General Third-Order Solutions for Irregular Waves in Deep Water

Abstract

The third-order analytical solutions for the strong interactions among three free-wave components are derived using two well-known perturbation methods, namely, the mode-coupling method and the Zakharov equation method. A term-by-term comparison of their solutions shows that the two methods render virtually identical results. The validity and convergence range of the solution are investigated for the interacting free-wave components of various frequencies but within the frequency range of storm seas. It is found that the solution may encounter two types of convergence difficulties, which occur, respectively, in the cases (1) when two of the interacting free-wave components are of quite different frequencies; and (2) when two of the interacting free-wave components are very close in frequency but the frequency of the third free-wave component is relatively larger or smaller.