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We numerically solve the nonlinear two-fluid Hall–Vinen–Bekharevich–Khalatnikov (HVBK) equations for superfluid helium confined inside a short Couette annulus. The outer cylinder and the ends of the annulus are held fixed whilst 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 boundaries. It also allows us to investigate further the boundary conditions associated with the HVBK model. The main result of our investigation is the anomalous motion of helium II when compared to a classical fluid. The superfluid Ekman cells always rotate in the opposite sense to a classical Navier–Stokes fluid due to the mutual friction between the two fluids, whilst the sense of rotation of the normal fluid Ekman cells depends on the parameter range considered. We also find that the tension of the vortex lines forces the superfluid to rotate about the inner cylinder almost like a rigid column.

We solve the nonlinear two-fluid Hall–Vinen–Bekharevich–Khalatnikov equations of motion of helium II for the first time and investigate the configuration of quantized vortex lines in Taylor–Couette flow. The results are interpreted in terms of quantities which can be observed by measuring the attenuation of second sound. Comparison is made with existing experimental results.

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