Circulation in the Coastal Ocean

292 Pages·1982·7.561 MB·English

by  G. T. Csanady (auth.)

Circulation in the Coastal Ocean
G. T. Csanady
Woods Hole Oceanographic Institution
Knowledge of coastal physics has developed
explosively during the past two decades. This
text presents the first synthesis of a new sub
field of dynamical oceanography, the dynamics
of coastal 'circulation', i.e. of motion on time
scales much longer than the period of tides. The
coastal ocean may consist of enclosed or open
shallow seas, such as the North American
Great Lakes, or continental shelf seas, which
are not much deeper than 1 00 m and have
typical widths measured in tens or hundreds of
kilometres. Earth rotation effects on the
motion in such seas are prominent and make
the study of the subject especially interesting
and challenging. The stimulus for the recent
upsurge of interest in this topic came partly
from public concern with the environment.
A knowledge of coastal ocean physics is a
prerequisite for a rational assessment of the
environmental impact of various accidental or
planned discharges of waste into the coastal
ocean.
Audience
This book will be of particular interest to
oceanographers, civil engineers, coastal engi
neers, and environmental scientists and may also
prove valuable for meteorologists and fluid
dynamicists.
Springer-Science+Business Media, B.V.
CIRCULATION IN THE COASTAL OCEAN
ENVIRONMENTAL FLUID MECHANICS
Managing Editor:
G. T. CSANADY, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
Editorial Board:
A. J. DAVENPORT, University of Western Ontario, London, Ontario
H. B. FISCHER, University of California, Berkeley, California
B. B. HICKS, Atmospheric Turbulence and Diffusion Laboratory, Oak Ridge, Tennessee
G. R. HILST, Electric Power Research Institute, Palo Alto, California
R. E. MUNN, University ofToronto, Ontario
J. D. SMITH, University of Washington, Seattle, Washington
G. T. CSANADY
Woods Hole Oceanographic Institution
Circulation in the
Coastal Ocean
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
library of Congress Cataloging in Publication Data
Csanady, G. T.
Circulation in the coastal ocean.
(Environmental fluid mechanics)
Bibliography: p.
Includes index.
1. Ocean circulation. 1. Title. II. Series.
GC228.5.C74 1982 551.47 82-11287
ISBN 978-90-481-8372-2 ISBN 978-94-017-1041-1 (eBook)
DOI 10.1007/978-94-017-1041-1
An Rights Reserved
Copyright © 1982 by Springer Science+Business Media Dordrecht
Originally published by D. Reidel Publishing Company, Dordrecht, Holland in 1982
Softcover reprint of the hardcover Ist edition 1982
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner
Table of Contents
FOREWORD ~
CHAPTER 1. FUNDAMENTAL EQUATIONS AND THEIR SIMPUFICATION 1
1.0. Introduction 1
1.1. The Equation of Continuity 2
1.2. Momentum Balance 3
1.2 .1. Reynolds Stresses 4
1.2.2. The Body Forces 4
1.3. Hydrostatic Approximation 5
1.3 .1. The Boussinesq Approximation 7
1.4. The Density Field 8
1.5. Quasi-Horizontal Motions 10
1.6. Surface and Bottom Stress 10
1.7. Interior Stresses 10
1.8. Linearization of the Equations 14
1.9. Shallow Water Equations 15
1.9 .1. The 'Local' and 'Global' Problem 16
1.10. Potential Vorticity Equation 17
1.11. Some Elementary Conceptual Models 19
1.11.1. Geostrophic Balance 19
1.11.2. Inertial Oscillations 20
1.11.3. Ekman Drift 21
CHAPTER 2. INERTIAL RESPONSE TO WIND 25
2.0. Introduction 25
2.1. Wind Setup Close to Coasts 25
2.1.1. Interior Velocity Distribution 26
2.2. Setup in a Basin of Arbitrary Size 29
2.2.1. Setup in a Rectangular Basin 31
2.3. Seiches in Narrow Basins 34
2.3.1. Rectangular Basin 35
2.3.2. Progressive Wave Interpretation 37
2.4. Evolution of Setup Along a Straight Open Coast 39
2.5. Longshore Wind and Sea Level 42
2.6. Wind Acting for a Limited Period 47
vi Circulation in the Coastal Ocean
2.7. Pressure Field-Induced and Frictional Interior Velocities 49
2.7.1. Local Problem for Impulsive Onshore Wind 52
2.7.2. The Case of Longshore Wind 54
2.8. Response of a Closed Basin to Sudden Wind 55
2.8.1. Circular Basin Model 57
2.8.2. The Large Basin limit 60
2.9. The Kelvin Wave 61
CHAPTER 3. THE BEHAVIOR OF A STRATIFIED SEA 64
3.0. General Remarks 64
3.1. Perturbation Theory 67
3.2. Normal Mode Equations 68
3.3. Stratification Model 71
3.4. Model of Forcing 73
3.5. Response of Continuously Stratified Model to Forcing 74
3.5.1. Sudden Longshore Wind 75
3.5.2. The Far Field 71
3.5.3. The Stratification-Limited Ekman Layer 78
3.5.4. Intermediate Distances 80
3.5.5. Conditions at the Coast 81
3.6. The Two-Layer Model 83
3.6.1. The Surface or Baratropic Mode 87
3.62. The Internal or Baroclinic Mode 88
3.7. Impulsive Longshore Wind 89
3.8. Cross-shore Wind 91
3.9. Two-layer Closed Basin 92
3.9.1. The Internal Kelvin Wave 95
3.9.2. Internal Kelvin Wave Propagation 97
3.10. Surfacing of the Pycnocline 99
CHAPTER 4. THE SUBTLE EFFECTS OF TOPOGRAPHY 105
4.0. Introduction 105
4.1. Wind Setup Over Variable Depth 105
4.1.1. Topographic Gyres 109
42. Windward and Leeward Shores 112
4.3. Seiches in Variable Depth Basins 115
4.4. Variable Depth and Earth Rotation 116
4.4.1. Sudden Cross-Shore Wind 120
4.42. Longshore Wind 122
4.4.3. Interior Velocities 123
4.5. Vorticity Waves 124
4.5.1. Topographic Wave in a Coastal Strip 127
4.5.2. Inclined Plane Beach-Coastal Strip Model 130
4.5.3. Basin-Wave Vorticity Wave Model 132
Table of Contents vii
4.6. Stratified Fluid Over Realistic Topography 133
4.6.1. Coastal Jet Over Sloping Beach 136
4.6.2. Vorticity Waves with Stratification and Bottom Slope 139
CHAPTER 5. TRANSIENT COASTAL CURRENTS 143
5.0. Introduction 143
5.1. Longshore Velocity and Tansport 144
5.2. Coastal Sea Level 150
5.3. Upwelling, Downwelling and Coastal Jets 151
5.4. Propagation of Flow Events 157
5.5. Climatology of Coastal Currents 168
CHAPTER 6. THERMOHALINE CIRCULATION 174
6.0. Introduction 174
6.1. Frictional Adjustment 175
6.2. Interior Velocities 177
6.2.1. The Shallow Water Limit 178
6.2.2. Deep Water Limit 179
6.2.3. Intermediate Depths 182
6.3. Simplified Parameterization of Interior and Bottom Stress 185
6.4. Steady Circulation Near a Straight Coast 186
6.4.1. Parallel Transport Model 187
6.4.2. Coastal Boundary Layer Model of Shelf Circulation 189
6.4.3. Coastally Trapped Flow Fields 192
6.5. Inclined Plane Beach Model 193
6.5.1. Flow and Pressure Field of a Coastal Mound 193
6.5.2. Wind Stress Along Portion of Coast 197
6.5 .3. Spacewise Periodic Longshore Wind Stress 200
6.6. Deep Ocean Influence 203
6.7. Periodic Cross-Shore Wind 205
6.8. Circulation in a Circular Basic with a Parabolic Depth Profile 208
CHAPTER 7. THERMOHALINE CIRCULATION 211
7.0. Introduction 211
7.1. Frontal Adjustment 214
7.2. Gravitational Convection 220
7.3. The "Nearly Homogeneous" Fluid Idealization 223
7.3.1. Advection and Diffusion of Freshwater 226
7 .3.2. Parallel Flow Model of Thermohaline Circulation 228
7.3.3. Determination of the Density Field 230
7.4. Mean Circulation on a Nearly Homogeneous Shelf 232
7 .4.1. Application of the Parallel Flow Model 233
7.5. Surface Elevation Distribution 234
7 .5.1. Two-Dimensional Density Field 235
7.5.2. Qualitative Effects of Longshore Density Variations 236
viii Circulation in the Coastal Ocean
CHAPTER 8. OBSERVED QUASI-STEADY FLOW PATTERNS IN SHALLOW
SEA 238
8.0. Introduction 238
8.1. Mean Circulation in the Mid-Atlantic Bight 239
8.2. Stonn Currents Over Atlantic Type Shelves 242
8.2.1. Statistical Analyses of Coastal Sea Level 243
8.2.2. Sea Level and Longshore Wind 247
8.2.3. Longshore Pressure Gradients 249
8.2.4. Effects of Cross-Shore Winds 254
8.3. Evidence of Moored Instruments 258
8.3.1. Longshore Flow and Momentum Balance 258
8.3.2. Cross-Shore Transport 261
8.4. Mean Circulation in Lake Ontario 262
8.5. Mean Circulation Over the Oregon Shelf 264
REFERENCES 267
INDEX OF NAMES 275
INDEX OF SUBJECTS 278
Foreword
For some time there has existed an extensive theoretical literature relating to tides
on continental shelves and also to the behavior of estuaries. Much less attention was
traditionally paid to the dynamics of longer term, larger scale motions (those which are
usually described as circulation') over continental shelves or in enclosed shallow seas
such as the North American Great Lakes. This is no longer the case: spurred on by
other disciplines, notably biological oceanography, and by public concern with the
environment, the physical science of the coastal ocean has made giant strides during the
last two decades or so.
Today, it is probably fair to say that coastal ocean physics has come of age as a deduc
tive quantitative science. A well developed body of theoretical models exist, based on
the equations of fluid motion, which have been related to observed currents, sea level
variations, water properties, etc. Quantitative parameters required in using the models
to predict e.g. the effects of wind or of freshwater influx on coastal currents can be
estimated within reasonable bounds of error. While much remains to be learned, and
many exciting discoveries presumably await us in the future, the time seems appropriate
to summarize those aspects of coastal ocean dynamics relevant to 'circulation' or long
term motion.
At the Woods Hole Oceanographic Institution I have for several years offered a grad
uate course on 'coastal dynamics', which was more or less such an account of the fluid
dynamics of circulation or non-tidal motion in enclosed and open shallow seas. The
present text grew out of the lecture notes for that course, although the topic evolved
considerably in the course of writing. It owes much to two review articles completed
recently (Csanady 1981a, c). The end product is more nearly a monograph than a text,
being more narrowly focused on long period motions than a reasonable coastal dynamics
course should be.
In writing a synthesis of a subject that represented for some years one's own central
research interest it is apparently unavoidable to end up with a considerable bias toward
using one's own results and illustrations. Legitimate reasons for this are intimate famil
iarity and easy availability, but an unfortunate side effect is to endow those results
and illustrations with an importance which is quite undeserved. The reader should make
appropriate allowances for this. I have tried to quote key original papers wherever appro
priate, but probably missed some. The literature of coastal oceanography is now so large
that to quote all important contributions would have interfered with the central goal of
this monograph, the synthesis of knowledge.
The philosophy of the approach adopted in this monograph to understanding circula
tion in the coastal ocean is briefly as follows. The observed total behavior of any shallow
ix