波动是自然界最宽泛的科学论题之一，尤以近岸水波为甚，而这相对于深水波，更加呈现出水波变化的丰富性和复杂性。《近海表面波动力学：波-流-海底相互作用》一书，以“波-流-海底相互作用”机制和Hamilton系统为主干，提出了旨在谋求广泛应用的若干典型的水波传播基本理论（例如，缓坡方程，短峰波）。在近来一个时期，人们极为关注水波演变的规律，正是起因于全球沿岸海洋工程的急剧发展。该书包含多种理论和概念（尤其是广义波作用量），可为沿岸海洋工程发展提供一个新基础，对物理海洋学家和工程师多有助益。在如何构造理论和推导方法技巧上，该书可谓详尽细微，不乏引人入胜的多个范例。这一切，使得该书能够拥有一个广泛多样的读者群，特别是下列专业的大学高年级本科生和研究生：海岸和海洋工程；物理海洋；流体力学；应用数学。
- 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 De*ion 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
