Dissipation of ripplon flow at the surface of superfluid 4He

Within the framework of quantum hydrodynamics of a superfluid helium surface, the momentum relaxation rate caused by the annihilation of two ripplons with phonon creation, inelastic phonon scattering with ripplon annihilation, and in the case of helium films one-particle ripplon scattering from the surface-level inhomogeneities introduced by the substrate roughness (new relaxation mechanism) was obtained for a ripplon gas at T≲0.25 K. The contribution from the inelastic phonon scattering is negligible at these temperatures. For a film at T≤0.15 K, one-particle scattering dominates, leading to a temperature dependence of the form K∝T ^5/3 for the convective thermal conductance.At higher temperatures, phonon creation with annihilation of two ripplons is the dominant mechanism, giving K∝T ⁻³. These results are in quantitative agreement with the available experimental data.