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.