Capillary Turbulence on the Surfaces of Quantum Fluids

Abstract We discuss the results of recent studies of weak turbulence in a system of capillary waves on the surface of liquid hydrogen and of helium 4 He in normal and superfluid state. It was observed that when the driving amplitude was sufficiently high, a steady state direct Kolmogorov-Zakharov cascade is formed involving a flux of energy towards high frequencies. The wave amplitude distribution follows a power-law over a wide range of frequencies, in agreement with the weak turbulence theory. It was found that the decay of capillary turbulence begins from the high-frequency end of the spectral range, while most of the energy remains localised at low frequencies. We show that this process can be accounted for in terms of a quasiadiabatic decay wherein fast nonlinear wave interactions redistribute energy between frequency scales in the presence of finite damping at all frequencies. Our numerical calculations based on this idea agree well with experimental data.