Maximum wave crest and height statistics of irregular and abnormal waves in an offshore basin

Irregular deep water sea states generated in a tank and represented by a JONSWAP spectrum have been investigated with respect to the statistics of the largest waves. The crests and heights of the maximum observed waves have been fitted by linear and second order statistical models. Special attention has been given to the extreme waves, which fulfil simultaneously the criteria for the crest and height abnormality indices. Statistically, the non-Gaussian behaviour of the considered wave fields has been demonstrated by means of the coefficients of skewness and kurtosis estimated from the time series. The estimates have been compared with second order theory. Moreover, analytical formulae taking into account the effects of spectral bandwidth and finite depth have been applied to improve the predictions of the normalized cumulants. The obtained results showed that the largest crests are well described by the models with correction of third order included, by means of the coefficient of kurtosis. The maximum wave heights and the observed abnormal extremes agree well with the second-order theory, although the linear predictions do not deviate much from the observations either. The laboratory results are compared with results for full-scale data gathered during a storm at the North Alwyn platform in the North Sea. The storm data show different statistical behaviour.