Volume 67, Number 1, July 2004
|Page(s)||56 - 62|
|Section||Condensed matter: structure, mechanical and thermal properties|
|Published online||01 June 2004|
Vortex waves in a rotating superfluid
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
Accepted: 30 April 2004
In a recent experiment, Finne et al. discovered an intrinsic condition for the onset of quantum turbulence in -, that , where α 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 inertial forces should overcome the dissipative forces and cause turbulence. Thus 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 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 is the crossover between damped and propagating Kelvin waves; thus, for , 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.
PACS: 67.40.Vs – Vortices and turbulence / 67.57.-z – Superfluid phase of liquid
© EDP Sciences, 2004
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