  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. In the
present work we suggest a quantitative scenario for the circular rolls as a
response of the system to external forcing. We consider two types of
axisymmetric forcing: bulk forcing (based on the resolvent analysis) and
boundary forcing using direct numerical simulation. Using the singular value
decomposition of the resolvent operator the optimal response is shown to take
the form of circular rolls. 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. The results for both types of forcing are compared with former
experimental works and previous numerical studies. Our findings 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 high enough Reynolds number it is possible to delineate between
linear and nonlinear response. For sufficiently strong forcing amplitudes, the
nonlinear response is consistent with the self-sustained states found recently
for the unforced problem. The onset of such non-trivial dynamics is shown to
correspond in state space to a deterministic leaky attractor, as in other
subcritical wall-bounded shear flows.
