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Fully non-linear statistics of wave crest elevation

This work concerns the calculation of the probability of exceedance of wave crest elevation. New statistics have been calculated for broad-banded, unidirectional, deep-water sea states by incorporating a fully non-linear 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 broad banded, fully non-linear, nature of the sea-state can be considered. The results have been compared to those of fully non-linear time-domain simulations and are shown to be in good agreement. The results indicated that in unidirectional seas the crest elevations of the largest waves could be much higher than would be predicted by linear or second-order theory. Hence, the occurrence of locally long-crested sea-sates offers a possible explanation for the formation of freak or rogue waves.

In contrast, with the inclusion of directional effects the non-linear increase in the maximum crest elevation rapidly reduces. Indeed, with realistic directional spreads the fully non-linear statistics are shown to lie between the linear and second order predictions. However, this result masks the fact that the non-linear wave profile may be significantly steeper, with implications for wave slamming and green-water inundation. Furthermore, by combining these short-term statistics with the long term statistics of storms, the return periods of a number of extreme field observations have been correctly estimated.

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Imperial College Road, Exhibition Road
United Kingdom
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