Vortex waves in a rotating superfluidK. L. Henderson1 and C. F. Barenghi2
1 School of Mathematical Sciences, CEMS, University of the West of England Bristol, BS16 1QY, UK
2 School of Mathematics and Statistics, University of Newcastle Newcastle upon Tyne, NE1 7RU, UK
(Received 14 January 2004; accepted in final form 30 April 2004)
In a recent experiment, Finne et al. discovered an intrinsic condition for the onset of quantum turbulence in - , that , where and 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 Navier-Stokes equation). The aim of this work is to supplement this qualitative condition q=1 with a quantitative calculation. By analysing both axisymmetric and non-axisymmetric 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.
67.40.Vs - Vortices and turbulence.
67.57.-z - Superfluid phase of liquid .
© EDP Sciences 2004