Probability Distribution Functions of Freak Waves: Nonlinear Versus Linear Model

Presented are the results of numerical experiments on calculation of probability distribution functions (PDFs) for surface elevations of water waves arising during the evolution of statistically homogeneous wave field. Extreme waves or freak waves are an integral part of ocean waving, and PDFs are compared both for nonlinear and linear models. Obviously, linear model demonstrates the Rayleigh distribution of surface elevations while PDFs for nonlinear equation have tails for large elevations similar to Rayleigh distribution, but with much larger σ.