Vortex waves and the onset of turbulence in $^3$He-B

TL;DR

This paper investigates the conditions under which Kelvin waves in superfluid helium-3 B become unstable and lead to turbulence, confirming a critical parameter value that marks the transition between damping and propagation of these waves.

Contribution

It provides a theoretical analysis confirming the experimental criterion q=1 as the threshold for Kelvin wave instability in superfluid helium-3 B.

Findings

Kelvin waves are marginally damped at q=1.

The transition from damping to propagation occurs at q=1.

The analysis applies to both axisymmetric and non-axisymmetric modes.

Abstract

In a recent experiment Finne et al. discovered an intrinsic condition for the onset of quantum turbulence in $^3$He-B, that q=alpha/(1-alpha')<1, where alpha and alpha' are mutual friction parameters. The authors argued that this condition corresponds to Kelvin waves which are marginally damped, so for q>1 Kelvin waves cannot grow in amplitude and trigger vortex reconnections and turbulence. By analysing both axisymmetric and non-axisymmetric modes of oscillations of a rotating superfluid, we confirm that in the long axial wavelength limit the simple condition q=1 is indeed the crossover between damped and propagating Kelvin waves.