International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 18, Pages 2913-2932
Transitional vortices in wide-gap spherical annulus flow
Department of Mathematics, The University of Benin, Ug bowo, Benin City PMB 1154, Nigeria
Received 19 August 2004; Revised 6 May 2005
Copyright © 2005 E. O. Ifidon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.