Nonlinear Behaviour of Sea Surface Waves Based on Low-Gradient Phase-Only Scattering Effects

Abstract

Nonlinear sea waves generated by the wind, including freak waves, are considered to be phenomena that can be modelled using the nonlinear (cubic) Schrodinger equation, for example. However, there is a problem with this approach which is that sea surface waves, driven by wind speeds of varying strength, must be considered to be composed of two distinct types, namely, linear waves and nonlinear waves. In this paper, we consider a different approach to modelling ‘nonlinear’ waves that is based on a solution to the linear wave equation under a low-gradient, phase-only condition. This approach is entirely compatible with the fluid equations of motion (the Navier-Stokes equations) and is thereby not based on a phenomenological model such as the nonlinear Schrodinger equation.