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

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&#39;)<1, where alpha and alpha&#39; 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.