On the kolmogorov and frozen turbulence in numerical simulation of capillary waves

Numerical simulation of dynamical equations for capillary waves excited by long-scale forcing shows the presence of both Kolmogorov spectrum at high wavenumbers (with the index predicted by weak-turbulent theory) and non-monotonic spectrum at low wavenumbers. The value of the Kolmogorov constant measured in numerical experiments happens to be different from the theoretical one. We explain the difference by the coexistence of Kolmogorov and “frozen” turbulence with the help of maps of quasi-resonances. Observed results are believed to be generic for different physical dispersive systems and are confirmed by laboratory experiments.