Skip to main content

Mathematical Modelling of Tides and Estuarine Circulation: The Coastal Seas of Southern British Columbia and Washington State

Mathematical Modelling of Tides and Estuarine Circulation: The Coastal Seas of Southern British Columbia and Washington State

P. B. Crean, T. S. Murty, J. A. Stronach

ISBN: 978-1-118-66916-7

Mar 2013, American Geophysical Union

471 pages

Select type: O-Book

Description

Published by the American Geophysical Union as part of the Lecture Notes on Coastal and Estuarine Studies Series, Volume 30.

Of the few major ports on the western seaboard of North America, two are located on the extensive complex of waters contained between Vancouver Island and the mainland coasts of British Columbia and the State of Washington. Prolific in marine life and supporting major fisheries, the importance of these waters is presently being enhanced by extensive developments in aquaculture. Increases in the discharge of domestic and industrial effluents and in the density of marine traffic, both commercial and recreational, emphasize the need for a quantitative understanding of the basic circulation and predictive capability with respect to major contingencies likely to occur. This work attempts a broad overview ranging from tidal and estuarine circulation, including the dynamical simulation of a major river plume and influences propagating in from the open boundaries, to the effects of storm surges and tsunamis.

1 INTRODUCTION 1

1.1 Physical Characteristics 1

1.2 Oceanographic Problems 12

1.3 Regional Oceanographic Description 14

2 FIELD OBSERVATIONS 45

BAROTROPIC MODELS 51

3 THE ONE-DIMENSIONAL: MODEL GF1 53

3.1 Introduction 53

3.2 Fundamental Equations  54

3.3 Finite-Difference Equations 54

3.4 The Computational Scheme 56

3.5 Results 60

3.6 Discussion 69

4 THE COMBINED ONE- AND TWO-DIMENSIONAL MODEL: GF2 71

4.1 Introduction 71

4.2 Fundamental Hydrodynamic Equations 71

4.3 Description of the Model 79

4.4 Summarized Sequence of Model Development 83

4.5 Non-Linear Tidal Interactions 90

4.6 The Simulation of Mixed Tides 93

4.7 Volume Transports 105

4.8 Energy Calculations 107

5 THE FINE GRID MODEL: GF3 115

5.1 Introduction 115

5.2 Description of the Model 115

5.3 Simulation of Mixed Tides 117

5.4 Applications of Results from GF2 and GF3 124

6 THE LIMITED AREA MODEL (LAM) AND SMALL-SCALE LIMITED AREA MODEL (SSLAM) 129

6.1 Local Area Modelling 129

6.2 The Limited Area Model (LAM) 130

6.3 The Small-Scale Limited Area Model (SSLAM) 133

7 THE OVERALL FINE-GRID MODEL: GF7 137

7.1 Introduction 137

7.2 Numerical Grid Scheme 137

7.3 Sensitivity Trials 140

7.4 Simulation of Mixed Tides 140

7.5 Horizontal Tidal Residual Circulation 146

8 NORMAL MODES 167

8.1 Introduction 167

8.2 Gravitational and Rotational Normal Modes 167

8.3 .Method of Determination 168

8.4 Oscillatory Response of the System 168

8.5 Internal Modes 172

9 STORM SURGES 178

9.1 Introduction 178

9.2 Model Development Considerations 178

9.3 Discussion of Results 181

9.4 Conclusibns 186

10 TSUNAMIS 187

10.1 Introduction 187

10.2 Simulation of the Tsunami of 23 June 1946 187

10.3 Future Tsunami Estimates 193

BAROCLINIC MODELS 203

11 THE UPPER LAYER MODEL: GF4 205

11.1 Introduction  205

11.2 Governing Equations 206

11.3 Boundary Conditions 210

11.4 F inite-Difference Equations 210

11.5 Results  222

11.6 Concluding Discussion 300

12 THE LATERALLY-INTEGRATED MODEL: GF5 302

12.1 Introduction 302

12.2 Governing Equations  303

12.3 Model Description 304

12.4 Finite-Difference Equations 304

12.5 Boundary Conditions 308

12.6 Review of Longitudinal Circulation 308

12.7 Model Results 310

12.8 Prescribed Lid Numerical Trials 329

12.9 Concluding Summary 334

13 THE THREE-DIMENSIONAL MODEL: GF6 336

13.1 Introduction 336

13.2 Fundamental Hydrodynamical Equations 337

13.3 General Trials of the Model 344

13.4 Residual Circulation 363

13.5 Conclusions 430

14 CONCLUDING DISCUSSION 432

14.1 Concluding Summary 443

REFERENCES 446

APPENDIX I 455

AUTHOR INDEX 463

SUBJECT INDEX 465