4TH-ORDER THEORY FOR MULTIPLE-WAVE INTERACTION

By using a Stokes-type expansion method, a fourth-order solution has been derived for nonlinear interaction among multiple directional wave trains. Since an arbitrary number of free-wave modes with arbitrary propagation directions can be imposed as first-order inputs, this solution may demonstrate more realistic wave fields, as compared to those obtained from periodic wave theories. For the cases of one and two free-wave modes, the present theory is found to coincide with conventional theories such as the Stokes and standing wave theories, indicating the validity and general applicability of the solution. As an application, two particular wave fields are calculated, involving 17 free wave modes, The results indicate that the third- and fourth-order components may produce isolated large crests in random wave fields, and that the fourth-order nonlinearity significantly contributes to low frequency modulation bound by wave trains.