General third-order solutions for irregular waves in deep water

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