Spin down of superfluid-filled vessels: theory versus experiment

TL;DR

This paper compares theoretical predictions and experimental results for the spin-down behavior of superfluid helium II in a vessel, confirming the accuracy of a recent analytic solution and exploring effects of temperature and vortex dynamics.

Contribution

It introduces a self-consistent analytic solution for superfluid spin-up and spin-down, validated against experiments, and investigates vortex effects near the lambda transition.

Findings

Excellent agreement with experiments at 1.57 K.

Vortex tension and pinning are minimal under certain conditions.

Spin-down time depends on temperature and viscous component fraction.

Abstract

The spin up of helium II is studied by calculating the spin-down recovery of a superfluid-filled container after an impulsive acceleration and comparing with experiments. The calculation takes advantage of a recently published analytic solution for the spin up of a Hall-Vinen-Bekharevich-Khalatnikov superfluid that treats the back-reaction torque exerted by the viscous component self-consistently in arbitrary geometry for the first time. Excellent agreement at the 0.5% level is obtained for experiments at $T=1.57\,{\rm K}$, after correcting for the non-uniform rotation in the initial state, confirming that vortex tension and pinning (which are omitted from the theory) play a minimal role under certain conditions (small Rossby number, smooth walls). The dependence of the spin-down time on temperature and the mass fraction of the viscous component are also investigated. Closer to the lambda point, the predicted onset of turbulence invalidates the linear Ekman theory.