Water wave mechanics for engineers and scientists

Robert G. Dean, Robert A. Dalrymple9810204213, 9810204205, 9789812385512, 9789810204204

This book is intended as an introduction to classical water wave theory for the college senior or first year graduate student. The material is self-contained; almost all mathematical and engineering concepts are presented or derived in the text, thus making the book accessible to practicing engineers as well.
The book commences with a review of fluid mechanics and basic vector concepts. The formulation and solution of the governing boundary value problem for small amplitude waves are developed and the kinematic and pressure fields for short and long waves are explored. The transformation of waves due to variations in depth and their interactions with structures are derived. Wavemaker theories and the statistics of ocean waves are reviewed. The application of the water particle motions and pressure fields are applied to the calculation of wave forces on small and large objects. Extension of the linear theory results to several nonlinear wave properties is presented. Each chapter concludes with a set of homework problems exercising and sometimes extending the material presented in the chapter. An appendix provides a description of nine experiments which can be performed, with little additional equipment, in most wave tank facilities.

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Table of contents :
Contents……Page 9
Preface……Page 13
1 Introduction to Wave Mechanics……Page 17
1.2 CHARACTERISTICS OF WAVES……Page 18
1.3 HISTORICAL AND PRESENT LITERATURE……Page 20
2. A Review of Hydrodynamics and Vector Analysis……Page 22
2.2 REVIEW OF HYDRODYNAMICS……Page 23
2.3 REVIEW OF VECTOR ANALYSIS……Page 35
2.4 CYLINDRICAL COORDINATES……Page 48
REFERENCES……Page 52
PROBLEMS……Page 53
3 Small-Amplitude Water Wave Theory Formulation and Solution……Page 57
3.2 BOUNDARY VALUE PROBLEMS……Page 58
3.3 SUMMARY OF THE TWO-DIMENSIONAL PERIODIC WATER WAVE BOUNDARY VALUE PROBLEM……Page 68
3.4 SOLUTION TO LINEARIZED WATER WAVE BOUNDARY VALUE PROBLEM FOR A HORIZONTAL BOTTOM……Page 69
3.5 APPENDIX: APPROXIMATE SOLUTIONS TO THE DISPERSION EQUATION……Page 87
PROBLEMS……Page 89
4 Engineering Wave Properties……Page 94
4.2 WATER PARTICLE KINEMATICS FOR PROGRESSIVE WAVES……Page 95
4.3 PRESSURE FIELD UNDER A PROGRESSIVE WAVE……Page 99
4.4 WATER PARTICLE KINEMATICS FOR STANDING WAVES……Page 102
4.5 PRESSURE FIELD UNDER A STANDING WAVE……Page 105
4.6 PARTIAL STANDING WAVES……Page 106
4.7 ENERGY AND ENERGY PROPAGATION IN PROGRESSIVE WAVES……Page 109
4.8 TRANSFORMATION OF WAVES ENTERING SHALLOW WATER……Page 116
4.9 WAVE DIFFRACTION……Page 132
4.10 COMBINED REFRACTION-DIFFRACTION……Page 139
References……Page 140
Problems……Page 142
5 Long Waves……Page 147
5.2 ASYMPTOTIC LONG WAVES……Page 148
5.3 LONG WAVE THEORY……Page 149
5.4 ONE-DIMENSIONAL TIDES IN IDEALIZED CHANNELS……Page 154
5.6 LONG WAVES WITH BOTTOM FRICTION……Page 162
5.7 GEOSTROPHIC EFFECTS ON LONG WAVES……Page 170
5.9 STORM SURGE……Page 173
5.10 LONG WAVES FORCED BY A MOVING ATMOSPHERIC PRESSURE DISTURBANCE……Page 179
5.11 LONG WAVES FORCED BY A TRANSLATING BOTTOM DISPLACEMENT……Page 182
PROBLEMS……Page 183
6.1 INTRODUCTION……Page 186
6.2 SIMPLIFIED THEORY FOR PLANE WAVEMAKERS IN SHALLOW WATER……Page 187
6.3 COMPLETE WAVEMAKER THEORY FOR PLANE WAVES PRODUCED BY A PADDLE……Page 188
6.4 CYLINDRICAL WAVEMAKERS……Page 196
6.5 PLUNGER WAVEMAKERS……Page 200
PROBLEMS……Page 201
7.1 INTRODUCTION……Page 203
7.2 WAVE HEIGHT DISTRIBUTIONS……Page 204
7.3 THE WAVE SPECTRUM……Page 209
7.4 THE DIRECTIONAL WAVE SPECTRUM……Page 218
7.5 TIME -SERIES SIMULATION……Page 223
7.6 EXAMPLE OF USE OF SPECTRAL METHODS TO DETERMINE MOMENTUM FLUX……Page 224
REFERENCES……Page 225
PROBLEMS……Page 226
8.1 INTRODUCTION……Page 228
8.2 POTENTIAL FLOW APPROACH……Page 229
8.3 FORCES DUE TO REAL FLUIDS……Page 237
8.4 INERTIA FORCE PREDOMINANT CASE……Page 253
8.5 SPECTRAL APPROACH TO WAVE FORCE PREDICTION……Page 270
REFERENCES……Page 271
PROBLEMS……Page 273
9.1 INTRODUCTION……Page 277
9.2 WAVES OVER SMOOTH, RIGID, IMPERMEABLE BOTTOMS……Page 278
9.3 WATER WAVES OVER A VISCOUS MUD BOTTOM……Page 287
9.4 WAVES OVER RIGID, POROUS BOTTOMS……Page 293
PROBLEMS……Page 298
10 Nonlinear Proper Ties Derivable from Small-Amplitude Waves……Page 300
10.2 MASS TRANSPORT AND MOMENTUM FLUX……Page 301
10.3 MEAN WATER LEVEL……Page 303
10.4 MEAN PRESSURE……Page 304
10.5 MOMENTUM FLUX……Page 305
REFERENCES……Page 309
PROBLEMS……Page 310
11 Nonlinear Waves……Page 311
11.2 PERTURBATION APPROACH OF STOKES……Page 312
11.3 THE STREAM FUNCTION WAVE THEORY……Page 321
11.4 FINITE-AMPLITUDE WAVES IN SHALLOW WATER……Page 325
11.5 THE VALIDITY OF NONLINEAR WAVE THEORIES……Page 338
REFERENCES……Page 340
PROBLEMS……Page 341
12.2 REQUIRED EQUIPMENT……Page 342
12.3 EXPERIMENTS……Page 346
REFERENCES……Page 361
Subject Index……Page 363
Author Index……Page 367