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 occasional predominance of three-dimensional waves in deep waters. Three-dimensional 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 transfer rates 2 orders of magnitude less than those for four-wave interactions in deep waters. Su and Green [1984] suggested that two-dimensional instabilities generate waves whose steepening beyond a critical point then triggers three-dimensional instabilities, a phenomenon known to occur in shallow 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 steepness never reaches critical values.