Hydrodynamic theory of fourth sound in clamped conditions

The hydrodynamic theory of fourth sound is developed in detail for the cases of a flat capillary and a porous superleak filled with superfluid helium whose normal fluid motion is completely clamped. The attenuation is calculated including rigorously all the thermal conduction effects in both the helium and the capillary walls. Also included in the case of the superleak are the Rayleigh scattering and the thermal effects of the resonator walls. Comparison of the superleak results with existing experiments leads to the conclusion that Q factors of fourth-sound resonators could be increased considerably.