3 research outputs found
Oscillatory superfluid Ekman pumping in Helium II and neutron stars
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
of Chandler & Baym (1986) with the spin-up experiments of Tsakadze & Tsakadze
(1980) in helium II and find the frequency agrees within a factor of four,
although the experiment is not perfectly suited to the application of the
linear theory. We argue that this oscillatory Ekman pumping mode, and not
Tkachenko modes provide 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 timescales.Comment: 25 pages, 6 figures, submitted to Journal of Fluid Mechanic