Branching of Navier-Stokes equations in a spherical gap

The branching of Navier-Stokes equations in the gap between two concentric spheres, of which the inner one rotates and the outer one is stationary, is investigated by using the continuation method proposed by Keller (1977) to solve the unsteady Navier-Stokes equations. It is shown that for the ratio of radii of 0.85, the branches of the flow modes with Taylor vortices do not bifurcate from the basic branch, as is true for flows in cylindrical gaps. It is also shown that the transition from the basic to other modes can only be achieved by unsteadiness or asymmetry.