M. Ioualalen et C. Kharif, ON THE SUBHARMONIC INSTABILITIES OF STEADY 3-DIMENSIONAL DEEP-WATER WAVES, Journal of Fluid Mechanics, 262, 1994, pp. 265-291
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.