Revisiting the two first instabilities of the flow in an annular rotor-stator cavity

The stability of the flow enclosed between a stationary and a rotating disk with a central hub is revisited by experimental visualizations and direct numerical simulations in the case of unmerged boundary layers. The first instability appears as circular rolls, denoted by CRs (type 2 instability), which propagate along the stator before vanishing in the vicinity of the hub. The calculations highlight the convective nature of these rolls, which is in agreement with previous experimental results (P. Gauthier, P. Gondret, and M. Rabaud, J. Fluid Mech. 386, 105 (1999)). It proves in particular that the CR instability observed in the experiment under permanent conditions is noise sustained. Above a second threshold, spiral rolls, denoted SR1 (type 1 instability), appear at the periphery of the cavity and can coexist with the circular rolls. The DNS shows that they appear through a supercritical Hopf bifurcation. The SR1 patterns appear to be very close to those emitted by the corner vortices obtained by Lopez and Weidman [J. Fluid Mech. 326, 373 (1996)] during the spin-down of a rotating disk in a fixed cylinder.