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arXiv · 1108.0478

Spin down of superfluid-filled vessels: theory versus experiment

C. A. van Eysden·A. Melatos
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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.

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C. A. van Eysden, A. Melatos. 2011-08-02. Spin down of superfluid-filled vessels: theory versus experiment. https://doi.org/10.1007/s10909-011-0385-6

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