A Semi-Empirical Wave Crest Distribution of Random Directional Wave Fields

Laboratory data of random directional wave fields have been used to investigate the combined effect of higher order nonlinearity and directional spreading on the wave crest distribution. Different sea states with a variety of combination of steepness and directional spreading have been considered, ranging from long to short crested wave fields. The analysis is also supported by numerical simulations. A 2-parameter Weibull distribution has been fitted to the experimental data and the related parameters have been parameterized as a function of a general version of the Benjamin-Feir Index for directional sea states recently presented by Mori et al. [1]. Long-term distributions of the one-dimensional and two-dimensional Benjamin-Feir Index have been studied based on the hindcast data from the North Atlantic and probabilistic models to describe them are proposed.