Transient growth of Kelvin waves on quantized vortices

Quantized vortex lines in helium II can be destabilized by a sufficiently large normal fluid velocity which is parallel to the vortex lines (Donnelly - Glaberson instability). We study what happens if the driving normal fluid is not steady but oscillates periodically with time. We show that in certain situations, although individual perturbations decay when time goes to infinity, a state of transient growth of Kelvin waves is possible, which may explain observations of a small and not reproducible longitudinal component of mutual friction.