ON THE OBSERVABILITY OF FINITE-DEPTH SHORT-CRESTED WATER-WAVES

A numerical study of the superharmonic instabilities of short-crested waves on water of finite depth is performed in order to measure their time scales. It is shown that these superharmonic instabilities can be significant - unlike the deep-water case - in parts of the parameter regime. New resonances associated with the standing wave limit are stu died closely. These instabilities 'contaminate' most of the parameter space, excluding that near two-dimensional progressive waves; however, they are significant only near the standing wave limit. The main resu lt is that very narrow bands of both short-crested waves 'close' to tw o-dimensional standing waves, and of well developed short-crested wave s, perturbed by superharmonic instabilities, are unstable for depths s hallower than approximately a non-dimensional depth d = 1, the study i s performed down to depth d = 0.5 beyond which the computations do not converge sufficiently. As a corollary, the present study predicts tha t these very narrow sub-domains of short-crested wave fields will not be observable, although most of the short-crested wave fields will be.