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Abstract: We solve numerically for the first time the two-fluid,Hall-Vinen-Bekarevich-Khalatnikov HVBK equations for a He-II-likesuperfluid contained in a differentially rotating, spherical shell,generalizing previous simulations of viscous spherical Couette flow SCF andsuperfluid Taylor-Couette flow. In axisymmetric superfluid SCF, the number ofmeridional circulation cells multiplies as $\Rey$ increases, and their shapesbecome more complex, especially in the superfluid component, with multiplesecondary cells arising for $\Rey > 10^3$. The torque exerted by the normalcomponent is approximately three times greater in a superfluid with anisotropicHall-Vinen HV mutual friction than in a classical viscous fluid or asuperfluid with isotropic Gorter-Mellink GM mutual friction. HV mutualfriction also tends to -pinch- meridional circulation cells more than GM mutualfriction. The boundary condition on the superfluid component, whether no slipor perfect slip, does not affect the large-scale structure of the flowappreciably, but it does alter the cores of the circulation cells, especiallyat lower $\Rey$. As $\Rey$ increases, and after initial transients die away,the mutual friction force dominates the vortex tension, and the streamlines ofthe superfluid and normal fluid components increasingly resemble each other. Innonaxisymmetric superfluid SCF, three-dimensional vortex structures areclassified according to topological invariants.



Author: C. Peralta, A. Melatos, M. Giacobello, A. Ooi

Source: https://arxiv.org/







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