Contributions of Nonlinear Spectral Components to the Probability Distribution of Rogue Waves Based on the Results of Numerical Simulation of the Euler Equations

Abstract

Based on the direct numerical modeling results of irregular nonlinear waves on the surface of deep water within the framework of three-dimensional potential equations of hydrodynamics, the contributions of various wave components (second, third, and difference harmonics) to the formation of probability distributions of extreme wave heights, as well as the amplitudes of crests and troughs, are determined. The simulation results are analyzed taking into account four- and five-wave nonlinear interactions. Various nonlinear harmonics participate in the formation of probability distributions in a nontrivial way, which is essentially not amenable to the principles of linear addition and the contribution of ordering by a small nonlinearity parameter.