目录 1 Preliminaries 1.1 Water Wave Theories in Historical Perspective 1.1.1 The Mild-Slope Equations 1.1.2 The Boussinesq-Type Equations 1.2 The Governing Equations 1.3 Lagrangian Formulation 1.4 Hamiltonian Formulation References 2 Weakly Nonlinear Water Waves Propagating over Uneven Bottoms 2.1 Modified Third-Order Evolution Equations of Liu and Dingemans 2.2 Fourth-Order Evolution Equations and Stability Analysis 2.3 Third-Order Evolution Equations for Wave-Current Interactions References 3 Resonant Interactions Between Weakly Nonlinear Stokes Waves and Ambient Currents and Uneven Bottoms 3.1 Introduction 3.2 Governing Equations and WKBJ Perturbation Expansion 3.3 Subharmonic Resonance 3.4 Dynamical System References 4 The Mild-Slope Equations 4.1 Introduction 4.2 Three-Dimensional Currents over Mildly Varying Topography 4.3 Two-Dimensional Currents over Rapidly Varying Topography 4.4 Three-Dimensional Currents over Rapidly Varying Topography 4.5 Two-Dimensional Currents over Generally Varying Topography 4.6 A Hierarchy for Two-Dimensional Currents over Generally Varying Topography References 5 Linear Gravity Waves over Rigid, Porous Bottoms 5.1 Introduction 5.2 A Rapidly Varying Bottom 5.3 Generally Varying Bottom References 6 Nonlinear Unified Equations over an Uneven Bottom 6.1 Introduction 6.2 Nonlinear Unified Equations 6.3 Explicit Spe Cases 6.3.1 Generalized Nonlinear Shallow-Water Equations of Airy 6.3.2 Generalized Mild-Slope Equation 6.3.3 Stokes Wave Theory 6.3.4 Higher-Order Boussinesq-Type Equations References 7 Generalized Mean-Flow Theory 7.1 Introduction 7.2 Governing Equations and Boundary Conditions 7.3 Averaged Equations of Motion 7.4 Generalized Wave Action Conservation Equation and Its Wave Actions References 8 Hamiltonian Description of Stratified Wave-Current Interactions 8.1 Introduction 8.2 Two-Layer Wave-Current Interactions 8.3 n-Layer Pure Waves 8.4 n-Layer Wave-Current Interactions over Uneven Bottoms References 9 Surface Capillary-Gravity Short-Crested Waves with a Current in Water of Finite Depth 9.1 Introduction 9.2 An Incomplete Match and Its Solution 9.3 Linear Capillary-Gravity Short-Crested Waves 9.3.1 System Formulation 9.3.2 Analytical Solutions and Kinematic and Dynamical Variables 9.3.3 Spe Cases 9.4 Second-Order Capillary-Gravity Short-Crested Waves 9.5 Third-Order Gravity Short-Crested Waves 9.5.1 The System Equations and the Perturbation Method 9.5.2 Third-Order Solution 9.5.3 Spe Cases 9.5.4 Short-Crested Wave Quantities 9.5.5 Short-Crested Wave Forces on Vertical Walls 9.6 Third-Order Pure Capillary-Gravity Short-Crested Waves 9.6.1 Formulation 9.6.2 Solution 9.6.3 Kinematical and Dynamical Variables References Appendices A γ,μ and v in (2.1.4) B ξ(3,1), φ3,1), A(3,2) ηj, τj, μj, λj and Vj in Chapter 2 C λ1 and λ2 in (2.3.44) D μj in (3.3.22) E I23, I33, I35,136 in Chapter 5 F Coefficients in (9.4.33) and (9.4.34) G Coefficients in (9.5.136)-(9.5.138) H Coefficients in (9.5.139) and (9.5.140) Subject Index
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