Successive wave crests in Gaussian seas

In this paper, following the theory of quasi-determinism of Boccotti [Boccotti P. Wave mechanics for ocean engineering. Oxford: Elsevier Science.], the necessary and sufficient conditions, for the occurrence of two successive wave crests of large heights in a gaussian sea, are given. It is proven that the first two-peaks part of the autocovariance function ψ(T) describes the structure of two successive-wave patterns. As a corollary, it is shown that the tail probability of the joint distribution of two successive wave crests is given by a bivariate Weibull distribution. The Weibull parameter is equal to ψ2*=ψ(T2*)/ψ(0). Here, T2* is the abscissa of the second absolute maximum of the autocovariance function ψ(T). The analytical results are in agreement with Monte Carlo simulations. Finally, as an application, the maximum expected wave crest pressure in an undisturbed deep water waves is evaluated by taking into account the stochastic dependence of successive wave crests.