Analysis of the Nonlinear Spectrum of Intense Sea Wave with the Purpose of Extreme Wave Prediction

Abstract

We propose a method for the analysis of groups of unidirectional waves on the surface of deep water, which is based on spectral data of the scattering problem in the approximation of a nonlinear Schrödinger equation. The main attention is paid to the robustness and accuracy of the numerically obtained spectral data. Various methods of choosing the wave number of the carrier wave, which rely on the analysis of the local Fourier transform and the zero-crossing wave analysis, are considered. The most robust wave numbers have been chosen on the basis of two model examples. A method for improving the accuracy of the soliton amplitude prediction, which uses the “feedback” in solving the associated scattering problem, is proposed. In the wave steepness range from 0.15 to 0.30, the accuracy of determining the amplitude of the soliton group by this technique lies in a range of 10%.