Flow bifurcation and transition in a gap between two-rotating spheres

This study investigates the flow bifurcation and transition between stable states in the gap between two concentric rotating spheres. Acontinuation method is used together with linear stability analysis to investigate the bifurcation structure of the discretized governing equations and to determine the stability of the calculated states. The constructed bifurcation diagram is used to illustrate the restricted range of Reynolds number within which each equilibrium state exists. The diagram also identifies the permissible transitions between these states and indicates their terminative states. In the present study, it is shown how appropriate control of the angular velocity of the outer sphere results in the evolution of the flow state through a series of permitted stable states. The time-dependent transitions between these states are investigated by means of a backwards-Euler time stepping formulation. The terminate state of transition process can also be used to confirm the stability of the flow. The flow evolution between each transition is illustrated by means of temporal sequences of the meridional streamlines and transition curves. The present results indicate that all the flow transitions in a gap between two rotating spheres are produced symmetrically with respect to the equator.