A NEW STATISTICAL DISTRIBUTION FOR THE SURFACE ELEVATION OF WEAKLY NONLINEAR WATER-WAVES

A new statistical distribution for the surface elevation of weakly non linear water waves is derived using the Pearson System of distribution s. The new distribution avoids some problems associated with previousl y proposed distributions. Namely, its probability density function is positive everywhere, unlike prior results obtained with Gram-Charlier series. Furthermore, it is derived without requiring the assumptions t hat the wavefield is unidirectional and narrow band, as made in some e arlier studies. The distribution obtained is a form of the beta distri bution and depends only on two parameters, the variance and the skewne ss of the sea surface elevation. The new distribution is compared to w ave data, measured on a reservoir, and found to give a reasonable fit.