Two stages of decay turbulence of capillary waves

Evolution of decay turbulence of capillary waves in deep water is considered in the framework of the isotropic kinetic equation. It is shown that the evolution comprises of two stages. During the first stage an arbitrary localized large-scale wave distribution explosively evolves into a small-scale Kolmogorov spectrum. The second stage starts at the moment the Kolmogorov spectrum reaches dissipative scales. For systems with non-linear damping, the characteristic time of this stage is much longer (up to thousand times) than the first stage. The energy distribution is close to the Kolmogorov spectrum and decaying follows a self-similar law.