f 1 5 . 4 cm/s and 3 8 3 cm/s. A s c a n be s e e n from F i g . 3 f o r t h e f i r s t 1. 72 h o u r s t h e bottom c u r r e n t s c a n be c h a r a c t e r i z e d by a mean c u r r e n t o f s p e e d 1.15 c m / s modulated by t h e p r e d i c t e d , p r i m a r i l y d i u r n a l , t i d a l c u r r e n t o f a m p l i L u d e ~ 1 c2m / s ; f o r t h e r e m a i n d e r o f t h e e x p e r iment t h e y a r e c h a r a c t e r i z e d by a mean c u r r e n t w i t h s p e e d 1.39 c m / s modulated by t h e same t i d a l c u r r e n t . The f i r s t 72 hours of t h e experiment, s t a r t i n g a t 1155 2 5 minutes l o c a l s t a n d a r d t i m e on 20 J u l y 1972, h e r e a f t e r i s d e s i g n a t e d as P e r i o d 1; t h e r e m a i n i n g 1.92 h o u r s o f t h e e x p e r i m e n t h e r e a f t e r i s d e s i g n a t e d a s P e r i o d 2. I n F i g . 4 a r e shown p r o g r e s s i v e v e c t o r d i a g r a m s f o r t h e c u r r e n t meters a t 3 and 1 8 m above t h e b o t t o m , CM3 and CM18. For CM18 o n l y 1.49 h o u r s o f d a t a was o b t a i n e d and t h u s o n l y t h e

243

TIME (hours) Pig. 3 . Time series of 4-hour averaged speeds at 20m above the bottom solid curve. The dotted and dashed curves are of a mean current of speed 15.4 cm/s and 39.5 cm/s, respectively, modulated by the predicted tidal current. Time 0 is 1 1 5 5 EST 20 July 1972.

_first 4 9 hours of data from CM3 is shown in this figure. A l though there is much variability, the flow at both levels is similar in that the direction of mean flow is about the same, slightly east of north, and oriented approximately along isobaths (cf. Fig. 1). The mean current directions at these two levels for this period is given in Table 2.

KM NORTH

00

20 I

1

M 3

a.

-0

L o

..

.Ao

0

0

0 . 00.

10 L Fig. 4 . Progressive vector diagram for current meters moored 3 and 18m above the bottom f o r the period when the current meter at 18m functioned. Symbols ( O f o r z = 3m, A for z = 18m) are given after each 24 hour period.

244

I n F i g . 5 a r e shown p r o g r e s s i v e v e c t o r d i a g r a m s f o r t h e f u l l r e c o r d s from t h e c u r r e n t meters a t 1 and 3 m , C M 1 and C M 3 . A s can be s e e n from t h i s f i g u r e i n t h e l a t t e r p a r t o f t h e e x p e r i m e n t , i n P e r i o d 2 , n o t o n l y i s t h e c u r r e n t s t r o n g e r it i s l e s s v a r i a b l e i n d i r e c t i o n as w e l l . A r e p r e s e n t a t i v e BBL t h i c k n e s s f o r P e r i o d 1, d u r i n g which CM18 f u n c t i o n e d f o r ~ 6 7 % of t h e t i m e , was % 2 0 m (see s u b s e q u e n t BBL T h i c k n e s s d i s c u s s i o n ) . S i n c e CM18 w a s a t 18m, it f u n c G n e d t o r a p p r o x i m a t e l y an i n t e g r a l number of d i u r n a l t i d a l p e r i o d s , and i t s a v e r a g e d i r e c t i o n of f l o w was a p p r o x i m a t e l y p a r a l l e l t o t h e i s o b a t h s , it i s i n f e r r e d t h a t t h e mean b o t t o m c u r r e n t d i r e c t i o n j u s t above t h e BBL f o r P e r i o d 1 w a s %15O, t h e a v e r a g e d i r e c t i o n v a l u e g i v e n f o r CM18 i n T a b l e 2 . Although no c u r r e n t d i r e c t i o n d a t a n e a r t h e t o p o f t h e BBL was o b t a i n e d d u r i n g P e r i o d 2 it seems r e a s o n a b l e t o e x p e c t t h a t t h e mean bottom c u r r e n t d i r e c t i o n f o r t h i s period w a s a l s o p a r a l l e l t o t h e d i r e c t i o n o f t h e i s o b a t h s (%,9O e a s t of n o r t h l o o k i n g downstream) t o + 6 O . m.

1 I

__.... e __.....,

u 0

5 I

m.

(..._........' __.. I

0.'

-..ax.''

'".. .? 1

'. . .

......

'0.

.......-

Fig. 5. P r o g r e s s i v e v e c t o r d i a g r a m from c u r r e n t meters moored 1 and 3 m above t h e bottom. Open c i r c l e s a r e drawn a f t e r each 24 hour i n t e r v a l .

That t h e bottom c u r r e n t s c a n b e c l a s s e d i n t o two f l o w regiemes i s a l s o i n d i c a t e d i n t h e t e m p e r a t u r e r e c o r d s . In F i g . 6 a r e shown t h e t e m p e r a t u r e t i m e s e r i e s o b t a i n e d from t h e t h e r m i s t o r s on t h e CM mooring. During P e r i o d 1 t h e tempe r a t u r e was w a r m e r ( b y % 0 . E o C ) and more v a r i a b l e t h a n i n Period 2 . The peaks i n P e r i o d 1 a r e a s s o c i a t e d w i t h p e r i o d s of weaker, e a s t w a r d f l o w . The l o g a r i t h m i c l a y e r a t S i t e B was Logarithmic J a y e r . e x p e c t e d t o be t h i c k e r t h a n a t S i t e A b e c a u s e t h e b o t t o m c u r r e n t s a t t h e f o r m e r s i t e were e x p e c t e d t o b e l a r g e r s i n c e it i s c l o s e r t o t h e a x i s of t h e F l o r i d a C u r r e n t . The o b s e r v a t i o n s showed t h a t a t S i t e B t h e bottom c u r r e n t s w e r e i n d e e d s t r o n g e r . The l o g a r i t h m i c l a y e r was a n t i c i p a t e d t o be t h i c k e r by t h e f o l l o w i n g l o g i c . S i n c e u,/V i s very nearly a c o n s t a n t f o r a l a r g e r a n g e o f R o , t h e t h i g k n e s s of t h e BBL

245

I

W OZ

3

s [L

w

5

1

1

I

I

I

I

1

+

a I W

I-

5 0

40

80

I20

I60

TIME (hours) Fig. 6. T i m e series p l o t s of t h e t e m p e r a t u r e r e c o r d s o b t a i n e d a t 1 9 m ( a ) and 5 m ( b ) above t h e b o t t o m . The c o a r s e a p p e a r a n c e i s due t o t h e l a r g e t i m e i n c r e m e n t ( 1 5 m i n u t e s ) u s e d when d i g i t i z i n g t h e cont,inuous t e m p e r a t u r e r e c o r d s .

w a s e x p e c t e d t o be h = . 4 u , / f , t h e t h i c k n e s s of t h e l o g a r i t h m i c l a y e r 61n = ( . 1 0 - . 1 5 ) h , and V was e x p e c t e d t o be a p p r e c i a b l y l a r g e r , t h e t y p i c a l 6 l n fog S i t e B should be l a r g e r t h a n f o r S i t e A. Using t h e r e l a t i o n g i v e n i n W , 6 l n = 2u,*/fV , which a l t h o u g h b a s e d on q u e s t i o n a b l e grounds g i v e s r e a s o n a g l e a n s w e r s , and t a k i n g u,/Vg = . 0 4 , a r e p r e s e n t a t i v e v a l u e f o r S i t e A ( s e e W F i g . 16) V = 1 5 - 4 0 c m f s , ( s e e p r e c e e d i n g sec i o n ) , and f =. 6 3 ~ 1 0 - ~ ; - ~ ~ p r e d i tc ht as t f o r S i t e B 4-llm $ The o b s e r v e d l o g a r i t h m i c l a y e r t h i c k n e s s , 5 m i n P e r i o d 1 and -3.2m i n P e r i o d 2 , w a s t h i n n e r t h a n e x p e c t e d . The t h i c k n e s s o f t h e o b s e r v e d l o g a r i t h m i c l a y e r as e x p e c t e d i n c r e a s e d w i t h i n c r e a s i n g c u r r e n t s p e e d . A t S i t e A b i n w a s s e e n t o be a s l a r g e a s 8m i n p e r i o d s o f s t r o n g f l o w .

-

.

The r e l a t i o n 6 1 = 2 ~ , ~ / f V i s e s s e n t i a l l y t h e same a s t h e frequently e x p r e s s i o n 6 1 n = ? . 1 0 - . 1 5 ) h For v a l u e s o f cf=u,/V e n c o u n t e r e d i n t h e a t m o s p h e r i c and t h e o c e a n i c boftom boundary layers.

246

. .

. .

*

. .

.

NUMBERS DENOTE TIME IN uouas

.Fig. 7. Four consecutive profiles of hourly averaged speeds on In z scale for every other hour.

In contrast, at Site B the largest value of 61n observed was -4m. Examples of logarithmic layers are given in Fig. 7. Friction velocit and rou hness arameter 5 . Because the l o g a r i t h m i d t % c E s & b e c t e d to be s5m or greater six rotors were placed within 5m of the bottom. Even with no data from one rotor this would give five points through which to fit the equation u(z) = u*/k

In z / z o ,

(1)

where u(z)=observed speed at height z above the bottom and k = von Karman's constant, which for comparison with W is taken to be . 4 0 , to determine u* and z o . However, as noted previously

247

61n was observed to be ~ 2 . 5 mto 3.2m, the rotor which failed was the lowest one, and the second lowest rotor did not always function properly. Thus typically usually three and sometimes four speed measurements were made in the logarithmic layer. For comparison W typically had five speed measurements in the logarithmic layer. As a result the u* and z0 values presented here are not considered as good as those determined by W at Site A. In Fig. 8 a,c are shown histograms of u* values determined from Eq(1) using hourly averaged speeds from Rotors 2 and 3 for periods when Rotor 2 functioned and the speeds in the logarithmic layer >4cm/s, the approximate thresh-hold speed for a Savonius rotor. For comparison histograms of uitvalues for the same period computed using for input data hourly averaged Rotor 3 and 4 speeds are shown in Fig. 8 b,d. To ~ 0 . 1cm/s the peaks in Fig. 8 a,b and Fig. 8 c,d occur at the same value of u*. For reasons given below the u* values determined for Rotors 2 and 3, the lowest rotors, when available, are thought to be better than those determined from Rotors 3 and 4. However, Rotors 3 and 4 functioned through-out the experiment while Rotor 2 did not. In Fig. 8a, are shown histograms of u* values determined from Rotors 3 and 4 hourly averaged speeds for, respectively, Periods 1 and 2. For Period 1 the peak is at u* = .45cm/s and for Period 2 it is at u* = .80cm/s. These values, thought to be representative for the Florida Current, may be underestimated by O.lcm/s since they were determined from Rotor 3 and 4 speeds (compare Fig. 8 a,b and Fig. 8 c,d). With u* = .45cm/s and Vg = 15cm/s, = .8Ocm/s and V 39cm/s, 6ln 3 2 ~ , ~ / f V = 4.3m, 5.2ma;odruperiods 1 and 2 , rgspectively. That the obgerved 6ln was less than predicted may be due to density stratification being significant in the BBL (cf. Monin and Yaglom (1970) Fig. 52). Without concurrent STD profiles or detailed bottom photographs it is not possible to infer if the BBL was stratified o r to infer the source of the stratification (temperature and salinity or suspended sediments). If stratification were important in the lower part of the BBL then Eq.(l) should include a linear correction term (E Eq. 7.33) Q

u(z)

u,/k[ln(z/zo)

+ Az)

(1')

where A is a measure of the stratification. The linear correction term in (1') is smaller for smaller z, thus the ub values determined from Eq.(l) using Rotors 2 and 3 speeds may be more accurate than those determined using Rotors 3 and 4. The geostrophic drag coefficient cf u+!Vg for periods 1 and 2, using the u* and V values used previously is .030 and .021, respectively. Sifice c is a slowly varying function of Ro = V /fzo (cf. W Fig. 16) tf;e rather large difference in the cf va'iues for these periods cannot be due to changes in Vg alone. Such a change in cf implies a change in Ro at least several orders of magnitude with Ro being considerably larger for Feriod 2. This suggests that z for Period 2 was appreciably smaller than for Period 1. fn Fig. 9 is shown zo as a function of time for those periods when Rotor 2 functioned

248

= 0

0

0

1

2

0

1

2

1

2

3

0

1

0

2

1

0

2

3

4

1

2

3

u, ( c m / s ) Fig. 8. Histogram of u* values determined from E q (1) and hourly averaged (a) Rotors 2 and 3 speeds for intervals in Period 1 ( 0 < hour d 7 2 ) when Rotors 2 worked and Rotor 2 speeds > 4cm/s, (b) Rotors 3 and 4 speeds for the same intervals in (a), (c) Rotors 2 and 3 speeds for intervals when Rotor 2 worked in Period 2 ( 7 2 < hours < 1 6 4 ) (d) Rotors 3 and 4 speeds for the same intervals in (c), (el Rotors 3 and 4 speeds in Period 1, and (f) Rotors 3 and 4 speeds in Period 2 .

properly and the speeds in the logarithmic layer >4 cm/s. Hourly averaged speeds were plotted as a function of In z and the zero intercept ( z o ) determined from straight lines fit by eye. This subjective method of estimating z,may yield values off by as much as an order of magnitude. Nonetheless some patterns are discernable in Fig. 9. The z o values for Period 1 are generally at least one order of magnitude larger than for Period 2 . Peaks ii: the z values often are associated with maximums in the currents ?cf. Figures 3 and 8, lines ~ 2 4 , 100, 1 2 5 , and 1 5 0 hours). After hour 1 0 5 in Period 2 there is a tendency for zo to decrease with time. Thus while the bottom at Site A appears to be characterized by a zo z.03 cm no comparable single value appears to be charcterize the bottom at Site B. The bottom at Site A is quite different than that at Site B. At Site A the bottom is a basement rock on which there is a thin film of sediment which does not always cover the hard bottom (personal communication C. Neuman, D. Cacchione and W. Gardner). At Site €3 the bottom consists of a silty sand of sufficient thickness such that no underlying hard surface is exposed (personal communication D. Cacchione and W. Gardner). In the vicinity of this site alternating strips of rippled and non-rippled Q

249

_Fig. 9. Time series plot of z o values read from plots of hourly averaged speed profiles on In z scale (cf. Fig. 6 ) for periods wIIenRotor 2 worked and Rotor 2 speeds 7 4cm/s. sediment, oriented downstream with widths order tens to hundreds of meters, are sometimes observed (ibid.). M. Wimbush Tpersonal communication) has observed small ripples of heights ?r 4cm forming, migrating and eroding away at a deep site in the Florida Straits, 26O6'N, 79031'W, where the bottom is also a silty sand. In addition he observed sediment going into suspension during periods of strong current. The reason for the large zo values in Fig. 9 for Period 1 is not known. zo values ranging from 1-10 cm may imply large bed forms with amplitudes .3 to 3m if the emperical relation zo =dl30 for rough surfaces ussd in W is assumed. Large sand ripples with amplitudes of several meters have been observed south of Site B in the Miami Trough (personal communication D. Cacchione and W. Gardner). However, no such features have been observed in the vicinity of Site B. It has been assumed in this study that the anchor weight on the CII mooring did not sink appreciably into the bottom. Assuming that it did sink as much as 40 cm only reduces the z o values in Period 1 by about a half. During times 8 4 hour < 130 zo 2, .lcm to within an order of magnitude. This value in not inconsistent with the bottom

250

being roughened by small ripples of amplitude % 4cm. F o r times 130 < hour < 164 zo % .001cm to within about an order of magnitude. This value is not inconsistent with the bottom being smooth and un-rippled. That there is a trend for zo to decrease after hour % 105 may be indicative of eroding small-scale ripples. Smith (1976) gives the following relation for zo when there is bedload transport 20

= 26.4 (Tb-Tc)/(Ps-P)g

+Zn,

(2)

where T b = the bottom stress (PU,~), = the critical bottom stress for initiation of bedload transport, p s = the sediment density, p = the water density, g = gravitational acceleration, and zn = the Nikuradse roughness parameter. The coefficient was determined for the quartz sand bottom of the Columbia River and is not expected to apply for the silty-sand bottom at Site B. However, Eq.(2) states that z o should vary directly In Fig. 10 u* values given in Fig. 8 with Tb and hence u*. a,c are plotted as a function of time. A comparison of this figure with Figures 3 and 9 shows that at times of strong current (e.g. hours % 24, 100, 1 2 5 , 150) zo is directly proportional to u* suggesting that during these periods bedload transport occurred.

4.0 -

3.0h

m

\

! 2.0i

V

v

S

3

I.0-

TIME ( h o u r s )

Fig. 10. Time series plot of uB values displayed in Fig. 7 a,c. Error bars are due to uncertainty in rotor heights above the bottom-and resolution of the speed values.

261

Thickness of the BBL. Using the u* values previously given as r e p r e s e n t x v e f o r Periods 1 and 2 in the expression h=.4u,/f gives a thickness of 29m and 51m for Periods 1 and 2 respectively. The speed profiles for Period 1 indicate h=20m which is slightly less than predicted. The highest z at which speed data was obtained was 20m. Consistent with the above predicted value, the speed profiles for Period 2 indicate a BBL thicker than 20m. It should be noted that the above BBL thicknesses are for mean conditions. During periods of strong flow when the tidal current reinforces the Floriaa Current h can be appreciably greater.

.

The predicted representative total Ekman Ekman veerin v e e r i G d = s i n - l ( C c f ) for Periods 1 and 2 respectively, is '8 and S C . Because of the limited data return from the current meters above z=3m (49 hours of data from the CM18 and 0 hours of data from CM34) only inferences about a. can be made from the data. Before discussing direction differences it is appropriate to discuss the accuracy of the current meter directions. The instantaneous direction values are resolved to f 2.8O. Twelve of these values were averaged to form a one minute averaged direction. Hence one might expect the one minute averaged directions to be resolved to f2.8°/(11)4 or 2, f0.84O and henze direction differences to be resolved to 2, f1.7O. Examination of the one-minute averaged direction histograms of CM1 and CM3 suggests that the directions are resolved to about a degree. The directim and veering values summarized in Table 2 are thought to be resolved to 2, f1.5O and 5 +3O, respectively. Table 2. Average currents and direction differences. The number in the current meter label is the nominal height above bottom in meters of the current meter vane. See text for explanation of time intervals and accuracy of direction and direction difference values. The average direction differences were computed by the method of Kundu (1976) and Weatherly (1972); the former values are given with correlation coefficients in parenthesis. Positive direction differences are consistent with Ekman veering. Time Interval Hours

0-49 0-49 0-49 0-72 0-72 72-158 72-158 0-158 0-158

Average Currents Current Speed Meter cm/s CM18 CM 3 CM 1 CM 3 CM 1 CM 3 CM1 CM 3 CM 1

14.2 9.2 6.4 9.2 6.6 24.2 15.8 17.3 11.4

Average Direction Differences

Direction Current Oo=North Meter Pair 14.7 26.6 17.4 18.2 8.2 12.0 345.3 13.6 351.3

Degrees

CM18,CM3-12.6(.963)-11.9 CM3,CMl 7.4(.997) 7.4

CM3,CMl

8.6C.991) 10.1

CM3,CMI

27.7(.972)

26.7

CM3,CMl

24.1(.966)

22.1

262

For the first 49 hours of the experiment, when CM18 functioned, the average veering between 3 and 18 m was ~ - 1 2 ~ where the negative sign indicates veering in the wrong sense for Ekman veering-. For the same period the average veering between 1 and 3 m was s7O. This value is nearly the same as the value for these levels for Period 1. Thus for Period 1 the average veering between 3 and 18m was probably close It is to the value for the period 0-49 hours, 1.e. -12O. interesting that the ovserved veering for Period 1 between 1 and 3m is the same, to within experimental accuracy, as the predicted .a for that period. W also found the observed and predicted average .a for his experiment to agree and to occur in the logarithmic layer, However, during Period 1 the currents were quite variable. The fluctuations in speed were comparable to the mean, the current flowed alternately eastward and northward, and the time scale of the fluctuations, 24 hours is comparable to the time scale for a planetary boundary layer 2n/f. Thus the agreement with stationary theory may be coincidental. From Fig. 5 and Table 2 it is apparent that the veering between 1 and 3m during Period 2 was substantial, ~ 2 7 ~ This . is over five times larger than the predicted .a for this period. That the observed veering was larger than that expected for a neutrally stratified BBL and that it occurred within the logarithmic layer may be indicative that the logarithmic layer was appreciably stably stratified (see the Weatherly and Van Leer paper in this volume). The veering between these levels is plotted as a function of time in Fig. 11. In particular for Period 2 and as noted also by W the veering in the logarithmic layer is directly proportional to the current speed. That the mean direction at 3m f o r Period 2 was along the direction of isobaths to within experimental accuracy suggests that little veering occurred in the BBL above z=3m during this period. Suitabiiit of the Savonius rotor as a BBL sensor. The current SDeeds : n T h n B L of the m d a C i k r e n t a r e u fficiently aiove the thresh-hold speed of =2-4cm/s to spin a Savonius rotor over 90% of the time. This is not always the case in the oceanic BBL (cf. Armi and Millard (1976)). This rotor has been calibrated for uniform flows; however, I am unaware of its being calibrated for boundary layer shear flows. Further, how much of the speed signal is due to rectification of the shear induced turbulent motions needs to be studied. For lack of information these effects have been assumed negligible. Intercomparison studies are in order to see if indeed this is the case. Q

I

253

S

‘ W

E

E

S

S

100

120

140

I 160

F i g . 11. T i m e s e r i e s p l o t o f h o u r l y a v e r d g e d c u r r e n t d i r e c t i o n ( a ) and s p e e d ( c ) d a t a from t h e c u r r e n t m e t e r a t 3m a b o v e t h e b o t t o m , a n d ( b ) h o u r l y a v e r a g e d d i r e c t i o n I n (b) p o s i t i v e values are d i f f e r e n c e between 3 a n d l m . c o n s i s t e n t w i t h Ekman v e e r i n g .

ACKNOWLEDGZMENTS The o b s e r v a t i o n s were made w i t h s u p p o r t f r o m t h e Office o f Naval R e s e a r c h u n d e r C o n t r a c t M 0 0 0 1 4 - 6 7 - A - 0 3 8 6 - 0 0 0 1 and t h e a n a l y s i s w i t h s u p p o r t from t h e N a t i o n a l S c i e n c e Foundat i o n u n d e r G r a n t GA-36458X and from t h e O f f i c e o f Naval Res e a r c h u n d e r C o n t r a c t N000-14-75-C201. P a r t of t h e a n a l y s i s was done w h i l e I w a s a v i s i t i n g s c i e n t i s t a t t h e I n s t i t u t e o f Oceanology o f t h e USSR Academy o f S c i e n c e s i n a program s p o n s o r e d by t h e N a t i o n a l Academy o f S c i e n c e s . The m o r a l and p r a c t i c a l s u p p o r t o f D r s . W.S. R i c h a r d s o n a n d P. N i i l e r d u r i n g t h e c o u r s e o f t h i s work i s g r a t e f u l l y a c k n o w l e d g e d . W . Campbell, S . F u r g a n g , D . Hunley a n d E . T a n k a r d , J r . a r e t h a n k e d for t h e i r I warmly t h a n k D r . W. a s s i s t a n c e i n making t h e o b s e r v a t i o n s . Powers, J. DeSzoeke a n d J . W e a t h e r l y for t h e i r a s s i s t a n c e i n the data analysis.

264

REFERENCES Arm?, L. and R.C. Millard, Jr. 1976. The bottom boundary layer of the-deep ocean. 2. Geophys. E . , 49834990.

e,

Businger, J.A., Wyngaard, J.C., Izumi, Y., and Bradley, E.F. 1971. Flux-profile relationships in the atmospheric surface layer. J . Atmos. 30, 788-794.

s.,

Businger, J.A. and S.P.S. Arya. 1974. Height of the mixed , layer in the stably stratified planetary boundary layer. Advances in Geo h sics, H.E. Landsberg and J. Van Mieghem, York, pp. 73-92. ed., Acad=i*ew Deardorff, J.W. 1970. A three-dimensional numeric investigation of the idealized planetary boundary layer. J. Geophys. Fluid Mech., 1,377-410. Hollister, C.D. 1973. Atlantic continental shelf and slope of the United States - texture of surface sediments from New Jersey to Southern Florida, Geological Survey Professional Paper 529-M, U.S. Government Printing Office, Washington, 23 pp. Kundu, P.K. 1976. bottom. 2.

-.

Ekman veering observed near the ocean Oceanogr., 6 , 238-242.

Monin, A.S. and A.M. Yaglom. 1970. Statistical Fluid Mechanics : Mechanics of Turbulence, MIT Press, Cambridge, Massachusetts, 769 PP

-

Smith, J.A., B . D . Zetter and S. Broiaa. 1969. Tidal modulation of the Florida Current flow. Marille Tech. J., 3 , 41-46. -

*.

Smith, J.C. 1976. Modeling of sediment transport on continental shelves, The Sea, Vol. 6, in press. Weatherly, G.L. 1972. A study of the bottom boundary layer of the Florida Current. 2. Oceanogr., 2, 54-72.

w.

266 COASTAL J E T S ,

M.

A N D PHYTOPLANKTON PATCHINESS

FRONTS,

J . BOWMAN a n d W .

E.

ESAIAS

Marine S c i e n c e s Research C e n t e r , S t a t e U n i v e r s i t y o f New York, Stony Brook,

11794

N e w York

ABSTRACT

A f r o n t a l s y s t e m h a s b e e n d i s c o v e r e d i n Long I s l a n d S o u n d , forming t h e inshore boundary o f a s t r o n g t i d a l l y induced c o a s t a l jet.

Regenerated each ebb t i d e , t h e f r o n t e x t e n d s f o r s e v e r a l around a l o c a l promontory,

kilometers

and a d j a c e n t t o a h i g h l y

p r o d u c t i v e s h a l l o w embayment. Chlorophyll-a

c o n c e n t r a t i o n s measured i n A p r i l w i t h i n t h e

j e t were t y p i c a l l y t w i c e b a c k g r o u n d ,

and suggest t h a t t h e system

may b e a n e f f e c t i v e m e c h a n i s m f o r t h e p e r i o d i c i n j e c t i o n a t t i d a l frequencies

o f h i g h c o n c e n t r a t i o n p h y t o p l a n k t o n p a t c h e s from t h e

i n s h o r e embayment i n t o t h e i n t e r i o r o f t h e S o u n d .

INTRODUCTION

Long I s l a n d S o u n d i s a m a j o r e s t u a r y some on t h e U . York,

S.

1 6 5 km i n l e n g t h ,

e a s t e r n s e a b o a r d , l y i n g b e t w e e n Long I s l a n d , N e w

and C o n n e c t i c u t .

The main c o n n e c t i o n t o t h e A t l a n t i c

Ocean i s a t t h e e a s t e r n mouth w h e r e t h e t i d e s ,

principally

d i u r n a l , are t r a n s m i t t e d t o t h e i n t e r i o r o f t h e Sound. t h e Sound, transport

strait

the tides

semi-

Within

approximate a q u a r t e r s t a n d i n g wave, w i t h

d e c r e a s i n g westward towards t h e East R i v e r ,

a tidal

(Bowman, 1 9 7 6 1 , c o n n e c t i n g t h e S ound a n d N e w York H a r b o r .

A horizontal salinity

R i v e r and an i n f l o w of t h r o u g h t h e East R i v e r ,

gradient,

derived from t h e Connecticut

low s a l i n i t y Hudson R i v e r e s t u a r y w a t e r drives a classical estuarine circulation.

L o n g i t u d i n a l h y d r o g r a p h i c s e c t i o n s ( W i l s o n , 1 9 7 6 ) show a p a r t i a l s t r a t i f i c a t i o n i n t h e c e n t r a l r e g i o n o f t h e Sound d u r i n g s p r i n g and summer; t r a n s v e r s e p r o f i l e s

across t h i s

central basin also

i l l u s t r a t e t h e s t r o n g summer p y c n o c l i n e s e p a r a t i n g s u r f a c e a n d bottom water (Cordon and Pilbeam,

1975).

Near s h o r e w a t e r s a r e

u s u a l l y w e l l m i x e d or p o s s e s s a w e a k l i n e a r v e r t i c a l g r a d i e n t .

256 These mixing zones are r e g i o n s where bottom g e n e r a t e d t u r b u l e n t t i d a l k i n e t i c e n e r g y i s s u f f i c i e n t t o mix downward t h e s u r f a c e buoyancy a r i s i n g from v e r t i c a l s a l i n i t y g r a d i e n t s Hunter,

(Simpson and

1974; Fearnhead, 1975).

The z o n e s

contract

(Gordon and Pilbeam, over the 9 m isobath.

and expand between neaus and s p r i n g s

1975) w i t h t h e boundary u s u a l l y c e n t e r e d T i d a l l y i n d u c e d f r o n t s a r e commonly

a t t h e s e mixing zone b o u n d a r i e s ;

found

t h i s paper d e s c r i b e s one such

r e g i o n w h i c h p o s s e s s e s s o m e i n t e r e s t i n g f e a t u r e s a n d w h i c h may b e i m p o r t a n t i n e j e c t i n g medium s c a l e patches

(2

-

1 0 km) p h y t o p l a n k t o n

i n t o t h e i n t e r i o r o f t h e Sound from a nearby h i g h l y

p r o d u c t i v e s h a l l o w embayment.

THE STUDY R E G I O N

The a r e a shown i n F i g u r e s 1 sistent tidal

f r o n t which

Old F i e l d P o i n t .

740

-

3 w a s chosen t o study a per-

f o r m s e a c h e b b a r o u n d C r a n e Neck

and

P r e v i o u s a e r i a l a n d s h i p s u r v e y s h a d shown

7 30

72O

v

10

MONTAWK POINT

41'

41'

ATLANTIC O C E A N

I 0 0 km

40 .- O

740

7 30

72O

F i g , 1. L o c a t o r map f o r L o x g I s l a n d S o u n d . s h e area shown i n F i g u r e 2 .

40' 71 O The i n s e t r e p r e s e n t s

257

Fig. 2. Long I s l a n d S o u n d c e n t r a l b a s i n . The i n s e t r e p r e s e n t s The s o l i d b a t h y m e t r i c l i n e i s t h e s t u d y a r e a shown i n F i g u r e 3 . 2 0 f e e t ; t h e d a s h e d l i n e i s 60 f e e t . Arrows d e l i n e a t e t i d a l c u r r e n t d i r e c t i o n s ; numerals speeds i n knots. Note t h e 1 . 4 k n o t t i d a l J e t a r o u n d Crane Neck. Local t i m e is "slack; ( f r o m NOS, 1 9 7 3 ) . e b b b e g i n s a t The Race sharp discontinuities c o n t r a s t s and

'L

i n chlorophyll-a

(easily visible color

3 : l c h l - a c o n t r a s t s ) a c r o s s t h e f r o n t a l zone

d u r i n g t h e s p r i n g d i n o f l a g e l l a t e bloom. The r e g i o n i s one of s h a r p l y s l o p i n g topography ( F i g . where d e p t h s d r o p s h a r p l y t o of

%

1 km.

35 m o v e r a h o r i z o n t a l d i s t a n c e

C r a n e Neck i s t h e e a s t e r n l i m i t o f S m i t h t o w n B a y ,

s h a l l o , ~( % 2 0 m )

embayment b o u n d e d by t h e E a t o n ' s

1 8 km t o t h e w e s t . t h e Bay

%

31, a

Neck p r o m o n t o r y

T i d a l c u r r e n t s a r e i n v a r i a b l y weak i n s i d e

(NOS, 1 9 7 3 ) .

Two u n g a u g e d s o u r c e s o f f r e s h w a t e r ,

Nissequogue R i v e r and Stony Brook Harbor,

although of small d i s -

charge represent. impartant n u t r i e n t sources.

(Long I s l a n d i s a

h i g h l y p o p u l a t e d g l a c i a l t e r m i n a l m o r a i n e ; most waste d i s c h a r g e i n the study region seepage.)

,

principally

r e s i d e n t i a l , is v i a c e s s p o o l

P r e l i m i n a r y o b s e r v a t i o n s h a v e s h o w n t h a t t h e Bay

268

F i g . 3. L o c a l s t u d y a r e a , s h o w i n g t h e s a m p l i n g t r a n s e c t , mean s u r f a c e convergence p o s i t i o n r e l a t i v e t o t h e bottom contours.

s u s t a i n s r e l a t i v e l y h i g h primary p r o d u c t i o n compared t o t h e i n t e r i o r o f t h e Sound. Tidal current charts

(NOS, 1 9 7 3 ) s h o w a l o c a l i z e d e a s t w a r d

t i d a l j e t a r o u n d C r a n e N e c k , t h a t commences some 2 1 1 2 h o u r s b e f o r e t h e t i d e i n t h e c e n t r a l b a s i n b e g i n s t o ebb ( F i g .

2).

Phase d i f f e r e n c e s due t o i n e r t i a l e f f e c t s i n t h e b a r o t r o p i c t i d e between t h e d e e p e r o f f s h o r e water and t h e s h a l l o w n e a r s h o r e

water c o n s t r a i n t h e j e t t o a narrow band e x t e n t , w i t h maximum c u r r e n t s where i n t h e c e n t r a l b a s i n .

%

Q ,

1 m sec-l,

1 . 5 km i n l a t e r a l t h e s t r o n g e s t any-

On e b b t i d e , S m i t h t o w n Bay w a t e r i s

f u n n e l l e d i n t o t h e j e t , c a r r i e d around Crane Neck,

and d i s p e r s e d

o f f s h o r e and downstream. Our h y p o t h e s i s i s t h a t t h i s t i d a l j e t i s a h i g h l y e f f e c t i v e mechanism f o r p e r i o d i c e j e c t i o n , a t t i d a l f r e q u e n c i e s , o f h i g h concentration phytoplankton patches i n t o t h e i n t e r i o r of t h e Sound.

R e s u l t s r e p o r t e d i n t h i s p a p e r do n o t d e f i n i t i v e l y

259 s u p p o r t t h i s c o n c l u s i o n ; however, w e have g a t h e r e d enough d a t a t o enJoy

some s p e c u l a t i o n on t h i s mechanism a n d t o d e s i g n f u t u r e

experiments f o r next spring.

DETAILS OF THE EXPERIMENT

(Fig. 3 )

A t r a n s e c t c o n s i s t i n g of f i v e anchored s t a t i o n s

was c o n d u c t e d o n A p r i l 1 4 , 1 9 7 6 , c e n t e r e d a r o u n d l o c a l s l a c k

water a f t e r f l o o d i n t h e c e n t r a l b a s i n . s a l i n i t y , chl-a,

and n u t r i e n t s

(NO2,

In s i t u temperature,

NO3,

P O b ) were d e t e r m i n e d

from s a m p l e s drawn w i t h a s e l f - c o n t a i n e d pumping s y s t e m (Hulse, 1975). T e m p e r a t u r e and s a l i n i t y were m e a s u r e d w i t h a P l e s s e y 6600 E s t i m a t e s o f p h y t o p l a n k t o n b i o m a s s were

T Thermosalinograph.

made w i t h a T u r n e r D e s i g n m o d e l 1 0 - 0 0 5 R

meter, .regularly

flow through fluoro-

calibrated via filtered extracts.

Frozen water

NO3 a n d

s a m p l e s were l a t e r a n a l y z e d i n t h e l a b o r a t o r y f o r N O 2 , PO4 u s i n g a T e c h n i c o n A u t o a n a l y z e r ,

C u r r e n t v e l o c i t i e s were

d e t e r m i n e d w i t h a d e c k r e a d o u t Endeco model 110 c u r r e n t meter lowered from t h e s h i p . navigation

A low f l y i n g a i r c r a f t p r o v i d e d r e a l t i m e

i n f o r m a t i o n t o t h e s h i p a n d was u s e d f o r a e r i a l

photography o f a computer c a r d seeding experiment. The e n t i r e e x p e r i m e n t l a s t e d t h r e e h o u r s .

A strong front

w a s c l e a r l y v i s i b l e b o t h from t h e a i r c r a f t and t h e s h i p d u r i n g t h e duration of the experiment.

Although

c o n s i d e r a b l e meander-

i n g was e x h i b i t e d , i t s mean p o s i t i o n , a s d e t e r m i n e d b y s u r f a c e c o n v e r g e n c e o f f l o a t a b l e s , i s s k e t c h e d i n F i g u r e 3. The component o f t i d a l v e l o c i t y t a n g e n t i a l t o t h e f r o n t

at station 5

(60' T ;

Fig.

4)

consisted of a remarkable j e t ,

limited i n horizontal extent t o c i t y c o r e ( z 7 0 cm s e c - l ) ,

z

1 . 5 km, a n d w i t h a h i g h v e l o -

3 m below s u r f a c e .

Both i n s h o r e

a n d o f f s h o r e c u r r e n t s were n e a r z e r o . Surface velocities perpendicular c o n s i s t e d o f a s h a l l o w (?.

t o the front

(Fig.

2 m), v i g o r o u s l y m i x e d ( R i

s u r f a c e l a y e r w i t h s t r o n g l a t e r a l and v e r t i c a l s h e a r . convergent

currents

?.

5 0 cm s e c - l

%

5) 0.02)

Surface

outside t h e front agree w e l l h a p 112

w i t h t h e t h e o r e t i c a l i n t e r f a c i a l p r o p a g a t i o n velocity(*)

260

T i d a l c u r r e n t v e l o c i t y (cm s e c - l ) F i g . 4. s u r f a c e f r o n t at s t a t i o n 5 (60° T ) .

tangential t o the

T i d a l c u r r e n t v e l o c i t y (cm s e c - l ) p e r p e n d i c u l a r t o t h e Fig. 5. The s l o p e of t h e f r o n t a l i n t e r f a c e s u r f a c e f r o n t at s t a t i o n 5. i n s h o r e of s t a t i o n 6 i s i n f e r r e d from t h e d e n s i t y f i e l d . The arrows i n d i c a t e streamlines.

261 I,

( G a r v i n e , 1 9 7 4 ) w h e r e hp i s t h e d e n s i t y c o n t r a s t

30 c m s e c - 1

a c r o s s t h e f r o n t , and h i s t h e s c a l e t h i c k n e s s of t h e l i g h t pool

of water i n s h o r e ( a shallow rocky bottom inshore of s t a t i o n 6 made i t i m p o s s i b l e t o s a m p l e t h e r e ; t h e d e p t h a n d s l o p e aD/ ax

of t h e f r o n t a l i n t e r f a c e have been i n f e r r e d from t h e d e n s i t y structure;

Fig.

8).

The c o n v e r g i n g s u r f a c e c u r r e n t u t h e n s a n k

beneath t h e front (with a t h e o r e t i c a l velocity sec-l;

3~ uaD

0.5

%

cm

G a r v i n e , 1 9 7 4 ) , a n d r e t u r n e d s e a w a r d as a d i f f u s e l a y e r

a t d e p t h w i t h maximum v e l o c i t i e s

'L

2 0 cm s e c - l .

Another f e a t u r e

o f t h e n e a r s u r f a c e c i r c u l a t i o n was u p w a r d e n t r a i n m e n t b e t w e e n s t a t i o n s 2 and

4.

S u r f a c e c u r r e n t s p e e d s t o w a r d t h e foam l i n e were c o n f i r m e d by a n a l y s i s o f a e r i a l p h o t o g r a p h s

of a seeding experiment.

L a r g e numbers o f c o m p u t e r c a r d s were d r o p p e d by s h i p , p a r a l l e l and p e r p e n d i c u l a r t o t h e f r o n t a l l i n e , gence determined. almost

zero;

and t h e r a t e o f conver-

S u r f a c e c o n v e r g e n c e i n s i d e t h e f r o n t was w e a k ,

v i g o r o u s d o w n w a r d a d v e c t i o n o f t h e c a r d s was n o t e d

a t t h e s u r f a c e f r o n t by t h e o b s e r v e r s a b o a r d s h i p . H y d r o g r a p h i c s e c t i o n s a r e shown i n F i g u r e s

T'C

2

0

3

4

--

--

6

5

0-

-

..

Fig.

6.

10

--_6.50

Vertical temperature (OC) section.

.

8.

-

Early

6

7.0

1

262

Fig. 7. Vertical salinity (O/oo) section. c o n t o u r i n t e r v a l between s t a t i o n s 5 and 6.

Note t h e b r e a k i n

0

5

10

15

20

25

30

F i g . 8. V e r t i c a l d e n s i t y (sigma-T) s e c t i o n . contour i n t e r v a l between s t a t i o n s 5 and 6 .

Note t h e b r e a k i n

263 development of t h e s e a s o n a l thermocline i s e v i d e n t both o f f s h o r e and i n s h o r e o f t h e j e t stream ( F i g . 6 ) .

Waters a r e r e l a t i v e l y

w e l l mixed w i t h i n t h e j e t w i t h t e m p e r a t u r e s

The s a l i n i t y s e c t i o n ( F i g .

%

6.5

-

6 . 7 5 O C.

7 ) i l l u s t r a t e s a weak h a l o c l i n e o f f -

s h o r e , b u t s t r o n g s t r a t i f i c a t i o n a t t h e f r o n t a l i n t e r f a c e , which

i s ‘ a t t r i b u t e d t o a plume o f low s a l i n i t y Stony Brook Harbor water e n t r a i n e d a r o u n d C r a n e Neck o v e r l y i n g u p w e l l e d Sound b o t t o m water ( s a l i n i t y

%

26.0).

T h e c h l - a maximum B t 1 2 m ( F i g . 9 ) l o c a t e d a t t h e 0 . 0 1 % l i g h t l e v e l , w e l l below t h e p h o t i c zone ( 0

-

6 m ) i s f o u n d so m e-

what i n s h o r e o f t h e j e t c o r e i n an area o f s t r o n g n u t r i e n t gradients ( F i g s . 10 20.25

at

%

-

20.30.

-

12), a n d i n w a t e r o f d e n s i t y ( s i g m a - T )

%

Outside t h e j e t , water of t h i s d e n s i t y i s found

5 m ; t h u s t h e o b s e r v e d d i s t r i b u t i o n s s u g g e s t s t r o n g down-

ward and eastward advection o f phytoplankton i n t o t h e j e t . Downstrean one might e x p e c t s h e d d i n g o f e d d i e s w i t h t h e c h l o r o p h y l l c o r e r e t u r n i n g back i n t o t h e p h o t i c zone.

0

5

10

15

20

25

30

Fig.

9.

V e r t i c a l c h l o r o p h y l l a (mg m - 3 )

section.

0

5

10

15

20

. . . .

.

25

30

Fig.

10.

Vertical inorganic n i t r i t e

( N O 2 ; u g m a t 1-I) s e c t i o n .

Fig.

11.

Vertical inorganic nitrate

“03;

Llgm a t 1-l) s e c t i o n .

0

2

4

3

5

6

5

10

15

20

25

30

Fig.

12.

V e r t i c a l l n o r g a n i c p h o s p h a t e (Pol,; ugm a t + - ‘ ) s e c t i o n .

Although w e y e t have no d i r e c t e v i d e n c e o f v o r t e x s h e d d i n g , f o u r evenly spaced (by one t i d a l e x c u r s i o n ) cusps i n t h e sandy s h o u l d e r on t h e n o r t h s h o r e o f t h e I s l a n d ( d e n o t e d A ,

B,

C,

D

i n F i g . 2 ) s u g g e s t t h e p r e s e n c e o f s c o u r i n g by p e r s i s t e n t e d d i e s of s i g n i f i c a n t dimension.

Lekan a n d W i l s o n ( i n p r e s s ) i n v e s t i -

g a t e d t h e s p a t i a l s t r u c t u r e of s u r f a c e (1 m) c h l - a ,

temperature,

a n d s a l i n i t y a l o n g a n e a s t w a r d t r a n s e c t i m m e d i a t e l y e a s t of t h e study zone. (contrasts

Several (scale ?J

i n t h i s area.

?J

8 km) p h y t o p l a n k t o n p a t c h e s

2 : l a b o v e b a c k g r o u n d ) were o b s e r v e d i n A u g u s t , 1 9 7 5 T h e s e p a t c h e s were f o u n d t o b e p o o r l y c o r r e l a t e d

with temperature and s a l i n i t y , suggesting p h y s i c a l mixing of

waters w i t h similar h y d r o g r a p h i c p r o p e r t i e s b u t d i f f e r i n g s t a n d ing stocks. DISCUSS I O N It i s i n t e r e s t i n g t o compare t h e s i m i l a r i t i e s of o u r s t u d y w i t h o t h e r e x a m p l e s o f c o a s t a l e n t r a p m e n t o f d i f f u s i n g f i e l d s by

266 shallow water fronts (e.g.

Csanady,

1971) and v o r t e x s h e d d i n g

i n t h e v i c i n i t y of l o c a l promontories ( e . g . Helseth,

1975).

Ebbesmeyer and

M e d e l s o f p h y t o p l a n k t o n h e t e r o g e n e i t y show t h a t

a minimum c r i t i c a l p a t c h s i z e e x i s t s b e l o w w h i c h e x p o n e n t i a l c e l l growth i n e x c e s s o f g r a z i n g by zooplankton i s u n a b l e t o k e e p p a c e w i t h a t t r i t i o n by d i f f u s i o n

( K i e r s t e a d and S l o b o d k i n ,

1 9 5 3 ; Okubc, 1 9 7 2 ; P l a t t , 1 9 7 5 ; P l a t t a n d Denman, 1 9 7 5 ; D u b o i s , 1975a, b ; Wroblewski and O ' B r i e n , 1975, 1 9 7 6 ) . However, none of these theories

e x p l a i n how a n o b s e r v e d p h y t o p l a n k t o n p a t c h g r e w

t o critical size in the first place, but "spontaneous

a s s u m e some f o r m o f

creation".

P a t c h g e n e r a t i o n mechanisms s u c h as s u d d e n n u t r i e n t e n r i c h ment r e s u l t i n g f r o m u p w e l l i n g e v e n t s o r b r e a k i n g o f s h e l f waves are w e l l documented ( e . g . ,

et al.,

in press).

internal

Beers e t a l . , 1 9 7 1 ; Walsh

We s u b m i t t h a t e j e c t i o n

o f waters w i t h h i g h

p h y t o p l a n k t o n b i o m a s s i n t o w a t e r s o f l o w b i o m a s s , v i a t h e mechanism o f t i d a l j e t c u r r e n t s ,

can r e p r e s e n t another important

mechanism f o r t h e g e n e r a t i o n

o f medium s c a l e p a t c h i n e s s i n e s t u -

a r i n e and c o a s t a l environments.

ACKNOWLEDGEMENTS

We t h a n k A k i r a O k u b o a n d P e t e r K . commenting on t h e p a p e r . pilot

M.

Gwinner,

Captain H.

Weyl f o r r e a d i n g a n d

Stuebe of t h e R / V

and p e r s o n n e l f r o m t h e Marine S c i e n c e s

Research Center are thanked f o r t h e i r r e s p e c t i v e r o l e s experiment.

Onrust,

in the

T h e p r o j e c t was p a r t i a l l y s u p p o r t e d b y t h e J o i n t

Awards C o u n c i l / U n i v e r s i t y Awards Committee o f t h e S t a t e U n i v e r s i t y

o f N e w Y o r k (SUNY) a n d t h e R e s e a r c h F o u n d a t i o n o f SUNY. C o n t r i b u t i o n 1 7 5 o f t h e M a r i n e S c i e n c e s R e s e a r c h C e n t e r (MSRC) o f t h e S t a t e U n i v e r s i t y o f New York a t S t o n y B r o o k .

267 REFERENCES

Beers, J. R . , S t e v e n s o n , M. R . , Eppley, R . W. and Grooks, E . R . , 1971. P l a n k t o n p o p u l a t i o n s and u p w e l l i n g o f f t h e c o a s t o f P e r u , June 1969. Fishery B u l l e t i n , 69:859-876.

M . J . , 1 9 7 6 . T h e t i d e s o f t h e E a s t R i v e r , New Y o r k . J o u r n a l of G e o p h y s i c a l R e s e a r c h , 8 1 : 1 6 0 9 - 1 6 1 5 .

Bowman,

G. T . , 1971. C o a s t a l e n t r a p m e n t i n Lake Huron. In: P r o c e e d i n g s of t h e F i f t h I n t e r n a t i o n a Z W a t e r P o Z l u t i o n Research Conference, JuZy-August 1970. III:11/1-11/7,

Csanady,

Pergamon P r e s s L t d . Dubois, D. M., 1975. A model o f p a t c h i n e s s f o r p r e y - p r e d a t o r plankton populations. EcoZogicaZ ModeZZing, 1 : 6 7 - 8 0 . Dubois, D. M . , 1975. Simulation of t h e s p a t i a l structuration of a patch of prey-predator plankton populations i n t h e southern b i g h t of t h e North Sea. Mkmoires S o c i d t d R o y a l e d e s S c i e n c e s d e L i e ' g e , V I I :7 5 - 8 2 . C . C . , and H e l s e t h , J . M . , 1975. A S t u d y of C u r r e n t P r o p e r t i e s and M i x i n g U s i n g Drogue Movements O b s e r v e d Durlng Summer and W i n t e r i n C e n t r a Z P u g e t S o u n d , W a s h i n g t o n . E v a n s - H a m i l t o n , I n c , S e a t t l e , 81 p p .

Ebbesmeyer,

.

On t h e f o r m a t i o n o f f r o n t s by t i d a l Fearnhead; P. G . , 1975. mixing around t h e B r i t i s h Isles. Deep-sea Research, 2 2 : 311-321. R. W., 1974. Dynamics o f s m a l l - s c a l e o c e a n i c f r o n t s . JournaZ o f PhysicaZ Oceanography, 4 : 5 5 7 - 5 6 9 .

Garvine,

Gordon, R . B . , and Pilbeam, C . C . , 1975. Circulation in central Long I s l a n d S o u n d . J o u r n a Z of G e o p h y s i c a Z R e s e a r c h , 8 0 : 414-422. Hulse, G. L . , 1975. The P l u n k e t : a shipboard water q u a l i t y monitoring system. Marine S c i e n c e s Research C e n t e r Technical Report, #22, 1 2 4 p p . The s i z e o f w a t e r K i e r s t e a d , H . , and Slobodkin, L. B . , 1953. masses c o n t a i n i n g p l a n k t o n b l o o m s . J o u r n a l of M a r i n e Research, 12:141-147. Spatial variability L e k a n , J. F., a n d v ! i l s o n , R . Z . , i n p r e s s . o f p h y t o p l a n k t o n b i o m a s s i n t h e s u r f a c e w a t e r s o f Long Island.

1 9 7 3 . T i d a Z C u r r e n t C h a r t s : Long I s l a n d Sound and B l o c k I s Z a n d S o u n d . National Oceanic a n d A t m o s p h e r i c A d m i n i s t r a t i o n , R o c k v i l l e , M a r y l a n d , 14 p p .

N a t i o n a l Ocean S u r v e y ,

Okubo, A . , 1 9 7 2 . A n o t e on s m a l l o r g a n i s m d i f f u s i o n a r o u n d an a t t r a c t i v e c e n t e r ; a m a t h e m a t i c a l model. J o u r n a l of t h e

Oceanographic S o c i e t y o f Japan, 2 8 : l - 7 .

268 P l a t t , T . , 1975. The p h y s i c a l e n v i r o n m e n t a n d s p a t i a l s t r u c t u r e 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 . MBmoires S o c i d t g RoyaZe

d e s S c i e n c e s de LiBge, V I I : 9 - 1 7 . P l a t t , T . , a n d Denman, K . L . , 1 9 7 5 . A general equation for the mesocale d i s t r i b u t i o n of phytoplankton i n t h e sea. Me m oir e s S o c i e t e R o y a l e des S c i e n c e s de L i e g e , V I I : 3 1 - 4 2 . Simpson, J . H . , and H u n t e r , J . R . , Sea. Nature, 250:404-406.

1974.

Fronts i n the I r i s h

W a l s h , J . J . , W h i t l e d g e , T . E . , C o d i s p o t i , L . A . , Howe, S . O . , W i r i c k , C . D . , and C a s t i g l i o n e , L. J . , i n p r e s s . The b i o l o g i c a l response t o t r a n s i e n t f o r c i n g s of t h e s p r i n g bloom w i t h i n t h e New York B i g h t . Wilson, R. E., 1976. G r a v i t a t i o n a l c i r c u l a t i o n i n Long I s l a n d Sound. E s t u a r i n e and C o a s t a l M a r i n e S c i e n c e s , 4 : 4 4 3 - 4 5 3 . A s p a t i a l model Wroblewski, J . S . , and O ' B r i e n , J . J . , 1976. of phytoplankton patchiness. Marine B i o l o g y , 35:161-175.

Wroblewski, J. S . , O ' B r i e n , J . J . , and P l a t t , T . , 1975. On t h e p h y s i c a l and b i o l o g i c a l s c a l e s o f phytoplankton patchiness i n t h e ocean. MBmoires S o c i & t 6 R o y a l e d e s S c i e n c e s de L i B g e , V I I I : 4 3 - 5 7 .

269

INTERNAL WAVES I N THE

NW

AFRICA UPWELLING

J. SALAT and J. FONT 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 Pesqueras, B a r c e l o n a ( S p a i n )

SUMMARY

Temperature p r o f i l e s t a k e n i n t h e t h e p r e s e n c e o f i n t e r n a l waves.

NW

A f r i c a u p w e l l i n g r e g i o n show

Some p r e l i m i n a r y arguments and hypo-

t h e s i s a r e drawn t r y i n g t o e x p l a i n t h e g e n e r a t i o n o f t h e s e waves and t h e i r r e l a t i o n s h i p w i t h coastal upwelling. INTRODUCTION I n t e r n a l waves a r e o b s e r v e d o f f C.Bojador

(26O 10' N, 14' 30' W )

d u r i n g an e x p e r i m e n t c o n c e r n i n g w a t e r mass c i r c u l a t i o n i n a s t r i p o f s t r o n g upwelling,

10 NM wide, a d j a c e n t t o t h e shore. I n t h i s r e g i o n , but i t

t h e c o n t i n e n t a l s h e l f has a g e n t l e s l o p e a n d i s v e r y narrow, w i d e n s p r o g r e s s i v e l y southwards,

(25O 10' N).

being

60

NM w i d e o f f C.Pen'a Grande

D u r i n g t h e time o f t h e experiment,

l y weak ( 4 m/s)

t h e wind was extreme-

o r i g i n a t i n g an e x t r e m e l y q u i e t sea s u r f a c e .

Such an e x p e r i m e n t c o n s i s t e d i n f o l l o w i n g a p a r c e l o f w a t e r t a g g e d by a d r i f t i n g f l o a t w i t h a l a r g e vane l o c a t e d a t 5 m below t h e s u r f a r e l e a s e d 6 NM o f f s h o r e ,

ce,

t h e l o c a l isobaths, d i f f e r e n t points,

i t moved southwards (190°),

parallel t o

w i t h an a v e r a g e v e l o c i t y o f 30 cm/s (Fig.1).

d u r i n g t h e f i v e h o u r s o f t h e experiment,

At 8

temperatu-

r e p r o f i l e s were r e c o r d e d i n t h e down a n d up e x c u r s i o n s o f a M a r t e k EBT sensor,

t h r e e o f them were r e p e a t e d i m m e d i a t e l y a f t e r r e a c h i n g

t h e surface. OBSERVATIONS

The t e m p e r a t u r e p r o f i l e s e r i e s r e v e a l s o s c i l l a t i o n s t h a t show a n e t upwards p r o p a g a t i o n . Such waves seem t o be g e n e r o t e d a t t h e b o t tom,

breaking a t t h e surface,

p r o b a b l y due t o a b s o l u t e l a c k o f s t r a -

tification.

By s t u d y i n g s e v e r a l o f such p r o f i l e s ( F i g . 2,3) t h e wave p e r i o d and a m p l i t u d e a s w e l l as t h e n e t upwards t r a n s p o r t ,

can be e s t i m a t e d

270

26.

r

16'

1s 1C

13'

Fig.1.

Map showing t h e p a t h o f t h e f l o a t d u r i n g t h e experiment i n d i -

c a t i n g t h e p o i n t s where t h e p r o f i l e s were t a k e n and t h e time, nutes,

i n mi-

a f t e r t h e b e g i n n i n g o f t h e experience.

"gross0 modo" by assuming t h a t t h e mouvement has an e q u a t i o n such as: x = xo

+

+

v t

A s i n (at

+ 'Q

),

where x i s t h e p o s i t i o n a t t h e i n s t a n t t, x,is

p u l s a t i o n and

'0

the i n i t i a l position,

A the amplitude o f the o s c i l l a t i o n ,

v the v e r t i c a l velocity,

its

i t s phase angle.

Since t h e p r o f i l e s a r e repeated i n m e d i a t e l y ,

we can t a k e 4 p o i n t s

o f e q u a l temperature a t 4 d i f f e r e n t i n s t a n t s . Then,

we have t h e f o -

l l o w i n g s e t o f equations: x. = x 1

tl Reducing,

0

+

< t2
A( sin(W,+'?)

-

-

sin(wt,+'f'))

then: sin(cJt3+Y))

consequently: t

3 ), and a l s o s i m i l a r t o x2- x4, g i v i n g

v ~ 0 . 8cm/s. Thus,

l o o k i n g a t such v a l u e s even o n l y a s an a p p r o x i m a t i o n , we c a n

e l l i m i n a t e t h e p o s s i b i l i t y o f such o s c i l l a t i o n s b e i n g a consequence o f s h i p a r sensor motion or,

because o f t h e i r p e r i o d ,

r e l a t e d w i t h ti-

d a l motions. The v a l u e s o b t a i n e d a r e v e r y d i f f e r e n t f r o m t h e ones o b s e r v e d by Johnson e t a l .

(1972) a t t h e same l o c a t i o n i n A u g u s t 72. The p e r i o d

o f t h e i r o b s e r v a t i o n s was t h a t o f t h e t i d a l s e m i d i u r n a l o s c i l l a t i o n . On t h e o t h e r hand,

t h e upwards n e t p r o p a g a t i o n o f t h e o b s e r v e d wa-

ve can be r e l a t e d t o t h e phenomenon o f c o a s t a l u p w e l l i n g q u o t e d by

S m i t h (1968) and a t t r i b u t e d t o some k i n d o f K e l v i n wave p r o p a g a t i n g p o l e w a r d s a n d h a v i n g a p r e c i a b l e a m p l i t u d e when t h e r e i s a resonance between t h e wave a n d t h e f o r c i n g d i s t u r b a n c e , f e s t w i t h o u t a p p a r e n t wind, Finally,

and c o u l d perhaps mani-

as o c c u r s i n o u r case.

we can a l s o say t h a t Mc N i d e r a n d O ' B r i e n

(1973) found,

i n t h e n u m e r i c a l s o l u t i o n o f t h e i r t h e o r e t i c a l model o f c o a s t a l upwe-

lling,

waves i n t h e l o n g s h o r e v e l o c i t y f i e l d whose upwards v e l o c i t y

o s c i l l a t e s between 1 and 2 cm/s,

which i s a l i t t l e h i g h e r than o u r es-

273

t i m a t e d value. CONCLUS IONS A l t h o u g h such o c c a s i o n a l o b s e r v a t i o n s can o n l y be considered as a p r e l i m i n a r y approach t o more s p e c i f i c studies,

t h e y a l l o w us t o draw

t h e f o l l o w i n g h y p o t h e s i s t o e x p l a i n t h i s phenomenon:

A c o n s t a n t h o r i z o n t a l c u r r e n t o v e r t h e bottom i n a sea. o f decreas i n g depth g i v e s p l a c e t o an o n d u l a t i o n t h a t propagates a g a i n s t such a c u r r e n t . T h i s phenomenon c o u l d be c o n s i d e r e d as i n t e r m e d i a t e between pure o s c i l l a t i o n and bottom t u r b u l e n c e , Then a c c o r d i n g w i t h Cox

(1963) we a r e i n presence o f a t u r b u l e n t motion t h a t i n v o l v e s v e r t i c a l oscillation. On t h e o t h e r hand,

t h i s o s c i l l a t i o n c o u l d a l s o be produced i n t h e

edge o f t h e c o n t i n e n t a l s h e l f p r o p a g a t i n g northwards f o l l o w i n g t h i s edge. T h i s f a c t i s a l s o quoted by Cruzado (1976) and i t a l s o agrees w i t h t h e o b s e r v a t i o n o f waves o f s i m i l a r c h a r a c t e r i s t i c s i n t h e acoust i c s c a t t e r i n g l a y e r s near t h e s h e l f edge i n t h i s r e g i o n . We a r e p r e s e n t l y d e s i g n i n g experiments t o be performed i n t h i s ar e a i n o r d e r t o o b t a i n a complete s e t o f d a t a a l l o w i n g a b e t t e r e x p l a n a t i o n o f t h i s phenomenon, p r o v i d i n g t h e c r i t i c a l p o l i t i c a l s i t u a t i o n o f t h e Sahara a l l o w s us t o c o n t i n u e o u r r e s e a r c h on c o a s t a l u p w e l l i n g processes o f f FW A f r i c a . REFERENCES

1963. I n t e r n a l waves. I n : M.N.Hil1

Cox, C.S.,

(Editor),

The Sea,

1:

752-763. Cruzado, A.,

1976. A f l o r a m i e n t o c o s t e r o en e l A t l C I n t i c o N o r o r i e n t a l . U n i v e r s i d a d de Barcelona, 97 pp.

Tesis Doctoral, Johnson,

D.R.,

Barton,

E.D.,

Hughes, P. and Mooers,

C.N.K.,

1975. C i r -

c u l a t i o n i n t h e Canary C u r r e n t u p w e l l i n g r e g i o n o f f Cab0 B o j a d o r i n August 1972. Deep Sea Res. 22(8): Mc Nider,

R.T.

and O'Brien,

o f c o a s t a l u p w e l l i n g . J.Phis. Smith,

R.L.,

J.J.,

547-558. 1973. A m u l t i - l a y e r t r a n s i e n t model

Oceanogr. 3(3):

258-273.

1968. Upwelling. 0ceanogr.Mar.Biol.Ann.Rev.

6: 11-46.

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276

A R E P O R T ON E N V I R O N M E N T A L S T U D I E S O F D R E D G E S P O I L D I S P O S A L S I T E S P A R T I : AN I N V E S T I G A T I O N OF A D R E D G E S P O I L D I S P O S A L S I T E P A R T 1 1 : D E V E L O P M E N T A N D USE O F A B O T T O M B O U N D A R Y L A Y E R P R O B E G.S.

COOK,

R.W.

and A . T .

MORTON,

MASSEY

Naval Underwater Systems Center, R h o d e I s l a n d 02840,

Newport Laboratory,

Newport,

USA

The c h a n n e l d r e d g i n g of m a t e r i a l from t h e Thames R i v e r i n New London, C o n n e c t i c u t , USA r e q u i r e d d r c d g c s p o i l d i s p o s a l b a r g c dumping a t a p r i m a r y s i t e 5 kin s o u t h of t h e r i v e r e n t r a n c e and p o s s i b l y a t an a l t c r n a t c s i t e

15 km s o u t h c a s t o f N e w London on t h e c o n t i n e n t a l s h e l f . S u r v e y s w c r c madc a t t h e p r i m a r y and a l t e r n a t e d i s p o s a l s i t e s i n o r d e r t o a s s e s s ambient e r o s i v c and t r a n s p o r t c o n d i t i o n s . The s u r v c y r e s u l t s showed t h a t a f t e r a n i n i t i a l s t a b i l i z a t i o n p e r i o d f o l l o w i n g s p o i l s dumping t h e r c was no m a j o r c h a n g e i n t h e s h a p c or a r e a o f the spoil pile.

T h i s was c o n f i r n i c d b y u n d e r w a t e r t e l e v i s i o n s u r v e y s t h a t

r e v e a l e d n o major c r o s i o n a l p r o c c s s c s o c c u r r i n g o n t h e s u r f a c c of t h c s p o i l pile.

E v i d e n c e w a s n o t c d , I i o v c v c r , o f l o c a l s o r t i n g and e r o s i o n a r o u n d

s p o i l c l u m p s d u r i n g pc.aIc

t i d a l flow.

i n d i c a t e d s i m i l a r c u r r c n t rcgimcs.

C u r r e n t m c a s u r c m e n t s a t t h c two s i t c s

Peak v c l o c i t i e s w c r c a b o u t 30-40 c m / s c r

a t b o t h sites b u t o c c u r i n d i f f e r e n t d i r e c t i o n s producing n e t c a s t c r l y d r i f t a t t h e New I.ondon D i s p o s a l S i t e and w c s t c r l y d r i f t a t t h e E a s t h o l e a l t e r nate s i t e . I n o r d e r t o d c t e r m i n e i f t h e s c l o c a t i o n s would a c t a s s p o i l c o n t a i n m c n t s i t e s i t was r e q u i r e d t o m c a z u r e t h o d y n a n i c p r o p e r t i c s o f t h e c u r r e n t s i n t h e bottom boundary l a y c r .

An i n s t r u n c n t was d c s i s n e d a n d c o n z t r u c t c d t o

m e a s u r e b o t h t h e v e r L i c a l c u r r e n t s h e a r and t t l r b u l e n t v e l o c i t y s t r u c t u r e w i t h i n one meter of t h e s e a f l o o r . Froin t h c b o t t o m c u r r e n t d a t a ::cynulds

were d c t e r n i i n c d by two m c t h o d s : 1)

s t r c s n c s i n t h c boundary l a y c r

f r o m p a r a m e L r i c f i t or t h e o b s e r v e d mean

v e l o c i t i c s t o a l o g a r i t h c i i c v c l o c i t y p r o f i l e a n d , 2 ) from c s t i m a t c s o f t h c r a t e o f k i n c t i c c n c r g y d i s s i p a t i o n u s i n g t h c Kolmogoroff H y p o t h e s i s f o r t h e i n e r t i a l s u b r a n g c and by a s s u u i n g a b a l a n c e bctwccn p r o d u c t i o n and d i s s i p a t i o n o f e n e r g y w i t h i n t h e boundary l a y e r .

276 R e y n o l d s s t r e s s e s o f 4-6 mum t i d a l c u r r e n t .

d y n c s / c m 2 wcrc e s t i m a t e d d u r i n g timcs of maxi-

I t was d c t c r m i n c d f r o m f l u m c t a n k s t u d i e s t h a t R e y n o l d s

s t r e s s e s o f 1 6 d y n c s / k m 2 o r g r c a t c r would b e r e q u i r e d t o e r o d e t h c p a r t i c u l a r s p o i l material.

I t is t h u s concluded t h a t for t h e s e sites under normal

c u r r e n t c o n d i t i o n s n o major e r o s i o n and t r a n s p o r t w i l l o c c u r .

INTRODUCTION Thc T h a n e s R i v e r i n N e w London, C o n n e c t i c u t , USA i s b e i n g d r c d g c d o f a b o u t o n e m i l l i o n c u b i c mctcrs o f m a t e r i a l t o i n c r c a s c c h a n n e l d e p t h .

This

p r o j e c t h a s c r e a t e d a r c q u i r c m e n t f o r a l o r n 1 d i s p o s a l s i t c t o accommodate t h e dredged s p o i l s .

The Mer~ London D i s p o s a l S i t c ( h e n c c f o r t h r c f c r r c d t o

a s NLDS) l o c a t e d a p p r o x i m a t c l y 5 km S o u t h o f t h c Tnames R i v e r c n t r a n c c ( F i g . 1 ) h a s b e e n d c s i g n a t c d a s a p r i m a r y s i t c a n d h a s r e c c i v c d a l l of t h e d r e d g e s p o i l s removed d u r i n g t h e f i r s t p h a s c s o f t h c p r o j c c t ( a b o u t one half million

i d ) .

Tnc E a s t H o l e D i s p o s a l S i t e ( h c n c c f o r t h r c f c r r c d t o

AS

EHUS) i n B l o c k I s l a n d Sound ( F i g . 1 ) has b c c n d c s i g n a t c d as a n a l t e r n a t e

site f o r possibly receiving f u t u r c drcdgc s p o i l s . The N a v a l U n d c r w a t c r S y s t c m s C c n t c r (NUSC) a t N c w p o r t , Ichodc I s l a n d h a s conducted cnvironmcntal s t u d i e s a t b o t h s i t c s s i n c e August, 1574.

A t the

NLDS f o u r b a t h y m e t r i c s u r v e y s wcrc made o v c r a two y c a r p c r i o d t o d e f i n c t h e b o u n d a r i e s of t h c d c p o s i t c d material and t o m o n i t o r c h a n g e s i n i t s volumc a n d g c o g r a p h i c d i s t r i b u t i o n .

A s u r v c y a t t h e OHDS w a s a l s o made t o

d e t e r m i n c a b a s e l i n e t o p o g r a p h y f o r u s e i n e s t i m a t i n g volumes o f s p o i l s i n t h c c v c n t t h a t t h c EHDS d c p r e s s i o n i s u s e d a s a f u t u r c d i s p o s a l s i t e . B c c a u s c o f t h c p o s s i b l y I i i g h c o n c e n t r a t i o n of p e t r o l e u m a n d h c a v y mct-

a l s i n t h e Thames R i v e r s c d i r n e n t s i t w a s a g r c e d t h a t t h e d i s p o s a l a r e a s h o u l d b e a c o n t a i n m c n t s i t c w h c r c tiic s e d i m e n t w i l l r c m a i n i n t h e a r e a o f dumping.

The c l i a r a c t c r i s t i c s o f t i d a l r u r r e n t s wcrc s t u d i e d a t t h e NLDS

a n d EHDS t o d e t e r m i n c t h e d c g r c c t o w h i c h t h c c u r r c n t r e g i m e i s c a p a b l e o f e r o d i n g and t r a n s p o r t i n g t h e d r e d g e s p o i l s . v i s i o n p i c t u r e s of

I n a d d i t i o n , u n d e r w a t e r tclc-

t h e s u r f a c c o f t h e NLDS s p o i l p i l e werc made t o o b s c r v c

e r o s i o n a l f e a t u r e s t h a t m i g h t f u r t h e r i n d i c a t e r e m o v a l o f s p o i l s by c u r rents.

C u r r e n t o b s e r v a t i o n s were made a t t h e s i t e s b y two m e t h o d s :

first,

c o n v e n t i o n a l t a u t - w i r c m o o r s w i t h t i m e a v e r a g i n g c u r r c n t mctcrs were i n s t a l l e d t o e v a l u a t e t h e l o n f tcrm c u r r c n t r e g i m e ; a n d s e c o n d , a s p e c i a l b o t t o m b o u n d a r y l a y e r c u r r c i i ~mctcr was d c v c l o p c d t o m c a s u r c s h o r t term t u r b u l e n t c u r r e n t f l u c t u a t i o n s w i t h i n o n c mctcr of t h e b o t t o m .

277 P a r t one p r e s e n t s

3

b r i e f r c v i c w of t h c b o t t o m c h a r a c t c r i s t i c s and

g e n e r a l c i r c u l a t i o n i n t h e d i s p o s a l areas.

P a r t I1 p r e s e n t s a d e t a i l e d

d i s c u s s i o n of t h e b o t t o m boundary l a y c r s t u d i e s and i n s t r u m e n t a t i o n .

72.05'

72.00'

71.55'

71.50'

41. 20'

41.15'

Fig.1.

L o c a t i o n o f t h e New L o n d o n , D i s p o s a l S i t c (NLDS) a n d t h e E a s t H o l e

D i s p o s a l S i t e (EHDS)

PART I:

CONVENTIONAL ENVIRONMENTAL STUDIES OF THE DISPOSAL SITES

BATHYMETRIC SURVEY F o u r b a t h y m e t r i c s u r v e y s were made a t t h e NLUS b e t w e e n November, 1 9 7 4 a n d A u g u s t 1 9 7 5 , a n d a b a s e l i n e s u r v e y of t h e EHDS w a s made i n A u g u s t , 1 9 7 6 The n a v i g a t i o n u s e d i n a l l s u r v e y s w a s a Decca D c l N o r t e Model 202A T r i s p o n d e r s y s t e m c a p a b l e of m e a s u r i n g d i s t a n c e s w i t h a n a c c u r a c y o f

meters o v e r a maximum r a n g e o f 40 km.

5

3

The e c h o s o u n d e r s y s t e m c o n s i s t s o f

a n ED0 Western Nodel 4034A u n i t p r o v i d i n g d i g i t a l d e p t h o u t p u t .

The n a v i -

g a t i o n s y s t e m , e c h o s o u n d e r a n d a d i g i t a l c l o c k were i n t e r f a c e d so t h a t a l l d a t a w a s r e c o r d e d on d i g i t a l t a p e f o r s u b s e q u e n t computer p r o c e s s i n g .

The

b a t h y m c t r i c d a t a were p l o t t e d a n d h a n d c o n t o u r e d a f t e r c o r r e c t i o n s were app l i e d f o r t i d a l l e v e l a n d s p e e d of s o u n d .

The e r r o r o f a b s o l u t e d e p t h i s

278

(t 1 f t . ) .

30 cm

estimated t o be

The f i r s t NLDS sur-vey i n November, 1 9 7 4 was made a f t e r t h e dumping o f t h e Thames R i v e r d r e d g e s p o i l s h a d b e g u n , a n d s i n c e t h e NLDS h a s b e e n a dumping g r o u n d f o r many y e a r s n o b a s e l i n e d a t a w a s a v a i l a b l e t o d e t e r m i n e t h e o r i g i n a l b o t t o m t o p o g r a p h y o f t h e area.

This survey revealed t h c pres-

e n c e o f two t o p o g r a p h i c h i g h s ( F i g . 2 ) i n t h e a r e a of t h e dumpinR g r o u n d : a r e l i c p i l e t o t h e N o r t h e a s t w i t h a minimum d e p t h of 1 1 . 0 m a n d o n e i n t h e c e n t e r of t h e c h a r t w h i c h i s t h e s p o i l p i l e f r o m t h e r e c e n t d r e d g i n g w i t h a minimum d e p t h o f 1 5 . 5 m .

72' -.

OS'Oor T--

1

04'30' I

I

I

41' 16'10'

41' 16'00'

20

Fig.2.

I

I

B a t h y m e t r y of 1 6 November 1 9 7 4 .

NLDS

279 The s p o i l s from c u r r e n t d r e d g i n g o p e r a t i o n s s t a n d o u t a s a d i s t i n c t c i r c u l a r mound w i t h s t e c p s l o p e s , p a r t i c u l a r l y toward t h e S o u t h e a s t and a comp a r a t i v c l y f l a t t o p bctwecn 15.5 and 16.5 m .

The d i a m e t e r of t h c mound

US-

i n g t h e 2 1 m c o n t o u r as a g u i d e i s on t h e o r d c r of 300 m . Thc second s u r v e y of F e b r u a r y , 1975 ( P i g . 3 ) shows d i f f e r e n c e s from t h e f i r s t s u r v e y : t h c minimum d e p t h of t h e s p o i l s p i l c dcsccnded from 1 5 . 5 m t o 17.5

ni

and t h e mound had widcncd t o a d i a m e t e r o f 400-450 m , tlie t o p s u r f a c e

became e x t r e m e l y f l a t w i t h more g r a d u a l s l o p e s . I t s h o u l d be n o t e d t h a t i n t h e November 1974 s u r v e y t h e e n t i r c s p o i l p i l c

was Wcst of 72O 4 ' 50" \I w h i l e i n t h i s s u r v c y t h c r e i s a s i g n i f i c a n t amount of m a t c r i a l e a s t of t h a t l i n e .

Another i m p o r t a n t f e a t u r c i s t h e 21 m con-

t o u r NE of tlie p i l e had s h i f t e d t o SW i n d i c a t i n g some s h o a l i n g toward t h e East.

Betwecn F e b r u a r y 1975 and August 1975 s u r v c y s t h e p o s i t i o n of t h e r e f e r e n c e dumping buoy w a s moved 100 m southward.

Tne August 1975 topography

shows t h a t d r e d g e s p o i l s dumped w i t h t h e new r e f e r e n c e d r a s t i c a l l y a l t e r e d t h e s h a p e of tlic o r i g i n a l s p o i l p i l c c o n f i g u r a t i o n g i v i n g i t an e l l i p t i c a l s h a p e t r c n d i n g t o t h e SE ( F i g . 4 ) . The August 1975 s u r v e y shows t h a t t h e o r i g i n a l mound a p p e a r s t o have sett l e d 0.5

-

1 . 0 m , however, t h c r c a p p e a r s t o be no s i g n i f i c a n t i n c r e a s e i n

t h e d i a m c t c r of t h a t p o r t i o n of t h e p i l e .

Again, t h e r e scems t o be s p o i l

t r a n s f e r t o t h e c a s t a s s o c i a t e d w i t h t h e s h i f t of t h e 20 m contour a t t h c b a s e of t h e s p o i l mound.

I n F e b r u a r y 1975 t h e maximum e a s t w a r d e x t e n t of

t h i s l i n e w a s a p p r o x i m a t e l y 7 2 O 4 ' 48" w h i l e i n August 1975 t h e l i n e moved a b o u t 100 m e a s 2 w a r d . The a d d i t i o n a l s p o i l s dumped t o t h c S o u t h e a s t of t h e o r i g i n a l mound have formed a n o t h e r t o p o g r a p h i c h i g h t h a t i s c o n t i n u o u s w i t h t h e f i r s t r e a c h i n g a minimum d e p t h of 1 6 . 5 m w i t h s t c c p e r s l o p e s t o t h e S o u t h e a s t .

Thc f i n a l s u r v e y of Scptcmbcr 1975 i s c s s c n t i a l l y t h c same a s t h e August survey (Pig. 5 . ) month.

Very l i t t l e dumping had t a k e n p l a c c d u r i n g t h e i n t e r v e n i n g

111 t h e n o r t h p o r t i o n of t h c p i l e t h e d e p t h i n c r e a s e d a b o u t 60 cm.

However, tlir o v e r a l l d i m e n s i o n s of t h e p i l e a r e a p p r o x i m a t e l y t h e same a n d \ t h e s l o p c s a t t h e edge of t h c p i l c a r c somcwhat l e s s .

The bottom topography

100 m from tlie p i l e edge rcmaincd unchanged. From t h e e v i d e n c e shown by tlic bathymctry t h e d r c d g c s p o i l s were dumpcd o v e r a r e l a t i v e l y s m a l l a r e a and have g c n c r a l l y m a i n t a i n e d t h e i r o r i g i n a l

280 72.

l------

05'00'

04'30'

41' 6'30'

41. 8'00.

I

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@ '

-

CWTOU INTLRVAL im DATUM Y W

mom

RCFfRENCE BUOY

41. 1'30.

Fig.3.

Bathymetry of 4 February 1975

-

NLDS

72' O'OQ

OC30'

I

, ,"I

NEW L W D W DISPOSAL SITE CONTOU

INTERVAL im

D A T W YLW

,

,

0 REfEREWCC 8uOI

Fig.4.

41. 15'30'

Bathymetry of 7 August 1975

-

NLDS

281

lm

C O N T O M INTERVAL DATUM YLW

"

0 REFERENCE BUOY

.- -Fig.5.

Bathymetry of September 1975

configuration.

-

NLDS

T h e r e a p p e a r s t o bc a p c r i o d of s e t t l i n g o r r o m p a c t i o n f o l -

l o w i n g d i s p o s a l t h a t r c o u l t s i n a f l a t t c n i n y , and d e c p c n i n g o f t h e t o p o f the p i l c .

A s s o c i a t e d w i t h t h i s , t h e p i l c sccms t o s p r c a d s l i g h t l y and t h e

b o r d e r i n g s l o p e s bccomc l c s s s t c c p .

Thcsc e f f e c t s a r e probably a s s o c i a t e d

w i t h c o m p a c t i o n of t h e s e d i m e n t s . UNDERWATER TELEVISION OBSERVATIONS The b a t h y m e t r i c s u r v e y s o f tlic d r c d g c s p o i l s madc a t s c v e r o l months o r y e a r l y i n t e r v a l s i n d i c a t e t i l e l o n g term s t a b i l i t y o f t h e s p o i l p i l c , howe v e r , t h c s e s u r v e y s c a n n o t r c v c a l s m a l l s c a l e p r o c c s s e s t h a t may b e o c c u r r i n g on t h e s p o i l s u r f a c e .

C o n s e q u e n t l y , a s e r i e s o f s c u b a d i v e s w e r e made

w i t h a hand h c l d u n d c r w a t e r t c l c v i s i o n s y s t e m t o d i r e c t l y o b s c r v e tile s t a t e of t h e s p o i l s .

The d i v i n g c x p l o r a t i o n was l i m i t e d b e c a u s e o f t h e p o o r v i s -

i b i l i t y w h i c h r a n g e d f r o m o n e t o t h r e e mctcrs d e p e n d i n g upon t h e s t a t e o f t h e t i d e and s e a c o n d i t i o n s . The t e l e v i s i o n u s c d was m a n u f a c t u r e d by t h e R e a l 8 C o r p o r a t i o n , w i t h a w i d e a n g l e R i b i c o f f l e n s w i t h a f o c a l l e n g t h ( i n w a t e r ) o f 60 cnl.

Attached

t o t h e camera was a n u n d e r w a t e r l i g h t t o p r o v i d e s u f f i c i e n t i l l u m i n a t i o n f o r operations i n the turbid water.

The c a m e r a was c o n n e c t e d by 100 q of

n e u t r a l l y b u o y a n t c a b l c t o a Sony V i c d o t a p c R c c o r d c r a n d a Sony T c l c v i s i o n . The v i d c o p h o t o s r c v c a l c d t h a t two d i s t i n c t t y p c s o f s u r f a c c s wcrc g c n c r a l l y f o u n d o n t h e t o p - o f t h e s p o i l s p i l c ; a t h i n l a y c r of f i n c . s i l t t h a t i m m c d i a t c l y w e n t i n t o s u s p c i i s i o n wlicn d i s t u r b c d ; arid

c o n s i s t i n g of s m a l l g r a v c l s t o n c s and s h c l l i r n p c n t s .

Fcaturcless d

surface

Tlic b o u n d a r y be-

t w e e n t h c s e two t y p e s o f s u r f a c e s w a s o f t c n c x t r c m c l y s h a r p a n d c x t c n d c d f o r t e n s o f meters i n a s t r a i g h t l i n e . The q u c s t i o n a s t o w h e t h e r t h e c o a r s c m a t c r i a l i s a l a g d c p o s i t l e f t from winnowing of f i n e m a t e r i a l o r s i m p l y a d e p o s i t o f c o a r s e s p o i l s i s d i f f i c u l t t o answcr.

C c r t a i n l y winnowing o c c u r s , howcvcr,

t h c s c d i m c n t bc-

low t h c f i n e s u r f a c c was s i m i l a r t o t h e s u r f a c e m a t c r i a l , a l t h o u g h more coh e s i v e a n d c o n t a i n e d no s t o n c s o r s h c l l m a t c r i a l .

Similarly, the coarsc

m a t e r i a l e x t e n d s a t l e a s t t o 5-10 c m d c c p a l t h o u g h t h e r e i s a g e n e r a l i n c r e a s e i n s i l t y material w i t h d e p t n . A n o t h e r common f e a t u r c of t h e s p o i l s a r e a i s t h c p r c s c n r e o f l a r g e c l u m p s o f f i n e c o h c s i v c m a t e r i a l t h a t r a n g c i n d i a m e t c r f r o m a b o u t 10-300 cm.

S m a l l c h a n n e l s 10-20 cm d c c p wcrc f o u n d a r o u n d t h e c l u m p s p r o b a b l y

c a u s e d by e r o s i o n a l t u r b u l c n c c c r c a t c d by i n t c r a c t i o n o f t h c mcati f l o w w i t h clumps.

I t w a s f o u n d t h a t d u r i n g slaclc water a n a r c a o f f i n c , s i l t y s a n d

d e p o s i t c d on t h e d o w n s t r c a m s i d c o f t h e c l u m p s .

I t was a n area of f i n c ,

s i l t y s a n d d e p o s i t c d o n t h c d o w n s t r c a m s i d c of t h e c l u m p s ( i . c . ,

following

an ebb o r f l o o d t i d c ) f i l l i n g t h e e r o d e d c h a n n e l and c x t c n d i n g outward t o a p p r o x i m a t e l y o n c h a l f t h c d i a m c t c r of t h c c l u m p .

The p e r m a n e n c e o f t h i s

d e p o s i t i s q u e s t i o n a b l e a s i t w a s o n l y o b s c r v c d d u r i n g p e r i o d s o f low c u r r e n t s ( s l a c k t i d e ) ; t h e s e d i m e n t may b c r c s u s p c n d c d d u r i n g p e r i o d s o f strong current. These o b s e r v a t i o n s i n d i c a t c t h a t t h c s u r f a c c o f t h c s p o i l p i l e h a s somc

l i m i t e d small s c a l e e r o s i o n and d c p o s i t i o n proccsscs o c c u r r i n g , but t h a t i n g e n e r a l t h e c o h e s i v e n a t u r e of t h c d r c d g c s p o i l s t h c m s c l v c s p r e v e n t s any m a j o r e r o s i o n a n d t r a n s p o r t a t i o n of m a t e r i a l u n d e r n o r m a l c u r r c n t c o n d i tions. CONVLNTIONAI, CURRENT MEASUREMENTS Thc b a t h y m e t r i c s u r v c y s a n d u n d c r w a t e r t e l e v i s i o n p i c t u r e s p r o v i d c d a n e s t i m a t e o f t h e s t a b i l i t y of d r c d g c s p o i l s i n t h c m a r i n e e n v i r o n m e n t i n a q u a l i t a t i v e manner.

S i n c e t h c c r o s i o n and t r a n s p o r t of t h c s p o i l s is solc-

l y due t o t h e ambient c u r r e n t s .

I n f o r m a t i o n i s r e q u i r c d o f t h c mean r u r -

r e n t a n d t h e t i d a l f l o w t h r o u g h o u t t h e water c o l u m n .

F o r t h e l o n g term

283 m e a s u r e m e n t s c o n v e n t i o n a l t a u t w i r e moors w i t h t i m e a v e r a g i n g c u r r e n t meters ! u e r e i n s t a l l e d a t t h e d e s i r e d l o c a t i o ~ ~; ~si - p ~ r i u l i sUI 14-35 d a y s .

I l c a s u r e m e n t s were made a t b o t h t h e NLDS a n d EllDS d u r i n g t h e p e r i o d s 10 ,December 1974

-

22 J a n u a r y 1975 and 6 August 1 3 7 5 t o 2 Scptcmber 1975.

T h r e e c u r r e n t meter n o o r i n p were d c p l o y c d a r o u n d t l i c p i l e d u r i n g e a c h of t h e measurement p e r i o d s ( F i g . 6 ) .

Each m o o r i n g c o n t a i n e d t h r e e c u r r e n t

meters; o n e n e a r s u r f a c e ( 3 m) o n e l o c a t e d a t t h e a p p r o x i m a t e d e p t h of t h e t o p o f t h e P i l e ( 1 5 m); a n d o n e 1 . 5 a b o v e t h c b o t t o m .

72O04' SURFACE BUOY

I

I

72°04'

06'

Fig.6.

C o n f i g u r a t i o n o f C u r r e n t Mcters a r o u n d t h e NLDS area

The ENDECO Type 1 0 5 C u r r e n t I k t e r s were u s e d w h i c h a r e a x i a l - f l o w

ducted

i m p e l l e r s y s t e m s d e s i g n e d f o r s h e l f and e s t u a r i n e e n v i r o n m e n t a l s t u d i e s . The c u r r e n t s p e e d and d i r e c t i o n i s r e c o r d e d o n c a r t r i d g e l o a d c d 16 mm f i l m

at

4 hour

intervals.

Data r e d u c t i o n i s d o n c b y t h e m a n u f a c t u r e r , a n d d a t a

a n a l y s i s w a s performed a t NUSC. A summary of t h e mean b o t t o m c u r r e n t v e l o c i t y , mean maximum f l o o d a n d

e b b v e l o c i t i e s a n d the h o r i z o n t a l k i n e t i c c n e r g y of t h e mean f l o w i s shown i n Table I.

284 TAGLL I

MEAN BOTTOM CURRENT VELOCITY (cm/sec)

-

NLDS

NLDS

Dec. 1974 7.1 cm/sec lO8'T

EHDS

Aug. 1975 7.5 c d s c c 0 8 8 O

June-Aug. 1975 8.6 rmleec 240° 1'

'r

Mean/Maximum Ebb & Flood C u r r e n t Spceds (cm/sec) EBB

43.2 cm/sec

E

41.4 cm/sec FLOOD

E

28.6 cm/sec

E

33.3 d s e c

F

37.1 cm/sec

F

39.8 cmlsec

F

R e p r e s e n t a t i v e time s e r i e s p l o t s of t h e mean s u r f a c e ( 3 m) and bottom

(20 m ) c u r r e n t s a t NLDS d u r i n g tile 10 December 1974 - 2 2 J a n u a r y 1975 ( F i g . 7) p e r i o d s show a s t r o n g , s e m i - d i u r n a l t i d a l component a t b o t h t h e s u r f a c e and bottom

T h i s i s p r o b a b l y c h a r a c t e r i s t i c of t h e mean f l o w i n

t h i s area throughout t h e y e a r .

As can be s e e n , q u i t e d i f f e r e n t c h a r a r t e r -

i s t i c s o c c u r a t t h e s u r f a c e and t h e bottom; a s e x p e c t e d , t h e c u r r e n t s p c e d s peak much h i g h e r a t t h e s u r f a c e .

A progressive vector plot for the current

meters NU & NL i s shown a t 3 m and a t t h e bottom i s shown i n F i g . 8.

The

n e t t r a n s p o r t i s much h i g h e r a t t h e s u r f a c e a s i n d i c a t e d by t h c p r o g r e s s i v e

-

v e c t o r diagrams. 0

tE

s

90

so 30

W

n m

n

v

0

I

0' 0

I

2

1

3

1

-.

I

2

3

4

I

4

so

I

so

I

2

1

I

I

2

3

1

3

4

1

4

5

1

5

F i g . 7 . R e p r e s e n t a t i v e t i m e series o b s e r v a t i o n s of c u r r e n t speed and d i r e c t i o n a t NLDS: a . c u r r e n t v e l o c i t y a t 3 m ; b . c u r r e n t v e l o c i t y a t 20 m North array.

285

200 W 0

-

100

2

100-

0

0

i

:\

z

1

1

i

1

1

1

9

0

1

1

1

1

,

1

1

1

DISTANCE (KM)

DISTANCE (KM) Fig.8.

1

P r o g r e s s i v e v e c t o r p l o t (PVP) of c u r r e n t v e l o c i t i e s shown in F i g . 7

Left, PVP a t 3 m ; R i g ' l t , PVP a t 20 m . PART 11: HEASUREMENTS OF THE BOTTOM BOUNDARY LAYER INSTRUMENTATION The i n s t r u m e n t d e s i g n e d and c o n s t r u c t e d t o measure t h e c h a r a c t e r of t h e near-bottom c u r r e n t s i n t h e d i s p o s a l s i t e areas i s shown i n F i g . 9 .

The

s y s t e m c a l l e d t h e "Boundary Layer Thing" (BLT) c o n s i s t s of 3 d u c t e d impel-

l e r c u r r e n t meters (DICEl's) mounted on h o r i z o n t a l s h a f t s which p i v o t v i a b a l l b e a r i n g mounts a b o u t t h e v e r t i c a l s t a i n l e s s s t e e l s u p p o r t s h a f t .

Each

h o r i z o n t a l s h a f t a l s o supports an instrument cylinder containing recording electronics.

T h i s u n i t i s f a i r e d w i t h h o r i z o n t a l p l a t e s and s e r v e s a l s o a s

a t r a i l i n g vane from which t h e d r a g of t h e c u r r e n t d i r e c t s t h e DICM d i r e c t l y i n t o t h e mean f l o w .

The e n t i r e s y s t e m i s envcloped in a shrouded cage f o r

p r o t e c t i o n and f o r ease i n s h i p b o a r d lrandling.

Tlie 1 . 5 m d i a m e t e r s t e e l

b a s e p l a t e (weight a b o u t 1 7 3 k g ) s e r v e s t o anchor and s t a b i l i z e t h e system even i n s t r o n g c u r r e n t s . The vane h o u s i n g s were trimmed s o t h e i r s l i g h t n e g a t i v e buoyancy o f f s e t t h e ( i n w a t e r ) weight of t h e DICM's,

t h u s minimizing b e a r i n g f r i c t i o n

against the vertical shaft. The D I C M u n i t s developed by S h o n t i n g (1968) f o r wave o r b i t a l

286

k’ig.9. The a s s e m b l e d BLT s y s t e m showing t h e c a g e d h o u s i n g e n c l o s i n g the t h r e e DICMs

281 m o t i o n s c o n s i s t o f a s i x b l a d e d m i c a r t a i m p c l l c r s c o n t a i n i n g m i n i a t u r e (b.2 0 . 5 gm) A l n i c o m a g n e t s .

A s t h e i m p e l l e r r o t a t e s t h e magnet f i c l d g e n e r a t e s

a v o l t a g e p u l s c as t h e y c u t t h r o u g h a m i n i a t u r e p i c k u p c o i l p l o t t e d i n a s m a l l p i l l b o x mounted on t h c s i d e o f t h e c y l i n d e r .

The s i g n a l s a r e l e a d

t h r o u g h e x t e r i o r w i r e s t o t h e c l e c t r o n i c s i n t:ic v a n e h o u s i n g . Each DICM was c a l i b r a t e d i n a tow t a n k o v e r s p e e d s o f 3-100 c m / s e c and e x h i b i t a very l i n e a r responsc with pulse frcqucnce d i r e c t l y proportioncd t o flow speed.

The r e s p o n s e of t h c D I C M t o o f f - a x i s f l o w v a r i e s a s t h e co-

s i n e of t h e o f f - a n g l e

f r o m 0 t o a b o u t 80 d e g r e e s .

Thc d i s t a n c e c o n s t a n t o b t a i n e d from t h e c a l i b r a t i o n s ( i d e n t i c a l f o r a l l s e n s o r s ) was 3 c m / s e c p e r c y c l c / s e c o r 18 cm p c r i m p e l l e r r o t a t i o n .

Since

t h i s i s a b o u t e q u a l t o t h e g e o m e t r i c p i t c h o f t h c i m p e l l c r t h e h i g h l y res p o n s i v e c h a r a c t e r o f t h e d u c t e d mctcrs is e v i d e n t . Thc r c s p o n s e o f t h e D I C M t o f l u i d a c c c l e r a t i o n s i s s p c c i f i c d by t h c r e s p o n s e d i s t a n c e ; t h e a x i a l l e n g t h of w a t c r p a r t i c l e s t r a v e r s e f o r tlie DICM o u t p u t t o r e g i s t e r 63% of t h e c h a n g c t o a s t e p i n c r c a s c i n s p e e d .

The

a c t u a l t r a v e r s e d i s t a n c e f o r d e t e c t i o n of t h e c h a n g e o f v c l o c i t y a l o n g t h e a x i a l f l o w must b c n o w c v c r , a t l e a s t t w o p u l s e s e p a r a t i o n s , o r 6 cm.

More-

o v e r , t h c p h y s i c a l d i m e n s i o n s of t h e DICM r e a l i s t i c a l l y l i m i t i t s ' a b i l i t y t o r c g i s t c r small velocity fluctuations.

Thus, t h e c y l i n d e r d i m e n s i o n s of

10 cm d i a m e t e r and 1 5 cm l e n g t h p r o h i b i t r e g i s t c r i n g t u r b u l e n t s c a l e s much smaller t h a n 20-30

C?,

along the flow a x i s .

DATA LOGGING AND PROCESSING

The p u l s e s i g n a l s o u t p u t from t h c DICM a r c t r a n s m i t t e d i n t o t h e v a n c h o u s i n g t o a c i r c u i t t o r e g i s t e r c a c h s i x t h p u l s e and t h e n t o a wave p e r i o d processor.

T h i s p r o d u c c s a s c r i e s of d i g i t a l v a l u e s p r o p o r t i o n a t c t o t h e

t i m e s p a c i n g b c t w c c n e a c h p u l s e p a i r w h i c h i s r c c o r d c d on a Mcmodyne Model

201 d i g i t a l c a s s e t t e r e c o r d c r .

Tile e n t i r e e l e c t r o n i c s , i n c l u d i n g a t i m e

s e q u e n c e s w i t c h and DC b a t t e r y s u p p l y i s c o n t a i n e d w i t h i n e a c h v a n e h o u s i n g Each s y s t e m b e i n g i n d e p e n d e n t .

Upon r e t r i e v a l o f t h e BLT e a c h c a s s e t t e

t a p e i s r e a d and c o n v e r t e d t o 7 t r a c k m a g n e t i c t a p e t o b e a n a l y z e d on a CDC

3300 Computer. The s a m p l i n g r a t e of t h e BLT c a n r c c o r d t h e D I C N p u l s c s c o n t i n u o u s l y o r b y usc o f t l i e s w i t c h i n : ; c i r c u i t s a m p l e a t g i v e n i n t e r v a l s a t p r e s e t spacinl;.

The amount o f d a t a ( i . c . ,

p u l s c s ) rccordcd is l i m i t e d by t h e t a p c

c a p a c i t y ; rougiily 1 6 , 0 0 0 d i z i t a l villucs o f time i n t e r v a l s p c r t a p c .

Note

t h e f a s t c r t m mean c u r r e n t t h e s h o r t e r t l i c r e a l t i m e r e c o r d , e.g.,

fq'r a

288 c u r r e n t speed of 90 cm/sec t h e r c c o r d i n g t i m c i s a b o u t 6 h o u r s ; f o r 10 cm/sec, 54 h o u r s .

For o u r a p p l i c a t i o n w e chose a r e c o r d i n g c y c l e of 17.5

This i n t e r v a l p r o v i d e d a b o u t 7 days re=

minutes on and 52.5 m i n u t e s o f f .

c o r d i n g f o r t h e normal t i d a l c u r r e n t s . DATA REDUCTION AND ANALYSIS

Since d a t a p o i n t s ( i . e . ,

instantancous velocity values) a r e ootained at

t h e r a t e of one f o r c v c r y 1 8 cm advance of w a t e r through t h e D I C M , t h e res u l t a n t sequence i s a p p r o p r i a t c f o r s p a t i a l / w a v c n u m b c r s p e c t r a l a n a l y s i s . The e n t i r e r e c o r d i s d i v i d e d i n t o non-overlapping scgments o f 120 p o i n t s e a c h ( z e r o f i l l i n g t h e l a s t scgment i f n e c e s s a r y ) .

Thc c n c r g y d e n s i t y

spectrum is found f o r e a c h segment and t h e r e s u l t i n g s p e c t r a a r e ensemble averaged t o o b t a i n a f i n a l s i n g l c e n c r g y d c n s i t y spectrum f o r t h e r e c o r d . Before s p e c t r a l a n a l y s i s f o r e a c h segment, w i l d d a t a p o i n t s a r e r e p l a c e d w i t h t h e a r i t h a t i c a v e r a g e of t h e good p o i n t s f o r t h a t segment and t h e a r i t h m e t i c a v e r a g e i s t h e n removed from t h e segment.

A 10%: t a p e r c o s i n e

d a t a window i s a p p l i e d and t h e e n e r g y d e n s i t y s p e c t r u m is c a l c u l a t c d u s i n g t h e FFT a l g o r i t h m .

The s p e c t r a a r e normalized s u c h t h a t t h e a r e a under t h e

curve i s equal t o t h e variance

0

of t h e o r i g i n a l series.

A p l o t of t h e e n c r g y d e n s i t y s p c c t r u m i n l o g / l o g form i s g e n e r a t e d .

The

o b j e c t i v e i n computing e n e r g y d e n s i t y s p e c t r a from t h e BLT d a t a is t o e s t i -

mate t h e r a t e of d i s s i p a t i o n of t u r b u l e n t k i n e t i c e n e r g y by v i s c o s i t y u s i n g t h e Kolmogoroff i n e r t i a l s u b r a n g e h y p o t h e s i s .

In t h e i n e r t i a l s u b r a n g e t h e

energy d c n s i t y spectrum f o r t h e l o n g i t u d i n a l v e l o c i t y component i s e x p e c t e d t o b e of t h e form @(Xi

where €

= 0.137 f 2/3 ~ 5 / 3

i s t h e d i s s i p a t i o n r a t e and k i s t h e wavenumber ( c y c l e / c m ) .

Among

t h e r e q u i r e m e n t s of t h e t u r b u l e n t f i e l d f o r Eq. ( 1 ) t o b e a p p l i c a b l e i s t h a t Reynold's number f o r t h e mean motion be l a r g e and t h a t t h e t u r b u l e n c e b e homogeneous and i s o t r o p i c t h r o u g h o u t t h e s m a l l s c a l e r a n g e , s p e c i f i c a l l y , t h e n e c e s s a r y c o n d i t i o n f o r t h e e x i s t e n c e of a n i n e r t i a l s u b r a n g e i s p r e c i s e l y ( B a t c h e l o r , 1960)

(y)

3/8 > > l

289 where U i s t h e R1.E v a l u e of tile t u r b u l e n t v e l o c i t y .

is t h e l e n g t h cor-

r e s p o n d i n g t o t h e wavenumber a t which t h e maximum i n t h e e n e r g y d e n s i t y spectrum o c c u r s and

v

=

1.3 x lo-'

cm2/sec is t h e k i n e m a t i c v i s c o s i t y .

Using a v a l u e of 4 . 0 cm/sec f o r U ( r e p r e s e n t a t i v e of t h e s t a n d a r d d c v i a t i o n s f o r t h e v e l o c i t y o b t a i n e d from t h e BLT measurements) and 40 cm f o r

4

( t h e energy containing s c a l e s should be approximately equal t o the

p r o d u c t o f t h e d i s t a n c e from t h e bottom and Von Karman's c o n s t a n t , 0 . 4 ) .

(gy'8P 34

(3)

s o t h a t t h e p r e c e d i n g c o n d i t i o n i s somewhat s a t i s f i e d and a l i m i t e d i n e r t i a l s u b r a n g e can b e e x p e c t e d . Thc observed s p e c t r a a r e , i n g e n e r a l , c o n s i s t e n t w i t h a -5/3 power law f o r a range of s c a l e s around 1 meter, a l t h o u g h t h i s v a l u e is l a r g e r t h a n would be e x p e c t e d f o r a l e g i t i m a t e i n e r t i a l s u b r a n g e a c c o r d i n g t o t h e prec e d i n g argliment.

The more r a p i d d e c r e a s e i n energy d e n s i t y w i t h i n c r e a s -

i n g wavenumber a t wavelengths g r e a t c r t h a n 0.01 r y c l c s / c m i s a t t r i b u t e d t o t h e DICM r e s p o n s e c h a r a c t e r i s t i c s .

The s p e c t r a i n d i c a t e no s i g n i f i c a n t i n -

p u t of e n e r g y a t t h e h i g h e r wavenumbers and i f t h e e n e r g y d e n s i t y spectrum

i s a monotonic, d e c r e a s i n g f u n c t i o n o f wavenumber w i t h a power law nowhere g r e a t e r t h a n -5/3 t h e n t h e a c t u a l d i s s i p a t i o n r a t e s h o u l d n o t exceed t h e v a l u e s d e t e r m i n e d from t h e s p e c t r a , t h u s p r o v i d i n g an upper l i m i t f o r t h e Reynold's stress and f r i c t i o n v e l o c i t y . The e n e r g y d i s s i p a t i o n r a t e f o r t h e r e c o r d i s e s t i m a t e d from t h e ensemb l e average energy density spectrum using

e v a l u a t e d f o r K = 0.01.

Every r e c o r d t h u s y i e l d s v a l u e s f o r t h e a v e r a g e

s p e e d , v a r i a n c e (and s t a n d a r d d e v i a t i o n ) and d i s s i p a t i o n r a t e . The d a t a o b t a i n e d from t h e BLT a r e t h e n r c l a t c d t o t h e mean c u r r e n t f i e l d and i t s ' e f f e c t on t h e bottom through c a l c u l a t i o n of t h e f r i c t i o n v e l o c i t y (U,). FRICTION VELOCITY Various techniques a r e a v a i l a b l e f o r estimating the f r i c t i o n veloFity

290

u* 3 where

7

1.

i s t h e K e y n o l d s ' s t r c s s and

(5)

p

is t h e water d e n s i t y .

L o g a r i t h m i c V e l p-c i-~ t y P r o f-~ ilc. I f t h e mean v e l o c i t y p r o f i l e i s

l o g a r i t h m i c t h e n , a c c o r d i n g t o P r a n d t l ' s mixin;:

length thcory (Schlicting,

1960).

for w h i c h

u2 - 8, u*l

2. tlie

Quadrcitir -

-

S-___ t r e s s Lciw.

5 . 7 5 log (z2/z,)

T h e r o u z h n c s s , h e i g h t , Zo, is d e f i n e d a s

d i s t a n c e above t h e b o t t o m a t w h i c h t h e m e a n v e l o r i t y i s z e r o .

6 then

,

u*2log(;)

U(Z) =

5.75

u*2

5 . 7 5 log (z/zo)

E -

and

'

=

'*2

w h e r e t h e d r a g coefficient

2

=

(7)

[

5 . 7 5 log (Z/ZO)

From E q .

291 Measurements by ( S t e r n b c r z ,

1969, 1 9 7 2 ) i n d i c a t e t h a t a t a h e i g h t o f 100 cm

a b o v e t h e b o t t o m CD i s a p p r o x i m a t e l y 3.1 x

T = p(3.1 x

therefore

qoo

The r o u g h n e s s h c i g l i t c o r r e s p o n d i n g t o t h i s v a l u e o f CD i s 7 . 5 5 x 10The v a l u e s o f CD d c t c r r , d n c d f r o m (10) u s i n g Zo a n d a t 2 5 cm a r e 3 . 5 5 x

3.

Dissipation katc.

and 4.76 x

-

7.58 x

2

cm.

cm a t 6 2 . 5 cm

respcrtively.

I f a b a l a n c e is a s s ume d t o e x i s t b e t w e c n p r o -

d u c t i o n a n d d i s s i p a t i o n of t u r b u l c i i t k i n e t i c e n e r g y i n t h e b o u n d a r y l a y e r (Hinze, 1959) t h e n

from which

I f P r a n d t l ' s mixing l e n g t h h y p o t h e s i s is also v a l i d then

w h e r e K = 0 . 4 is Von Karman's

constant.

Sincc T/p

=

U,2

,

Eq.(14)

yields

I f tile d i s s i p a t i o n rates d e t e r m i n e d f r o m t h c s p e c t r a a r e a c c u r a t e t h e n Eq.

(13) g i v c s p o t e n t i a l l y tlie b e s t mct hod f o r e s t i m a t i n g tlic f r i c t i o n v e l o c i t y o r b o t t o m stress b e c a u s e : d c p c n d e n c c on a l o g a r i t h m i c v e l o c i t y p r o r i l e i s n o t n e c e s s a r y a n d ; a n e s s e n t i a l l y t u r b u l e n t q u a n t i t y is f o u u d f r o m t u r b u -

292 l e n c e measurements i n s t e h d of mean flow mcasurements o n l y . Because of b e a r i n g p r o b l e m s no more t h a n two D I C M ' s o p e r a t e p r o p e r l y a t t h e same t i m e s o i t was n o t p o s s i b l c t o d c t c r m i n e i f t h e v e l o c i t y p r o f i l e s were a c t u a l l y l o g a r i t h m i c .

A t Lest, t h e mean v e l o c i t i e s could o n l y be

p l o t t c d on s e m i l o g g r a p h papcr and t h e s t r a i g h t l i n e s e x t r a p o l a t e d t o z e r o v e l o c i t y t o f i n d t h e roughness h e i g h t s , which v a r i e d from 3 t o 5 cm, somcwhat l a r g e r t h a n b u t n o t i n c o n s i s t e n t w i t h v a l u e s o b t a i n e d by ( S t e r n b e r g , 1972). For a l l c a s e s where r e l i a b l e d a t a was o b t a i n e d s i m u l t a n e o u s l y from two D I C M ' s t h e f r i c t i o n v e l o c i t y was c a l c u l a t e d from b o t h Eq.

( 5 ) and ( 1 3 ) .

For t h e s e c a s e s t h e f r i c t i o n v e l o c i t y was a l s o c a l c u l a t e d i n d e p e n d e n t l y f o r b o t h DICll's u s i n g Eq.

(5) and Eq. (11) w i t h t h e a p p r o p r i a t e d r a g c o e f f i -

i e n t , depending on t h e h e i g h t of t h e DICM.

For t h e remaining c a s e s where

o n l y one DIW gave r e l i a b l e d a t a t h e f r i c t i o n v e l o c i t y was found u s i n g Eqp. (15) and ( 1 1 ) . RESULTS The ULT was p l a c e d a t t h e NLDS f o r a p e r i o d of one week b e g i n n i n g 22 September 1975 and a t t h e EHDS f o r 2!5 days b e g i n n i n g on 4 August 1975.

In

b o t h c a s e s one of t h e D I C M ' s was n o t o p e r a t i n g due t o e l e c t r o n i c malfunct i o n s t h a t o c c u r r e d w h i l e t h e i n s t r u m e n t was on t h e bottom.

A t t h e NLDS

t h e d a t a w a s r e c o v e r e d from t h c meters a t 100 cm and 25 cm above tlie b o t tom, w h i l e a t t h e EHDS t h e meters a t 62.5 and 25 cm p r o v i d e d good d a t a . R e p r e s e n t a t i v e t i m e s e r i e s p l o t s of s p e e d a t t h e 25 cm and 100 cm l e v e l s

are shown i n Fig:. 10.

The e n e r g y s p e c t r a ( F i g . 11) computed f o r b o t h rec-

o r d s are v e r y s i m i l a r w i t h s i m i l a r t o t a l e n e r g y d e n s i t y l e v e l s and t h e de-

crease of e n e r g y w i t h i n c r e a s i n g f r e q u e n c y i s t h e same.

The c u r r e n t d a t a o b t a i n e d from t h e BLT i s most e a s i l y r e l a t e d t o t h e e f f e c t of t h e c u r r e n t s on t h e bottom through t h e f r i r t i o n v e l o c i t y o r Reynolds stress (Cq. 5 ) . I f t h e boundary s h e a r stress

To

r e q u i r e d t o e r o d e t h e sediment i s

known t h e n tlie t h r e s h h o l d f r i c t i o n v e l o c i t y the

U,

u,,

can b e c a l c u l a t e d .

If

v a l u e s computed froin t h e c u r r e n t d a t a a l o n e are g r e a t e r t h a n t h i s

threshhold f r i c t i o n v e l o c i t y , then e r o s i o n w i l l occur, i f n o t , the sediment can be c o n s i d e r e d s t a b l e .

293

2

40

z

9

30

t

l3

z 0

2o 10

' 0

20

+o

6.0

8.0

100

I20

U Q I60

10.0

TIME (MINUTES)

Fig.10.

BLT record at 25 cm (upper) and 100 cm (lower)

I

I -I

-2 LOG WAVEWM9ER

Fig.11.

(CY-')

Wavenumber spectrum for BLT current speed 100 cm above bottom

294

Measurements in a flume tank at the Massachusetts Maritime Academy have shown that for dredge spoils taken from the Thames River a mean velocity of approimately 52.5 cm/sec at a height of 15.25 cm above the bottom (half the height of the flume tank) was sufficient to cause significant erosion and material transport., By applying the Quadratic Stress Law to this data it is possible to calculate the threshhold friction velocity.

From Equation

'10, the drag coefficient Co at 15.24 cm is 5.69 x

T~ = p C D

d = 15. 68'dy/crn2

16 dy/cm

2

.

and from Equation ( 5 )

U,o

=

3.96 cm/sec

.

The major objective of the BLT, therefore, is an accurate assessment of the friction velocity or stress values for the NLDS and the EHDS to determine whether or not the currents in either location are large enough to produce a friction velocity greater than 4 cm/sec or a stress greater than

16 dy/cm2. A summary of the BLT measurements at the NLDS are presented in Table 2 and those from the EHDS in Table 3 .

Wherever possible, the friction velo-

city for each record was calculated by the different methods discussed above. The variability of the friction velocity among these estimates for any record and the variability between records is not unexpected.

The reasons

for this variability are:

(1) The assumption of a logarithmic velocity profile is probably not Previous work by

valid in approximately 15% of the cases given here.

others has indicated that up to 40% of the profiles measured were not logarithmic. (2)

The drag coefficient used in the quadratic stress equation is known

to vary from less than 2 x

to more than 4 x 10-3 depending on the bed

configuration with corresponding variation in the roughness height. (3)

Von Karman's constant used in methods 5 and 6 is unknown for fluids

containing suspended sediment. Furthermore, it should be noted that the quadratic stress law is derived

296 from t h e l o g a r i t h m i c v e l o c i t y p r o f i l e e q u a t i o n and t h e r e f o r e i s n o t a t r u l y i n d e p e n d e n t c a l c u l a t i o n of f r i c t i o n v e l o c i t y f o r t h e same roughness The d i f f e r e n c e i n t h e methods i s i n t h e v a l u e s of t h e roughness

height.

heights used.

The d r a g c o e f f i c i e n t (CD) i n t h e q u a d r a t i c stress e q u a t i o n

i s a n e m p i r i c a l v a l u e of 3.1 x

s p e c i f i e d f o r a h e i g h t of 100 cm which

c o r r e s p o n d s t o a roughness h e i g h t o f .0758 c m .

However, p l o t s of mean

v e l o c i t y p r o f i l e i n d i c a t e roughness h e i g h t s an o r d e r of magnitude g r e a t e r than t h i s value.

C o n s e q u e n t l y , f r i c t i o n v e l o c i t i e s c a l c u l a t e d from t h e

q u a d r a t i c s t r e s s e q u a t i o n a r e , i n most c a s e s , s m a l l e r t h a n t h o s e c a l c u l a t e d from t h e l o g a r i t h m i c v e l o c i t y p r o f i l e e q u a t i o n . Because of t i m e l i m i t a t i o n s o n l y one t h i r d of t h e e n e r g y d e n s i t y s p e c t r a

were examined t h r o u g h t h i s method t o o b t a i n k i n e t i c e n e r g y d i s s i p a t i o n rates.

F r i c t i o n v e l o c i t i e s c a l c u l a t e d t h r o u g h t h i s method t e n d t o a g r e e

more c l o s e l y w i t h v a l u e s c a l c u l a t e d from t h e q u a d r a t i c stress e q u a t i o n t h a n t h o s e o b t a i n e d from t h e l o g a r i t h m i c p r o f i l e method. The f r i c t i o n v e l o c i t i e s c a l c u a l t e d from t h e d i s s i p a t i o n r a t e s do n o t depend on v a l u e s of e i t h e r Von Karman's c o n s t a n t o r t h e d r a g c o e f f i c i e n t (CD) i n t h e q u a d r a t i c stress e q u a t i o n o r on a l o g a r i t h m i c v e l o c i t y p r o f i l e . T h e r e f o r e , t h e s e v a l u r s a r e a c o m p l e t e l y independent measure of f r i c t i o n v e l o c i t y and a r e c o n s i d e r e d t o be t h e most r e l i a b l e e s t i m a t e s . A t b o t h t h e EHDS and NLDS t h e e n e r g y d e n s i t y s p e c t r a and d i s s i p a t i o n

rates f o r t h e lower D I C M ' s are g e n e r a l l y g r e a t e r t h a n t h o s e f o r t h e upper m e t e r , which f o r a c o n s t a n t ( w i t h h e i g h t ) f r i c t i o n v e l o c i t y i s c o n s i s t e n t with theory. If 9

u,

=

( x z q 1/3

where K i s Von Karman's c o n s t a n t e q u a l t o 0 . 4 , Z t h e h e i g h t above t h e b o t tom and

C

is the dissipation rate.

Then f o r a c o n s t a n t

U,

and

which i s g r e a t e r t h a n rates ( C

C2

since

Z2

is g r e a t e r than Z 1 .

the dissipation

) f o r t h e EHDS f o l l o w t h i s r e l a t i o n s h i p q u i t e c l o s e l y ; t h o s e

a t t h e NLUS n o t a s w e l l .

296 The v a l u e s f o r f r i c t i o n v e l o c i t y o b t a i n e d f r o m e q u a t i o n (13 ) c a l c u l a t e d from t h e d i s s i p a t i o n r a t e method a l o n e , b u t s i m i l a r t o t h o s e o b t a i n e d from t h e l o g a r i t h m i c v e l o c i t y p r o f i l e s .

This suggests t h a t t h e value of

0 . 4 f o r Von Karman's c o n s t a n t i s h i g h s i n c e a l o w e r v a l u e would r e d u c e t h e

u,

from t h e l o g a r i t h m i c v e l o c i t y p r o f i l e e q u a t i o n t o v a l u e s t h a t would

b e more i n a g r e e m e n t w i t h t h e

u,

from t h e o t h e r m e t h o d s .

F u t u r e work

a l o n g t h e s e l i n e s m i g h t g i v e a n e s t i m a t e of Von Karman's c o n s t a n t f o r w a t e r s c o n t a i n i n g suspended m a t e r i a l . An e x a m i n a t i o n o f T a b l e s 2 and 3 i n d i c a t e s t h a t most o f t h e f r i c t i o n v e l o c i t i e s m e a s u r e d a t b o t h t h e NLDS and t h e EHDS a r e less t h a n 2 c m / s e c and t h a t a p r a c t i c a l upper l i m i t might be set a t approxi mat el y 2.5 cm/sec. T h i s v a l u e i s o b v i o u s l y much less t h a n t h e 4 c m / s e c m e a s u r e d a s t h e t h r e s h hold f r i c t i o n v e l o c i t y i n t h e flume t a n k , hence i t r a n be concluded t h a t t h e s p o i l s d e p o s i t e d a t t h e NLDS a r e c o m p a r a t i v e l y s t a b l e u n d e r n o r m a l cond i t i o n s and v e r y l i t t l e e r o s i o n , i f a n y , s h o u l d o c c u r d u e t o r u r r e n t f l o w .

CONCLUSIONS

The r e s u l t s o f t h i s s t u d y d e m o n s t r a t e t h a t t h e e x i s t i n g BLT i s a u s e f u l d e v i c e w i t h s e v e r a l l i m i t a t i o n s , f o r s t u d y i n g t h e b o t t o m b o u n d a r y l a y e r and w i t h f u r t h e r development h a s t h e p o t e n t i a l f o r b e i n g a n e x c e l l e n t boundary layer instrument.

S p e c i f i c a l l y , measurements a r e o b t a i n e d of o n l y t h e

l o n g i t u d i n a l t u r b u l e n t v e l o c i t y component a n d , a l t h o u g h t h i s i s a n o r d e r o f m a g n i t u d e improvement o v e r t e c h n i q u e s m e a s u r i n g o n l y t h e mean f l o w , t h e Reynolds stress is s t i l l d e te r m in e d i n d i r e c t l y .

The n e x t v e r s i o n o f t h e

BLT w i l l a l l o w measurement o f b o t h t h e v e r t i c a l and h o r i z o n t a l v e l o c i t y components s o t h a t t h e R e y n o l d s s t r e s s c a n b e d e t e r m i n e d d i r e c t l y .

Sensors

o t h e r t h a n t h e DICM a r e b e i n g i n v e s t i g s t e d , f o r e x a m p l e , t h e e l e c t r o m a g n e t i c c u r r e n t meter, i n o r d e r t o a c h i e v e improved s m a l l s c a l e r e s o l u t i o n and a l o w e r v e l o c i t y t h r e s h h o l d ; t h e p r e s e n t BLT r e q u i r e s a mean c u r r e n t of 1 5 cm/sec o r g r e a t e r t o y i e l d r e l i a b l e measurements whereas t h e n e x t v e r s i o n of t h e B1.T w i l l b e d e s i g n e d t o o p e r a t e a t a much l o w e r v a l u e ; c o n s e q u e n t l y i t s h o u l d a l s o b e p o s s i b l e t o e x a m i n e t h e e f f e r t s o f wave a c t i o n on t h e b o t t o m w i t h o r w i t h o u t t h e p r e s e n c e o f a mean c u r r e n t , w h i c h ( e s p e c i a l l y d u r i n g s t o r m c o n d i t i o n s ) may c o n t r i b u t e h e a v i l y t o s e d i m e n t t r a n s p o r t .

TABLE I1

%oo*Q 22

Sep

’75

1341

cmlsec

37.453.5

UZ5*U

Q’UlOO

- NEW u’u25

cmlsec

30.5%4.1

.u9

LONDON DISPOSAL S I T E

Aii

U*l

u*2

u*4

cmlsec

cm/sec

cm/scc

cm/scc

u*5

E

cm/sec cmlsec

.13

6.9

2.0

2.1

2 .o

2.2

.27

3.1

2.2

1.5

2.0

.21

1451

37.455 .O

28.554.6

.13

.16

10.6

1601

27.952.6

16.052.6

.09

.16

6.6

1.9

1.2

1.1

1.1

.04

.21

6.2

1.8

1.2

1.1

1.4

.07

1711

21 .9+2 .8

15.723.3

.13

1821

6.754.9

.73

0.4

1931

22.352.5

.11

1.2

2041

36.7+4.4

.12

2 .o

2151

22.622.8

.12

1.3

2301

10.2k1.3

.13

0.6

0011

S.7+6.2

.71

0.5

0121

14.652.2

.15

0.8

0231

31.124.3

27.154.9

.14

.18

4 .O

1.2

1.7

2.3

2.2

.26

0341

26.623 .5

19.753.1

.13

.16

0451

25.153.3

.13

.17

5.9 6.6

1.7 1.9

1.4 1.4

1.3 1.5

1.8

18.753.1

2.0

.14 .21

0601

8.253.9

6.552.7

.48

.42

1.7

0.5

0.5

0711

14.251.9

.26

8.2

2.4

0.8 1.4

2 .o

2.4

.33

23 Sep ’75

0821

24.354.6

0931

24.6T3.6

.13 16.154.2

.19 .15

1.4

3

’I

Aug. ‘ 7 5

TJ25fa

T725fu

cm/scc

cm/scc

1837

27.123.2

21.753.1

1947

11.652.1

2.353.0

TABLLIII

u/Uloo

-

EAST HOLE DISPOSAL SITES

u / U ~ ~A

0

U*1 cm/scc

.ll

.18

u*2 cm/sec

cmtscc

.14

5.4

2.4

1.6

1.o

1.28

3.3

1.4

0.7

0.7

cm/scc

c m2/SCC 3

1.4

.07

2057 2207

26.e3.0

16.723.0

.ll

.17

9.3

4.1

1.6

2317

33.e3.7

26.953.6

.ll

.13

6.1

2.7

2 .o

1.2

1.5

-08

0027

17.852.3

14.2+2 - .9

.15

.20

3.6

1.6

1.1

0.9

1.o

.02

0137

14. e 2 . 2

10.952.3

.15

.20

3.1

1.4

0.8

1517

21.424.2

15.224 .2

.19

.27

6.2

2.7

1.3

1.5

1617

32 .M_3.3

26 .2&5.4

.10

.20

5.8

2.5

1.9

1.2

1.4

.07

1757

34 .0+3 .5

28.123.7

.10

.12

5.9

2.6

2 .o

1.1

1.4

.07

1907

34.855.2

27.554.8

.14

.17

7.3

3.2

2.1

1.2

1.9

.16

2017

27.e5.4

19.754.0

.19

.20

8.1

3.5

1.7

0.8

1.2

.03

2127

11.153.5

2237

13.823.2

12.422.7

.23

.21

1.4

0.6

0.8

2347

26.e3.3

4.5+3.8

.12

-17

4.5

2 .o

1.6

0.9

1.2

.03

5 Aug.

‘75

.31

299 ACKNOWLEDGEMENTS

We are i n d e b t e d t o Mr. John Roklan f o r d e s i g n of t h e BLT e l e c t r o n i c s and t o D r . David S h o n t i n g f o r h i s h e l p i n p r e p a r i n g t h e m a n u s c r i p t . T h i s work was s u p p o r t e d by U. S . Army Corps of E n g i n e e r s , Waltham, M a s s a c h u s e t t s and t h e U. S. Naval F a c i l i t i e s E n g i n e e r i n g Command, Philadelphia, Pennsylvania. REFERENCES Batchelor, G. K . ,

1960.

The Theory o f Homogeneous T u r b u l e n c e

Cambridge U n i v e r s i t y P r e s s , London H i n z e , J. O . ,

1959.

Turbulence

McGraw-Hill Book Company, N e w York Schlichting, H.,

1968.

Boundary l a y e r t h e o r y

McGraw-Hill Book Company, New York S h o n t i n g , D. C . ,

1968. A u t o s p e c t r a of Observed P a r t i c l e Motions i n Wind

Waves,

J. Mar. R e s . Vol 26(1):43-65 S t e r n b e r g , R. W . ,

1968.

F r i c t i o n f a c t o r s i n t i d a l channels with d i f f e r i n g

bed r o u g h n e s s . Marine Geology 6:243-260 S t e r n b e r g , R. W . ,

1972. P r e d i c t i n g i n i t i a l m o t i o n and b e d l o a d t r a n s p o r t o f

sediment p a r t i c l e s i n t h e shallow marine environment.

In:

S h e l f Sediment T r a n s p o r t , S w i f t , Duane and P i l k e y , Eds.

Dowden, H u t c h i n s o n and Ross, I n c . , S t r a n d s b u r g , PA 61-82

This Page Intentionally Left Blank

301 SUBJECT INDEX 62,

Autocorrelation,

63,

68,

approach, 2 2 1 ,

70.

230,

232,

235.

load Transport Meter, 2 2 9 ,

230,

232,

Bagnold's

123,

Bearing flows,

124.

Bed

- form, 2 2 5 , 2 3 0 , 2 3 2 .

-

load, 2 3 0 ,

232,

235. 235.

Bottom

-

boundary layer, 2 7 , 99, 209,

-

103-105, 237.

107,

239-241,

coefficient, 2 , current, 2 3 7 , friction, 4 ,

29,

109, 244,

24,

43,

240,

49,

40,

115,

245,

16, 40,

239,

37,

30, 110,

42,

247,

45,

120,

118,

51,

54,

153-157,

252,

275-277,

275,

284.

285,

56,

83,

159-162, 296.

47.

242,

244.

205.

118, 2 2 1 .

homogereous layer,

- m i x e d l a y e r , 101, 1 0 2 .

-

topography, 2 3 8 ,

240.

Boundary condition, 2 , 146,

147,

165,

4-6, 169,

168,

Boundary layer, 5 9 - 7 9 , 136,

-

142,

149,

atmospheric,

103,

benthic, 8 3 ,

86,

bottom,

83,

166,

176,

94,

184,

107-112,

129,

110,

18, 2 7 - 3 2 ,

175-177, 84,

170,

87,

16,

13,

185,

36,

40,

47,

132,

185, 215.

115, 194,

123,

118,

198, 232,

131,

239,

256.

130.

96,

209,

218.

see bottom boundary layer.

surface, 2 7 - 2 9 ,

37,

turbulent, 9 9 ,

101.

42,

Boussinescq approximation, Brunt-Vaisala

45,

51,

170,

frequency, 5 4 ,

165,

170.

172.

56,

108, 1 5 5 ,

160-lh2.

B-spline,

1-5,

14-18,

Buoyancy,

167,

170,

177,

179,

182,

184, 256.

76-79,

83,

209,

221,

232,

Bursting, 6 1 ,

24,

Chebyshev polynomials, Chlorophyll-a

27,

14,

36. 235.

15.

concentration,

Coriolis parameter, 4 9 ,

30-32,

108,

255,

257,

259,

263,

265.

156,

172,

187,

191,

237.

Current

- measurements , 61, 6 2 , 83, 8 6 , 9 0 ,

92-95,

275,

276,

282.

302

-

meter, 83, 244,

-

86,

251,

profile, 103,

104,

143,

145,

Cyclosonde,

87,

259,

I,

276,

15,

153,

101,

187,

283-285,

16,

18,

191,

198,

204,

240-242,

296.

24,

27,

28,

36,

38,

42,

44,

45,

47,

107,

115,

118,

120,

124,

126,

132,

134,

136,

147,

194,

198,

230,

240,

251,

272,

275,

290-292.

247,

290-92.

103-107,

115,

118.

104,

Density distribution,

140-

194,

198,

241,

261.

Diffusion coefficient, s e e eddy diffusivity. 120,

Drag coefficient, Eddy, 62-65,

-

141,

-

84,

-

157,

107-109,

145,

237,

239,

158,

166,

263,

265,

266.

129,

130,

133,

135,

136,

139-

statistical independence, 70. 1-4,

viscosity, 47,

-

97,

143.

171.

102,

131,

6,

bottom, 56,

158,

16,

18,

22-25,

27-31,

40,

42,

43,

45,

191.

157,

159,

boundary,

7,

136,

153,

Ekman layer,

-

96, 102,

diffusivity,

142,

202.

187,

165,

188,

170,

194,

198,

204,

205.

178.

frictional, 204. geostrophic, 204. laminar,

169,

179.

surface,

165,

167,

103,

turbulent, 161,

162,

194,

Ekman veering, 200,

Estuary,

202,

104, 237,

103,

237,

221,

188,

109,

112,

110,

115,

120,

155-157,

159,

239.

104,

240,

222,

191.

107,

251,

232,

112,

110,

114,

120,

187,

194,

252.

235,

255, 9,

Finite difference scheme, 1 ,

266.

I I ,

13,

24,

35,

36.

Fluorometer, 259. 170,

Fourier decomposition, Frictional flow, 188, 237,

156,

110,

239,

240,

246,

247,

250,

Fronts, 255,

256,

259,

260,

266.

Froude number,

153,

177.

198.

101,

Friction velocity,

172,

155,

158,

158, 251,

160-162,

187, 289,

194, 291,

202, 292,

204,

225.

Geostrophic

-

current, 103,

107,

109,

- drag coefficient, 3,

30,

I l l , 120.

114,

115,

118,

120,

205,

294-296.

205.

303

-

interior, 1 8 8 ,

191.

shear, 2 0 0 . velocity, 1 5 6 - 1 5 9 ,

161,

194,

198,

237.

Geothermal heat flux, 1 5 8 . Halocline, 2 6 3 . Ice boundary, 1 6 5 . Interfacial propagation velocity, 2 5 9 . Intermittence, 5 4 ,

-

60,

61,

67,

71,

76,

79,

86,

241.

quasi-period, 7 5 - 7 7 .

Internal waves, see waves. Isobaths, 2 3 7 ,

239,

Isopycnals, 1 0 3 ,

240,

105,

242-244,

252.

200.

Jet

-

-

coastal, 2 5 5 ,

259.

stream, 2 6 3 . tidaf, 2 5 8 .

Kinematic viscosity, 1 0 7 ,

108,

Laplace transform, I ,

172.

Lilly equations, 1 7 4 ,

179.

Logarithmic layer, 9 9 ,

187,

202,

202,

289.

204,

237,

239,

240,

244-248,

252.

Mass transfer coefficient, 2 1 0 ,

211,

213,

177,

180.

215,

218.

Mean

-

density, 1 6 6 ,

168,

170,

-

field, 1 6 5 ,

-

surface slope, 2 2 2 .

-

velocity, 8 4 ,

169,

171,

85,

96,

171,

282-285,

124,

296.

134,

168,

171,

173,

177-180,

247,

269,

275,

282,

290,

292,

Mixed-layer, 1 5 6 ,

157,

166,

168-170,

-

well, 1 5 3 ,

-

wind, 4 9 - 5 1 .

slab, 1 8 7 ,

185,

205.

surface, 2 5 9 . 162,

177.

Monin-Obukov length, 1 3 0 , Nutrient, 2 5 7 ,

259,

263,

158. 266.

Orr-Sommerfeld equation, 1 7 9 .

153,

222,

155,

157,

230,

237,

185,

256.

294.

165,

239,

166,

242,

243,

304

255,

Phytoplancton patchiness, Pressure gradient, 7 8 , 165,

166,

Reynolds stress, 5 9 ,

157,

flux,

101.

177-179,

288.

112,

161,

144,

170,

177,

180, 2 5 5 .

170,

174,

175,

167, 60,

112,

I l l ,

bulk,

266.

79,

62,

143,

160,

63,

144,

167,

Richardson n u m b e r , 101,

-

265,

188.

205.

107,

Reynolds number, 96,

263,

169,

Return flow, 188, 2 0 4 ,

94,

258,

108.

Prandtl number,

Pycnocline,

256,

71,

182,

168,

72,

75,

76,

184, 232,

170,

174,

78,

235.

175,

79,

276,

83-86, 289-292

177.

179.

130.

gradient,

- turbulent, 1 6 0 . Roll waves, see waves 157,

Rossby number,

174,

250,

290-292,

294,

-

rate, 6 0 ,

230,

67,

142,

239,

202,

240,

237,

244,

239,

247.

240,

246-

247,

255,

256,

259,

265.

232.

84,

86,

87,

105, 2 8 7 .

time, 2 2 9 . 176.

Schmidt number,

Secondary currents, 2 2 5 , Sediment, 1 2 4 , 209-212,

-

188, 2 3 7 ,

141,

296.

Salinity profile, 2 4 1 , Sampling, 2 2 9 ,

175,

126,

Roughness parameter,

232.

126-130,

2 1 8 , 221,

132-134,

222,

225,

136-139, 229,

concentration profile, 2 0 9 - 2 1 1 , 123,

suspended,

124,

128-130,

230,

213, 132,

141,

146,

147,

232,

235,

248-250.

149,

215.

134-137,

139-141,

146,

148, 247. Sensor, 51, 5 4 , 269,

-

61,

62,

65,

67,

acoustic travel time, 8 7 - 9 0 .

- benthic acoustic stress, 9 4 ,

-

95.

scattering, 86. thermistor, 5 4 . volume averaging, 8 6 ,

Settling velocity,

129,

Shear, 2 9 ,

45,

-

83-87,

272.

42,

flow, 5 4 ,

43,

59,

87.

138, 1 3 9 , 252,

166-168,

259.

252.

141.

89,

90,

93-97,

241,

252,

306

-

meter, 8 7 - 8 9 , stress, 3 ,

. . -

94.

15,

bottom, 2 ,

27,

221,

boundary, 1 2 4 ,

velocity, 1 2 3 , 205.

222,

130,

30,

96,

232,

125,

134,

127,

135,

166,

209.

291,

292.

250. 133,

136,

138-141,

139,

187,

141.

194,

198,

200,

204,

120,

123,

230.

Stratification, 4 9 , 129,

29, 230,

132,

50,

103-105,

134-136,

162,

167,

168-170,

205,

247,

255,

174,

263,

107-110,

138,

140-141,

178,

179,

115, 145,

181,

118, 146,

187,

153-157,

194,

198,

204,

269.

Stress

- fluctuating stress tensor, 1 6 6 ,

170.

- shear stress, see shear.

-

wind stress, 4 , 198,

12,

13,

16,

28,

36,

30,

37,

42,

188,

191,

204.

Sub 1aye r

-

elastic, 9 9 . viscous, 9 9 ,

126,

204,

209.

Surface

-

elevation, I ,

-

waves, 5 1 .

current, 2 6 1 . layer, 1 6 5 ,

.

13,

15,

17,

29,

36,

40,

42,

43,

45.

187.

boundary layer, see boundary layer.

Suspension, 9 9 ,

-

3,

166,

249,

282.

suspended load, 2 3 0 ,

232,

235.

suspended particles, 2 3 2 . suspended sediment, see sediment.

Temperature profile, 5 0 , 247.

259,

265,

51,

102-104,

107,

115,

118,

153,

241,

272.

Thermal

-

diffusivity, see eddy diffusivity.

-

wind balance, 1 9 4 ,

Thermocline, 4 9 - 5 1 ,

198,

54,

56,

200,

205.

101,

102,

263.

Thickne s s

-

boundary layer, 5 1 ,

62,

126,

131,

198,

251,

261.

155,

158,

77,

103,

200,

110,

221,

112,

229,

118,

232,

120,

237,

121,

239,

244,

306

-

Ekman layer, 5 6 ,

103,

115,

110,

logarithmic layer, 2 3 9 ,

187,

188,>194, 204,

205.

245,

246.

78,

239,

242,

251,

257-259,

83, 96,

106,

107,

115, 221,

Tidal

-

-

amplitude, 2 2 2 , current, 2 7 , front, 256,

230.

28,

49,

71,

jet, see jet. kinetic energy, 256. motion, 272. period, 2 4 4 ,

255,

Time series, 6 0 , 252,

284,

Upwelling,

64,

258, 67,

272. 68,

292.

269,

Velocimeter,

272,

273.

see current meter.

Velocity profile, see current profile. Vortex, s e e eddy. Waves

-

-

276.

257.

internal, 5 1 ,

54,

56,

160,

161,

Kelvin, 272. roll,

153,

160-162.

surface, 5 1 . Tollmien-Schlichting,

Wind stress, see stress. Zooplankton, 266.

178,179.

170,

266,

269.

244,