Spin-up of a two-component superfluid: Self-consistent container feedback

Abstract

The coupled dynamic response of a rigid container filled with a two-component superfluid undergoing Ekman pumping is calculated self-consistently. The container responds to the back-reaction torque exerted by the viscous component of the superfluid and an arbitrary external torque. The resulting motion is described by a pair of coupled integral equations for which solutions are easily obtained numerically. If the container is initially accelerated impulsively then set free, it relaxes quasi-exponentially to a steady state over multiple time scales, which are a complex combination of the Ekman number, superfluid mutual friction coefficients, the superfluid density fraction, and the varying hy..