Stability of weak turbulence Kolmogorov spectra

Sergey Senchenko

Department of Physics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark.

Abstract: As it was first found by A.I. Dyachenko, Y.V. Lvov and V.E. Zakharov, the 1D nonlinear dynamics of deep water surface gravity waves is governed by five-wave interaction processes. In order to get the statistical description of a stochastic wave field one can use a pair correlation function. The kinetic equation for the pair correlators was derived and its stationary solutions were found. This solutions turned out to be power-like, i.e. of quasi-Kolmogorov type. In the present paper we derive the linearized kinetic equation and investigate the stability of stationary solutions with respect to time-dependent 1D perturbations.