Torsional Oscillations of a Rotating Column of $^3$He-B

TL;DR

This paper analyzes how temperature-dependent mutual friction affects vortex oscillations in rotating superfluid helium-3 B, identifying a critical condition for the transition between damped and propagating Kelvin waves related to turbulence onset.

Contribution

It provides a theoretical analysis of vortex oscillations in superfluid helium-3 B, linking mutual friction parameters to the transition between damped and propagating Kelvin waves.

Findings

The condition q=1 marks the crossover between damped and propagating Kelvin waves.

At q>1, vortex perturbations are unlikely to cause turbulence.

Results align with experimental observations of turbulence onset in $^3$He-B.

Abstract

We have analysed the axisymmetric and non-axisymmetric modes of a continuum of vortices in a rotating superfluid. We have investigated how changing the temperature affects the growth rate of the disturbances. We find that, in the long axial wavelength limit the condition q=alpha/(1-alpha')=1, where alpha and alpha' are temperature-dependent mutual friction parameters, is the crossover between damped and propagating Kelvin waves. Thus at temperatures for which q>1, perturbations on the vortices are unlikely to cause vortex reconnections and turbulence. These results are in agreement with the recent discovery of Finne et al (2003} of an intrinsic condition for the onset of quantum turbulence in $^3$He-B.