Issue |
Europhys. Lett.
Volume 67, Number 1, July 2004
|
|
---|---|---|
Page(s) | 56 - 62 | |
Section | Condensed matter: structure, mechanical and thermal properties | |
DOI | https://doi.org/10.1209/epl/i2004-10081-1 | |
Published online | 01 June 2004 |
Vortex waves in a rotating superfluid
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:
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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