Relation between occurrence probability of freak waves and kurtosis/skewness in unidirectional wave trains under single-peak spectra

Abstract

An accurate prediction about the occurrence probability of freak waves in unidirectional wave trains, commonly regarded as typical configurations to define the environmental conditions of operation, is crucial for avoiding disasters and losses in marine activities. Based on a two-dimensional High Order Spectral numerical wave tank, here the quantitative relation between the occurrence probability of freak waves and kurtosis/skewness considering the influence of Benjamin-Feir Index and relative water depth is investigated. A wide range of 25 single-peak spectral waves is simulated for data collection and further statistical analysis. Results show that the correlation between the occurrence probability of freak waves and skewness depends on the Benjamin-Feir Index and no uniform linear relation is deduced. In contrast, the occurrence probability of freak waves has a strong correlation with kurtosis, irrespective of Benjamin-Feir Index, relative water depth, and peak enhancement factor. An empirical formula for the occurrence probability of freak waves is obtained: Pfreak(%) = 0.29kurtosis-0.82, a little deviation from the one based on the Modified Edgeworth-Rayleigh (MER) weakly nonlinear model.