  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.
