Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 6 1 1999 10.5194/npg-6-1-1999 http://www.nonlin-processes-geophys.net/6/1/1999/ http://www.nonlin-processes-geophys.net/6/1/1999/npg-6-1-1999.html http://www.nonlin-processes-geophys.net/6/1/1999/npg-6-1-1999.pdf 1 10 0000-00-00 Diffusion model of interacting gravity waves on the surface of deep fluid V. E. Zakharov A. N. Pushkarev Arizona Center of Mathematical Science, Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA L.D. Landau Institute for Theoretical Physics. Russian Academy of Sciences, 117940 GSP-1 Moscow V-334, ul. Kosygina 2, Russia A simple phenomenological model for nonlinear interactions of gravity waves on the surface of deep water is developed. The S_nl nonlinear interaction term in the kinetic equation for wave action is replaced by the nonlinear second-order diffusion-type operator. Analytical and numerical studies show that the new model gives a reasonably good description of a real situation, consuming three order of magnitude less computer time.