A Weibull-Stokes Model For the Distribution of Maximum Wave And Crest Heights

Abstract

The present paper describes a model for the distribution of maximum wave and crest heights in a given sea state. The standard Rayleigh and Weibull distributions for wave and crest heights are modified using a third order Stokes expansion of the wave envelope. The maximum wave or crest height in a record is calculated using the asymptotic Gumbel distribution. It was validated by fitting the model distributions to North Sea measurement data and provided much better predictions of maximum crest and wave heights than standard models. To make up for the fact that directionality and spectral shape are not taken into account in the model, correction terms (specific to the studied site) are introduced and mainly one of them will give the optimized mean wave number to consider in the model. The proposed model is relatively easy to apply and could be an effective tool to determine extreme wave and crest heights for offshore structure design purposes.