An Experimental and theoretical study of torsional oscillations in uniformly rotating liquid helium II

Abstract

Measurements have been made of the period (2π/Ω) of small torsional oscillations of an Andronikashvili disk system, superposed on a uniform rotation with angular velocity ω₀. If the changes in period are expressed formally as an effective density of liquid ρ' that moves with the disks it is found that, for sufficiently rough disk surfaces and sufficiently small amplitudes of oscillation: (i) for ω₀ ≫ Ω, ρ'/ρ_s increases monotonically from 0 to 1 with increasing ω₀ and increasing disk separation; (ii) for ω₀ ≪ Ω, ρ'can be either positive or negative; when plotted as a function of disk separation it shows a resonance-dispersion type of behaviour. These results can be explained by the vortex line model of Onsager and Feynman in terms of a transverse wave motion of the vortex lines, if it is supposed that the ends of the lines tend to stick to a sufficiently rough surface. The theory of these vortex waves has been worked out in some detail. The behaviour of the liquid is determined by a parameter v = ϵ/ρ_sk, where ϵ is the energy of unit length of vortex line and k is the circulation round a line; comparison of theory and experiment gives v = (8·5 ± 1·5) × 10^-4 cm²s^-1, some 25% less than Feynman’s theoretical estimate. In the final section some consequences of the existence of vortex waves are discussed.