The anomalous motion of superfluid helium in a rotating cavity

We numerically solve the nonlinear two-fluid Hall-Vinen-Bekharevich-Khalatn ikov (HVBK) equations for superfluid helium confined inside a short Couette annulus. The outer cylinder and the ends of the annulus are held fixed whi lst the inner cylinder is rotated. This simple flow configuration allows us to study how the vortex lines respond to a shear in the presence of bounda ries. It also allows us to investigate further the boundary conditions asso ciated with the HVBK model. The main result of our investigation is the ano malous motion of helium II when compared to a classical fluid. The superflu id Ekman cells always rotate in the opposite sense to a classical Navier-St okes fluid due to the mutual friction between the two fluids, whilst the se nse of rotation of the normal fluid Ekman cells depends on the parameter ra nge considered. We also find that the tension of the vortex lines forces th e superfluid to rotate about the inner cylinder almost like a rigid column.