Numerical Simulation of Nonlinear Wave Dynamics

The following sections are included:

• Introduction

• General Initial Boundary-Value Problem

• High-Order Spectral (HOS) Method

  • Mathematical Formulation

  • Numerical Implementation

  • Error Considerations

  • Relation to Frequency-Domain Perturbation Results

• Applications of HOS to Nonlinear Wave-Wave, Wave-Current, and Wave-Bottom Interactions

  • Stokes Waves

  • Wave Steepening

  • Modulation of a Stokes Wave Train Due to Type I Instabilities

  • Evolution of a Wave Packet

  • Nonlinear Three-Dimensional Waves Due to a Moving Surface Disturbance

  • Nonlinear Wave Interaction with Ambient Current

  • Generalized Bragg Scattering of Surface Waves by Bottom Ripples

• HOS Method for Nonlinear Wave Interaction with Submerged Bodies

  • Mathematical Formulation

  • Numerical Implementation

  • Application to Nonlinear Wave Diffraction by a Submerged Circular Cylinder

• High-Order Spectral Element (HOSE) Method

  • Mathematical Formulation

  • Numerical Implementation

  • Application of HOSE to the Study of Stability of Standing Waves in a Circular Tank

• Mixed Euler-Lagrangian Method

  • Cauchy's Integral Formulation

  • Green's Integral Formulation

  • Numerical Implementation

  • Application to Two- and Three-Dimensional Breaking Waves

  • Application to Steep Crescent Waves

  • Application to Free-Surface Flow Over an Impulsively Started Point Sink

  • Application to Plunging Wave Impact on a Vertical Wall

  • Application to Nonlinear Wave Interaction with Floating Bodies