Transient growth of Kelvin waves on quantized vortices

TL;DR

This paper investigates how oscillating normal fluid velocities can cause transient growth of Kelvin waves on quantized vortices in helium II, potentially explaining observed non-reproducible mutual friction components.

Contribution

It introduces the concept of transient Kelvin wave growth under oscillatory normal fluid flow, extending understanding of vortex instability beyond steady conditions.

Findings

Transient Kelvin wave growth occurs despite eventual decay of perturbations.

Oscillatory normal fluid flow can induce non-reproducible mutual friction effects.

The study explains observations of small, inconsistent longitudinal mutual friction components.

Abstract

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.