Simulation of flow between concentric rotating spheres. Part 1. Steady states

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Abstract
Axisymmetric spherical Couette flow between two concentric differentially rotating spheres is computed numerically as an initial-value problem. The time-independent spherical Couette flows with zero, one and two Taylor vortices computed in our simulations are found to be reflection-symmetric about the equator despite the fact that our pseudospectral numerical method did not impose these properties. Our solutions are examined for self-consistency, compared with other numerical calculations, and tested against laboratory experiments. At present, the most precise laboratory measurements are those that measure Taylor-vortex size as a function of Reynolds number, and our agreement with these results is within a few per cent. We analyse our flows by plotting their meridional circulations, azimuthal angular velocities, and energy spectra. At Reynolds numbers just less than the critical value for the onset of Taylor vortices, we find that pinches develop in the flow in which the meridional velocity redistributes the angular momentum. Taylor vortices are easily differentiated from pinches because the fluid in a Taylor vortex is isolated from the rest of the fluid by a streamline that extends from the inner to the outer sphere, whereas the fluid in a pinch mixes with the rest of the flow.