Studying the equations of the quasi-kinetic approximation for nonlinear gravity waves in a finite-depth water

The system of equations that was obtained previously in [1] in the approxim ation of three-wave nonresonant interactions for the rate of spectrum evolu tion partial derivative N(k)partial derivative t and the attenuation rate b eta(k) of nonlinear waves in a finite-depth water and that was called the " quasi-kinetic" approximation is studied analytically and numerically. The s tudy is aimed at assessing the character of nonlinear transfer P(k) = parti al derivative N(k)partial derivative t and determining the dependence of th e attenuation race on wave number k and depth h. Three-wave processes are s hown to generate multiple harmonics in a narrow-band spectrum of waves. In this connection, a structural similarity is established between the equatio n for partial derivative N(k)partial derivative t obtained in the above app roximation and the kinetic equation for resonance semidispersive waves disc ussed in [3]. Nonlinear transfer and nonlinear attenuation rates of wave co mponents are estimated numerically in the quasi kinetic approximation in th e case of unidirectional waves, A numerical evolutionary solution of the qu asi-kinetic system of equations is obtained in the same case. II is shown t hat three-wave processes cause the behavior of shallow-water waves to be cl ose to that observed in experiments.