Flow between two rotating concentric spheres

The vortex flow field formed at large Reynolds numbers between two rotating concentric spheres can be calculated using finite difference approximations of the Navier-Stokes equations. It is found, however, that the number of vortices calculated changes with the spatial resolution. This is explained by the appearance of one or more extrema of the dependent flow variables in the meridional direction. The spatial-resolution problem can be overcome if an accuracy condition is introduced which can be derived from the periodicity of the solution and the ratio of the radii of the spheres. Since the solution is time dependent, the time step must be restricted.