Numerical Verification of the Weak Turbulent Model for Swell Evolution

The purpose of this article is numerical verification of the theory of weak turbulence. We performed numerical simulation of an ensemble of nonlinearly interacting free gravity waves swell by two different methods solution of primordial dynamical equations describing potential flow of the ideal fluid with a free surface and, solution of the kinetic Hasselmann equation, describing the wave ensemble in the framework of the theory of weak turbulence. In both cases we observed effects predicted by this theory frequency downshift, angular spreading and formation of Zakharov-Filonenko spectrum Iomega omega -4. To achieve quantitative coincidence of the results obtained by different methods, one has to supply the Hasselmann kinetic equation by an empirical dissipation term Sdiss modeling the coherent effects of white-capping. Using of the standard dissipation terms from operational wave predicting model WAM leads to significant improvement on short times, but not resolve the discrepancy completely, leaving the question about optimal choice of Sdiss open. In a long run WAM dissipative terms overestimate dissipation essentially.