Instabilities of steep short-crested surface waves in deep water

Abstract

The stability of steep short-crested gravity waves in deep water is investigated, thanks to an improvement of the numerical procedure originally developed by Ioualalen and Kharif [J. Fluid. Mech. 262, 265 (1994)]. This study predicts their potential evolution: For very steep waves, it is shown that: (i) Near the two-dimensional standing wave limit, they are unstable to class I modulational perturbations; (ii) near the two-dimensional progressive wave limit, they are unstable to class II perturbations, yielding to “horseshoe-patterned” fields; and (iii) fully three-dimensional waves match the two limits continuously, i.e., class II surpasses class I for the steepest waves.