Instabilities of finite-amplitude water waves

Abstract

A numerical investigation of normal-mode perturbations of a finite-amplitude Stokes wave has revealed regions of instability lying near resonance curves given by the linear-dispersion relation. It is found that, for small amplitude, the dominant instability is two-dimensional (of Benjamin-Fier type) but, for larger amplitudes, the dominant instability becomes a three-dimensional perturbation. Results are compared with recent experimental observations of steep wave trains.