Turbulent capillary cascade near the edge of the inertial range on the surface of a quantum liquid

In the dissipative range at frequencies above the inertial frequency range, the turbulent cascade of capillary waves on the surface of liquid helium and hydrogen decays according to an exponential law. The characteristic frequency of the quasi-Planck distribution is determined by the spectral characteristic of an exciting force. In the case of harmonic pumping on the surface of superfluid helium in the discrete turbulence regime, energy condensation is observed near the high-frequency edge of the inertial range. The effect is due to the influence of discreteness in the spectrum of the eigenfrequencies of surface excitations and in the turbulence distribution on the energy transfer through the cascade.