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

Abstract

This 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.

Surface gravity waves from direct numerical simulations of the Euler equations: A comparison with second-order theory

“…Provided the BFI is sufficiently large, results have shown that the deviation from the Gaussian statistics can be more significant than in second-order theory. Recently, similar findings have also been discussed by Gibson et al (2007), who have investigated the wave crest distribution by combining a fully nonlinear wave model with reliability methods, which are used for design and safety assessment of marine structures.…”

Investigation of the effect of the bed slope on extreme waves using First Order Reliability Method

“…This follows from the result that the peaks of a Gaussian process are Rayleigh distributed [34]. Similar method was previously used by Gibson et al [35] and Jensen [36]. We look at the peak statistics with no extra sorting related to statistical independence.…”

Evolution of weakly nonlinear random directional waves: laboratory experiments and numerical simulations

“…However, they have not been applied to the computation of random directional wave fields over a large spatial domain due to the computational burden. A promising method that allows the prediction of statistical properties of fully nonlinear waves was recently presented by Gibson, Swan & Tromans (2007), who combined the fully nonlinear wave model by Bateman et al (2001) with a spectral response surface method; this study, however, was limited to unidirectional waves. In several studies (see e.g.…”