Shapes, histories and statistics of non-linear wave crests in random seas

How large an air-gap should be provided beneath the deck of an offshore structure? For steel space-frames, the structure has relatively little effect on the large ocean waves that pass through it. Thus, the assessment of an adequate air-gap reduces to two issues: at what elevation is the local mean water level on which the waves ride, and how tall are the crests of the largest waves? This second question, the height of large crests, is tackled in this paper with a novel approach. The non-linearity of steep waves is modelled using the Creamer-transform and a spectral response method is used to analyse the model and deduce the statistics of the extremes of the resulting process. The non-linearity modelled by the Creamer-transform makes extreme crests higher. Also, the average shape of these large crests is different from the average shape of an extreme linear crest (NewWave), there being a more important contribution from high-frequency components.