Two-dimensional nonlinear energy transfer over the spectrum of waves in a finite-depth water in the three-wave quasi-kinetic approximation

The three-wave quasi-kinetic approximation developed earlier by the author and M.M. Zaslavskii [1] is used to numerically study two-dimensional nonlin ear energy transfer over the spectrum of gravity waves in a finite-depth wa ter. The geometry of nonlinear transfer and its dependence on the shape of the two-dimensional wave spectrum are first found. The dependence of the in tensity of transfer on the wave steepness and the dimensionless depth param eter k(p)h is determined. It is found that if k(p)h > 1, the intensity of n onlinear transfer is negligibly small. On the basis of numerically solving the quasi-kinetic system of equations, the rate of wave-spectrum evolution at one point through nonlinear interactions is studied. The time scales on which multiple harmonics appear are obtained as functions of the wave steep ness and the depth parameter k(p)h. It is shown that if k(p)h > 0.6, the sh ape of the two-dimensional wave spectrum essentially does not evolve, and i f k(p)h less than or equal to 0.3, a multiple-harmonic peak arises on time scales on the order of a few fundamental periods. The rate of evolution is approximately proportional to the wave steepness squared and depends on the shape of the spectrum.