Torsional Oscillations of a Rotating Column of $^3$He-B

Abstract

We have analysed the axisymmetric and non-axisymmetric modes of a continuum of vortices in a rotating superfluid. We have investigated how changing the temperature affects the growth rate of the disturbances. We find that, in the long axial wavelength limit the condition q=alpha/(1-alpha')=1, where alpha and alpha' are temperature-dependent mutual friction parameters, is the crossover between damped and propagating Kelvin waves. Thus at temperatures for which q>1, perturbations on the vortices are unlikely to cause vortex reconnections and turbulence. These results are in agreement with the recent discovery of Finne et al (2003} of an intrinsic condition for the onset of quantum turbulence in $^3$He-B.