The appearance of vortices in the flow of helium II between rotating cylinders

We argue that the appearance of quantized vortices in laminar Taylor-Couette flow of helium II is a problem for which free energy minimization should give valid results even in the presence of dissipation. We (approximately) reduce the problem to an equivalent problem in solid-body rotation, for which the solution for the low-lying states has been obtained by Fetter. We then use approximations to the solution for solid-body rotation to predict the appearance of vortices for the general Taylor-Couette problem. These results compare moderately well with the existing data, which now seem relatively incomplete.