Appearance of vortices in rotating He II

The conditions for the appearance and disappearance of quantized vortices in rotating superfluid helium are examined. Our approach is based on the two-fluid model of He II. Using a local-momentum-conservation equation, appropriate when the appearance and disappearance of vortices is on a short time scale compared with normal fluid viscous times, we find that the free-energy theory has to be modified. The new theory predicts hysteresis between increasing and decreasing angular velocity, as observed in some experiments. The theory is applied to some experiments on uniformly rotating superfluid, and also to experiments on Couette flow. Finally, we consider the stability of a vortex row between rotating cylinders to perturbations independent of the direction of the rotation axis.