Mechanisms of the equilibrium-range formation in the wind-wave spectrum. Numerical simulation

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The issue of the equilibrium-range formation in the wind-wave spectrum is studied by a direct numerical simulation. The evolution equation of wind-wave spectrum is numerically solved with using an exact calculation of the Hasselmann kinetic integral and involving various modifications of known parametrizations for the wave-pumping mechanism due to wind and the wave-dissipation mechanism due viscosity of the upper layer. It is shown that the balance of the last two mechanisms is responsible for a formation of stationary part of the wind-wave spectrum. This balance allows establishing any prescribed form of the equilibrium part of the spectrum, if the proper representations of input and dissipation mechanisms are chosen.