Extreme Waves and Stochastic Wave Groups

We introduce the concept of stochastic wave groups to explain the occurrence of extreme waves in nonlinear random seas, according to the dynamics imposed by the Zakharov equation (Zakharov, 1999). As a corollary, a new probability of exceedance of the crest-to-trough height which takes in to account the quasi-resonance interaction is derived. Furthermore, a generalization of the Tayfun distribution (Tayfun, 1986) for the wave crest height is also proposed. The new analytical distributions explain qualitatively well the experimental results of Onorato et al. (2004, 2005) and the numerical results of Juglard et al. (2005).