Narrow-Banded Nonlinear Waves in Water of Intermediate or Great Depth

The following sections are included:

• Introduction

• Evolution Equations for Slowly Modulated Weakly Nonlinear Waves Over Horizontal Seabed

  • Intermediate Depth

  • Deep Water Limit

• Uniform Stokes' Waves

• Side-Band Instability of Stokes' Waves

• Permanent Envelopes in Deep Water: Nonlinear Solutions of the Evolution Equation

• Transient Evolution of One-Dimensional Wave Envelope on Deep Water

  • Evolution of a Single Pulse

  • Evolution of the Front of a Uniform Wavetrain

  • Periodic Modulation of a Uniform Wavetrain — Evolution Beyond the Initial Stage of Instability

• Infragravity Waves Over Slowly Varying Depth

  • Equation for Long Waves Forced by One Train of Short Waves

  • Short-Wave Envelope

  • Mean Sea-Level

  • Free and Bound Infragravity Waves

• Infragravity Waves Over Periodic Bars

• Remarks on Third-Order Effects of Short Waves Over Slowing Varying Depth

• Diffraction of Steady Stokes' Waves by a Thin Wedge or a Slightly Slanted Breakwater

• Soliton Envelopes in the Wake of a Ship

• Second-Order Diffraction by a Vertical Cylinder

  • First-Order Solution

  • The Second-Order Problem

  • Second-Order Forcing

  • Second-Order Boundary-Value Problems

  • Response to

  • Response to

  • Sample Numerical Results

• Appendix 13.A Asymptotic Behavior ξ₀ in the Far-Field

• Appendix 13.B Weak Radiation Condition