Numerical study of the equations of nonlinear swell in the directional approximation

Numerical methods are employed to study the equations of directional approx imation, which were derived previously by Zakharov and Smilga [10] for Hass elmann's kinetic equation and which were transformed by Zaslavskii [12] to the form that admits self-similar solutions. Numerical solutions to Zaslavs kii's equations are obtained in a limited hand of wave numbers. It is shown that, in the region of-a spectral peak, the numerical solutions are in clo se agreement with the analytic solutions derived by Zaslavskii [12]. Howeve r, these solutions differ in the region away;from the spectral peak. A comp arison of the above solutions with the numerical solution of the initial ki netic equation obtained previously by the author [9] testifies to their goo d agreement and to-a wide range of validity of the directional approximatio n. The results of this comparison of solutions make it possible to give an efficient analytic approximation for a self-similar spectrum of swell, whic h is suitable for use: in numerical models of wind waves.