Stability Regimes of Finite Depth Short-Crested Water Waves

Abstract

Stability regimes of three-dimensional surface gravity waves are provided in this study. The stability regimes for waves in water of finite depth differ significantly from those for waves in deep water. In particular, these waves are no longer unstable to phase-locked horseshoe-patterned disturbances, and the perturbed wave fields have more complex geometry than those in deep water. It is also shown that there is a critical restabilization value of the depth parameter below which the timescales of the surface wave variations shorten exponentially. This critical value depends on the wave steepness and the degree of three-dimensionality of the unperturbed wave field. Finally, it is predicted that these waves are quasi-observable.