The kinetic equation solutions and Kolmogorov spectra

The Hasselmann kinetic equation (KE) for stochastic nonlinear surface waves is studied numerically with the aim of searching for features of the Kolmogorov turbulence (KT). To this aim, solutions of the KE for the long-term wave-spectrum evolution are executed. As far as the total wave action N and wave energy E are not preserved simultaneously in the course of the KE solution, two versions of the numerical algorithm are used, preserving values of N or E in separate. In every case, the KE solutions result in formation of the self-similar spectrum shape, Ssf(ω), with the frequency tail Ssf(ω) ∼ ω-4, independently of the N- or E-fluxes generated by the nonlinear interactions. This urges us to state that the used KE does not obey to regulations of the KT. The reason of this fact resides in the mathematical feature of the kinetic integral, which, in any case of solving the KE, results in formation of the nonlinear energy-transfer tail of kind Nl(ω) ∼ - ω-4, what stabilizes the spectral tail in form SSf(ω) ∼ ω-4.