Spin-up of a two-component superfluid: Analytic theory in arbitrary geometry

Abstract

The impulsive spin-up of a two-component superfluid and its container is solved analytically for the first time in arbitrary geometry, generalizing the extensively studied case of single-fluid spin-up. The superfluid is modelled by the Hall-Vinen-Bekarevich-Khalatnikov (HVBK) two-fluid equations, neglecting nonhydrodynamic processes like vortex tension and pinning, which are weak in certain applications (e.g. neutron stars) and confined to boundary layers in the inviscid HVBK component in other applications (e.g. helium II spin-up in smooth-walled containers). Both components of the flow are found to be columnar. The spin-up time depends on the geometry, mutual friction coefficients, B, B0, ..