Wave motion is one of the broadest scientific subjects in nature, especially water waves in the near-shore region which present more richness and complexity of variability with respect to deep-water waves. Dynamics of Surface Waves in Coastal Waters: Wave-Current-Bottom Interactions develops the typical basic theories (e.g. mild-slope equation and shore-crested waves) and applications of water wave propagation with an emphasis on wave-current-bottom interactions and Hamiltonian systems. In recent times, the interest in water wave propagation has accelerated because of rapid developments in global coastal ocean engineering.
This book lays a new foundation for coastal ocean engineering and includes numerous theories and concepts (generalized wave actions in particular), making it beneficial to physical oceanographers and engineers. The book has detailed illustrations and stimulating examples showing how the theory works, and up-to-date techniques, all of which make it accessible to a wide variety of readers, especially senior undergraduate and graduate students in fluid mechanics, coastal and ocean engineering, physical oceanography and applied mathematics.
Hu Huang is a professor of fluid mechanics at Shanghai University.
Author(s): Hu Huang
Edition: 1st Edition.
Publisher: Springer
Year: 2010
Language: English
Pages: 236
Tags: Механика;Механика жидкостей и газов;Гидромеханика;
Cover......Page 1
Dynamics of Surface Waves in Coastal Waters (Springer, 2009)......Page 3
ISBN 978-3-540-88830-7......Page 4
Preface......Page 6
Acknowledgements......Page 9
About the Author......Page 11
Table of contents......Page 12
1.1 Water Wave Theories in Historical Perspective......Page 15
1.1.1 The Mild-Slope Equations......Page 16
1.1.2 The Boussinesq-Type Equations......Page 17
1.2 The Governing Equations......Page 18
1.4 Hamiltonian Formulation......Page 19
References......Page 20
2.1 Modified Third-Order Evolution Equations of Liu and Dingemans......Page 23
2.2 Fourth-Order Evolution Equations and Stability Analysis......Page 29
2.3 Third-Order Evolution Equations for Wave-Current Interactions......Page 40
Reference......Page 49
3.1 Introduction......Page 50
3.2 Governing Equations and WKBJ Perturbation Expansion......Page 51
3.3 Subharmonic Resonance......Page 53
3.4 Dynamical System......Page 59
References......Page 64
4.1 Introduction......Page 65
4.2 Three-Dimensional Currents over Mildly Varying Topography......Page 66
4.3 Two-Dimensional Currents over Rapidly Varying Topography......Page 70
4.4 Three-Dimensional Currents over Rapidly Varying Topography......Page 77
4.5 Two-Dimensional Currents over Generally Varying Topography......Page 82
4.6 A Hierarchy for Two-Dimensional Currents over Generally Varying Topography......Page 85
References......Page 89
5.1 Introduction......Page 91
5.2 A Rapidly Varying Bottom......Page 92
5.3 Generally Varying Bottom......Page 97
References......Page 105
6.2 Nonlinear Unified Equations......Page 106
6.3.1 Generalized Nonlinear Shallow-Water Equations of Airy......Page 108
6.3.3 Stokes Wave Theory......Page 109
6.3.4 Higher-Order Boussinesq-Type Equations......Page 110
References......Page 113
7.1 Introduction......Page 114
7.2 Governing Equations and Boundary Conditions......Page 115
7.3 Averaged Equations of Motion......Page 116
7.4 Generalized Wave Action Conservation Equation and Its Wave Actions......Page 120
References......Page 121
8.1 Introduction......Page 123
8.2 Two-Layer Wave-Current Interactions......Page 124
8.3 n-Layer Pure Wavesl......Page 129
8.4 n-Layer Wave-Current Interactions over Uneven Bottoms......Page 132
References......Page 136
9 Surface Capillary-Gravity Short-Crested Waves with a Current in Water of Finite Depth......Page 137
9.2 An Incomplete Match and Its Solution......Page 138
9.3.1 System Formulation......Page 142
9.3.2 Analytical Solutions and Kinematic and Dynamical Variables......Page 144
2. Wave Period and Phase Velocity......Page 145
9.3.3 Special Cases......Page 146
3. Three-Dimensional Deep-Water Surface Capillary-Gravity Short-Crested Waves......Page 147
9.4 Second-Order Capillary-Gravity Short-Crested Waves......Page 148
1. Surface Elevation......Page 153
3. Wave Speed......Page 154
5. Wave Pressure......Page 155
9.5.1 The System Equations and the Perturbation Method......Page 156
1. First-Order Solution......Page 159
2 Second-Order Solution......Page 160
3. Third-Order Solution......Page 164
1. Standing Waves......Page 171
2. Stokes Waves......Page 173
1. Surface Elevation and Wave Steepness......Page 175
2. Phase Velocity, Water-Particle Velocities and Accelerations......Page 176
3. Wave Pressure......Page 179
9.5.5 Short-Crested Wave Forces on Vertical Walls......Page 181
9.6.1 Formulation......Page 188
1. First-Urder Solution......Page 190
2. Second-Order Solution......Page 191
3. Third-Order Solution......Page 196
1. Surface Elevation, Wave Height and Wave Steepness......Page 207
2. Phase Velocity，Water-Particle Velocities，Accelerations and Trajectories......Page 211
3. Wave Pressure......Page 216
References......Page 218
A y,μ and v in (2.1.4)......Page 220
B S(3,1), p(3,2)，nj, Ji, μj ,λj and Vj in chapter 2......Page 221
C λ1 and λ2 in (2.3.44)......Page 227
D μj in (3.3.22)......Page 228
E I23，I33，I35，I36 in Chapter 5......Page 229
F Coefficients in (9.4.33) and(9.4.34)......Page 232
G Coefficients in (9.5.136) (9.5.138)......Page 234
H Coefficients in (9.5.139) and (9.5.140)......Page 236
Subject Index......Page 240
