Abstract
We discuss our present knowledge of the flow and stability of helium II between concentric cylinders. The flow problem for helium II leads us to consider the formation of quantized vortices in the uniform rotation of helium II in an open bucket as well as quantized circulation states and vortices in a rotating annulus. We then consider how to treat the first appearance of vortices in the presence of shear, which allows us to characterize the basic flow which must be examined for stability. The results suggest an explanation for heretofore unexplained experiments. Future directions for research on the stability of helium II are suggested.
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