Spatio-temporal behaviour in an enclosed corotating disk pair

We present a numerical investigation of the flow between corotating disks w ith a stationary outer casing - the enclosed corotating disk pair configura tion. It is known that in such a geometry, axisymmetric and three-dimension al flow regimes develop depending on the value of the rotation rate. The th ree-dimensional flow is always unsteady owing to its wavy structure in the radial-tangential plane. Axisymmetric regimes exhibit first a pitchfork bif urcation, characterized by a symmetry breaking with respect to the inter-di sk midplane, before a Hopf bifurcation is established. The regime diagrams for these bifurcations are given in the (Re, G)-plane, where Rc(= Omegab(2) /v) is the rotational Reynolds number and G(= s/(b-a)) is the gap ratio. Fo r values of G smaller than a critical limit G(c) similar to 0.26, there exi sts a range of rotation rates where the motion becomes time-dependent befor e bifurcating to a steady symmetry breaking regime. It is shown that for G greater than or equal to G(c) the transition to unsteady three-dimensional how occurs after the pitchfork bifurcation, and the flow structure is chara cterized by a shift-and-reflect symmetry. The transition to three-dimension al flow is consistent with experimental observations made by Abrahamson et al. (1989) where multiple solutions develop (known as the intransitivity ph enomenon) with the presence of quasi-periodic behaviour resulting from succ essive vortex pairings. On the other hand, for smaller values of gap ratio, the three-dimensional flow shows a symmetry breaking. Finally, it is found that the variation of torque coefficient as a function of the rotation rat e is the same for both the axisymmetric and three-dimensional solutions.