Dynamics of Surface Waves in Coastal Waters Wave-Current-Bottom Interactions develops the typical basic theories (e,g. mild-slope equation and shorecrested 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.

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 Special 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 Special 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 Special 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