Orateur
Description
Rotor-stator flows are known to exhibit instabilities in the form of circular and spiral rolls. While the spirals are known to emanate from a supercritical Hopf bifurcation, the origin of the circular rolls is still unclear. A quantitative scenario for the circular rolls as a response of the system to external forcing is suggested. Two types of axisymmetric forcing are considered: bulk forcing (based on the resolvent analysis) and boundary forcing using direct numerical simulation. The linear gain curve shows strong amplification at non-zero frequencies following a pseudo-resonance mechanism. The optimal energy gain is found to grow rapidly with the Reynolds number (based on the rotation rate and interdisc spacing $H$) in connection with huge levels of non-normality. Presented results suggest that the circular rolls observed experimentally are the combined effect of the high forcing gain and the roll-like form of the leading response of the linearised operator. For sufficiently strong forcing amplitudes, the nonlinear response is consistent with the self-sustained
states found recently for the unforced problem.
