Weak turbulent approach to the wind-generated gravity sea waves

We performed numerical simulation of the kinetic equation describing behavior of an ensemble of random-phase, spatially homogeneous gravity waves on the surface of the infinitely deep ocean. Results of simulation support the theory of weak turbulence not only in its basic points, but also in many details. The weak turbulent theory predicts that the main physical processes taking place in the wave ensemble are down-shift of spectral peak and 'leakage' of energy and momentum to the region of very small scales where they are lost due to local dissipative processes. Also, the spectrum of energy right behind the spectral peak should be close to the weak turbulent Kolmogorov spectrum which is the exact solution of the stationary kinetic (Hasselmann) equation. In a general case, this solution is anisotropic and is defined by two parameters—fluxes of energy and momentum to high wave numbers. Even in the anisotropic case, the solution in the high wave number region is almost proportional to the universal form ω−4. This result should be robust with respect to change of the parameters of forcing and damping. In all our numerical experiments, the ω−4 Kolmogorov spectrum appears in very early stages and persists in both stationary and non-stationary stages of spectral development. A very important aspect of the simulations conducted here was the development of a quasi-stationary wave spectrum under wind forcing, in absence of any dissipation mechanism in the spectral peak region.