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Oscillatory superfluid Ekman pumping in helium II and neutron stars

Published online by Cambridge University Press:  16 October 2015

C. Anthony van Eysden
C. Anthony van Eysden*
Affiliation:
Department of Physics, Montana State University, Bozeman, MT 59717, USA Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden
*
†Email address for correspondence: anthonyvaneysden@montana.edu
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Abstract

The linear response of a superfluid, rotating uniformly in a cylindrical container and threaded with a large number of vortex lines, to an impulsive increase in the angular velocity of the container is investigated. At zero temperature and with perfect pinning of vortices to the top and bottom of the container, we demonstrate that the system oscillates persistently with a frequency proportional to the vortex line tension parameter to the quarter power. This low-frequency mode is generated by a secondary flow analogous to classical Ekman pumping that is periodically reversed by the vortex tension in the boundary layers. We compare analytic solutions to the two-fluid equations by Chandler & Baym (J. Low Temp. Phys., vol. 62, 1986, pp. 119–142) with the spin-up experiments by Tsakadze & Tsakadze (J. Low Temp. Phys., vol. 39, 1980, pp. 649–688) in helium II and find that the frequency agrees within a factor of four, although the experiment is not perfectly suited to the application of linear theory. We argue that this oscillatory Ekman pumping mode, and not Tkachenko modes, provides a natural explanation for the observed oscillation. In neutron stars, the oscillation period depends on the pinning interaction between neutron vortices and flux tubes in the outer core. Using a simplified pinning model, we demonstrate that strong pinning can accommodate modes with periods of days to years, which are only weakly damped by mutual friction over longer time scales.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Complex Fluids: Quantum fluids Geophysical and Geological Flows: Rotating flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 783 , 25 November 2015 , pp. 251 - 282
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© 2015 Cambridge University Press 

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