Stability of weak turbulence Kolmogorov spectra
Department of Physics, Technical University of Denmark,
2800 Kongens Lyngby, Denmark.
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.