We present a numerical investigation of the flow between corotating disks with a
stationary outer casing – the enclosed corotating disk pair configuration. It is known
that in such a geometry, axisymmetric and three-dimensional flow regimes develop
depending on the value of the rotation rate. The three-dimensional flow is always
unsteady flowing to its wavy structure in the radial-tangential plane. Axisymmetric
regimes exhibit first a pitchfork bifurcation, characterized by a symmetry breaking
with respect to the inter-disk midplane, before a Hopf bifurcation is established.
The regime diagrams for these bifurcations are given in the (Re, G)-plane, where
Re(= Ωb2/ν) is the rotational Reynolds number
and G(= s/(b−a)) is the gap ratio. For values of G
smaller than a critical limit Gc ∼ 0.26, there exists a range of rotation rates
where the motion becomes time-dependent before bifurcating to a steady symmetry
breaking regime. It is shown that for G [ges ] Gc the transition to
unsteady three-dimensional flow occurs after the pitchfork bifurcation, and the flow structure is
characterized by a shift-and-reflect symmetry. The transition to three-dimensional
flow is consistent with experimental observations made by Abrahamson et al. (1989)
where multiple solutions develop (known as the intransitivity phenomenon) with the
presence of quasi-periodic behaviour resulting from successive 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 rate is the same for both the axisymmetric and three-dimensional solutions.