Distribution of Crest Amplitudes in Severe Seas With Breaking

A theoretical model is presented for the probability distribution of wave crest amplitudes in severe seas states with wave breaking. As the severity of a sea state increases, nonlinearities cause an increase in the amplitudes of the largest wave crests with a subsequent modification of the distribution of wave crest amplitudes from the linear Rayleigh theory. In this paper, a theory for the probabilities of these nonlinear crest amplitudes is first reviewed based on earlier work. The further limitations on these nonlinear crest amplitudes by wave breaking are then considered. As a result, a theoretical model is presented to account for both: 1) the nonlinear increase in the highest wave crests, and 2) the selective reduction of some fraction of these high crests due to wave breaking. This model is then verified using several sets of laboratory data for severe breaking seas having approximate JONSWAP wave spectra.