Fully Nonlinear Statistics of Wave Crest Elevation Calculated Using a Spectral Response Surface Method: Applications to Unidirectional Sea States

Abstract

AbstractThis paper concerns the calculation of the probability of exceedance of wave crest elevation. The statistics have been calculated for broadbanded, unidirectional, deep-water sea states by incorporating a fully nonlinear wave model into a spectral response surface method. This is a novel approach to the calculation of statistics and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. Furthermore, in contrast to theoretical distributions, the broadbanded, fully nonlinear nature of the sea state can be considered. The results have been compared with those of fully nonlinear time-domain simulations and are shown to be in good agreement. The results indicate that in unidirectional seas the crest elevations of the largest waves can be much higher than would be predicted by linear or second-order theory. Hence, the occurrence of locally long crested sea states offers a possible explanation for the formation of freak or rogue waves.