Vortex waves in a rotating superfluid
Abstract
In a recent experiment, Finne et al. discovered an intrinsic condition for the onset of quantum turbulence in ^{3}HeB, that q = α/(1  α') < 1.3, where α and α' are mutual friction parameters. The authors put forward a qualitative argument that q is the ratio of dissipative and inertial forces on the superfluid, so for q < 1 inertial forces should overcome the dissipative forces and cause turbulence. Thus 1/q would play, for a quantum fluid, the same role played in classical fluid dynamics by the Reynolds number (the ratio of inertial forces and dissipative forces in the NavierStokes equation). The aim of this work is to supplement this qualitative condition q = 1 with a quantitative calculation. By analysing both axisymmetric and nonaxisymmetric modes of a continuum of vortices in a rotating superfluid, we find that in the long axial wavelength limit the condition q = 1 is the crossover between damped and propagating Kelvin waves; thus, for q > 1, perturbations on the vortices are unlikely to cause vortex reconnections and turbulence. Besides the relevance to the experiment of Finne et al., the spectrum of oscillations which we find is relevant to the study of torsional oscillations of a rotating superfluid and generalises to three dimensions the spectrum of Kelvin waves on an isolated vortex line.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 July 2004
 DOI:
 10.1209/epl/i2004100811
 Bibcode:
 2004EL.....67...56H