Statistical modeling of the sea surface in the presence of abnormal waves

Abstract

A wide range of fundamental and applied problems requires a detailed description of the statistics of abnormal sea waves (freak waves or rouge waves). These waves are characterized not only by a change in ener-gy, but also by strong nonlinearity, leading to extreme values of the higher cumulants. The possibilities and limitations of modeling the probability density function (PDF) of sea surface elevations by a two-component Gaussian mixture at extreme values of skewness and excess kurtosis are analyzed. The parameters of a two-component Gaussian mixture are calcu-lated from known values of statistical moments. Model PDFs in the form of a two-component Gaussian mixture are compared with PDFs based on direct wave measurement data, and also compared with the known Gram-Charlier distribution. It is shown that with positive values of the excess kurtosis, the PDF in the form of a two-component Gaussian mixture can be constructed at the limit values of the skewness and excess kurtosis ob-tained in different regions of the World Ocean. With large negative values of the kurtosis, the shape of the probability density function is strongly dis-torted, which indicates the limit of applicability of a two-component Gaussian mixture to the description of such situations.