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Spin Down of Superfluid-Filled Vessels: Theory Versus Experiment

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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 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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  1. School of Physics, University of Melbourne, Parkville, VIC, 3010, Australia

    C. A. van Eysden & A. Melatos

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  1. C. A. van Eysden
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van Eysden, C.A., Melatos, A. Spin Down of Superfluid-Filled Vessels: Theory Versus Experiment. J Low Temp Phys 165, 1 (2011). https://doi.org/10.1007/s10909-011-0385-6

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