Hydrodynamics and third sound in thin superfluid helium films

Abstract

The linearized hydrodynamic equations for thin superfluid films, which were developed by the author and solved previously by an analytical approximation, 1 have now been solved numerically to yield the velocity and attenuation of thirdsound waves. The numerical solution covers a much wider range of film thicknesses and third-sound frequencies than was accessible by the analytical approximation. The numerical results coincide with the analytical approximation over the range where the latter was expected to be valid, i.e., for very thin films and low frequencies. Outside that region the striking deviations are in the attenuation coefficient ~, which is plotted in Fig. 1 as a function of film thickness at T = 1.3°K