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

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 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.