ON THE SUBHARMONIC INSTABILITIES OF STEADY 3-DIMENSIONAL DEEP-WATER WAVES

A numerical procedure has been developed to study the linear stability of nonlinear three-dimensional progressive gravity waves on deep wate r. The three-dimensional patterns considered herein are short-crested waves which may be produced by two progressive plane waves propagating at an oblique angle, gamma, to each other. It is shown that for moder ate wave steepness the dominant resonances are sideband-type instabili ties in the direction of propagation and, depending on the value of ga mma, also in the transverse direction. It is also shown that three-dim ensional progressive gravity waves are less unstable than two-dimensio nal progressive gravity waves.