Transitional vortices in wide-gap spherical annulus flow

We develop a semianalytic formulation suitable for solving the Navier-Stokes equations governing the induced steady, axially symmetric motion of an incompressible viscous fluid confined in a wide gap between two differentially rotating concentric spheres. The method is valid for arbitrarily high Reynolds number and aids in the presentation of multiple steady-state flow patterns and their bifurcations. In the case of a rotating inner sphere and a stationary outer sphere, linear stability analysis is conducted to determine whether or not the computed solutions are stable. It is found that the solution transforms smoothly into an unstable solution beginning with asymmetric vortex pairs identified near the point of a symmetry-breaking bifurcation which occurs at Reynolds number 589. This solution transforms smoothly into an unstable asymmetric vortex solution as the Reynolds number increases. Flow modes whose branches have not been previously reported are found using this method. The origin of the flow modes obtained are discussed using bifurcation theory.