Extreme Events in Nonlinear Random Seas

Abstract

In this paper, the occurrence of extreme events due to the four-wave resonance interaction in weakly nonlinear water waves is investigated. The starting point is the Zakharov equation, which governs the dynamics of the spectral components of the surface displacement. It is proven that the optimal spectral components giving an extreme crest are solutions of a well-defined constrained optimization problem. A new analytical expression for the probability of exceedance of the wave crest is then proposed for the prediction of freak wave events.