Generating deep water three-dimensional waves by coupling four-wave and five-wave interactions

Su [1982a, b] reported the results of experiments that demonstrate the occa sional predominance of three-dimensional waves in deep waters. Three-dimens ional waves require the interaction of five- (or more) wave modes. However, both instability analysis MacLean, 1982] and numerical simulation [Lin and Perrie, 1997a, b] demonstrate that five-wave interactions have nonlinear t ransfer rates 2 orders of magnitude less than those for four-wave interacti ons in deep waters. Su and Green [1984] suggested that two-dimensional inst abilities generate waves whose steepening beyond a critical point then trig gers three-dimensional instabilities, a phenomenon known to occur in shallo w water. We report the results of simulations that confirm the coupling of four- and five-wave interactions in deep water but show that this coupling occurs in response to decreases in spectral width rather than increases in wave steepness. In contrast to the shallow water scenario, the wave steepne ss never reaches critical values.