Statistics of Second-order Stokes Waves and of their Extremes

Abstract

A general method is presented for estimating distributions of the characteristic wave parameters of second-order Stokes waves. The second-order Stokes waves are expressed as a sum of a linear part (Gaussian process), and a non-linear part (quadratic transformation of a Gaussian process). Using Rice's formula the mean upcrossing intensities are estimated for different sea levels. The Transform Gausssian Process Method is then used to obtain the distributions. A numerical example is shown where the distributions of crest period vs crest amplitude are estimated.