Europhys. Lett.
Volume 67, Number 1, July 2004
Page(s) 56 - 62
Section Condensed matter: structure, mechanical and thermal properties
Published online 01 June 2004
Europhys. Lett., 67 (1) , pp. 56-62 (2004)
DOI: 10.1209/epl/i2004-10081-1

Vortex waves in a rotating superfluid

K. 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 $\chem{{}^{3}He}$- $\chem{B}$, that $q=\alpha/(1-{\alpha'})<1.3$, where $\alpha$ and $\alpha'$ 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 $\chem{{}^{3}He}$.

© EDP Sciences 2004