The flow in a completely filled rotating cylinder driven by the
counter rotation of the top endwall is investigated both numerically
and experimentally. The basic state of this system is steady and
axisymmetric, but has a rich structure in the radial and axial
directions. The most striking feature, when the counter rotation is
sufficiently large, is the separation of the Ekman layer on the top
endwall, producing a free shear layer that separates regions of flow
with opposite senses of azimuthal velocity. This shear layer is
unstable to azimuthal disturbances and a supercritical
symmetry-breaking Hopf bifurcation to a rotating wave state
results. For height-to-radius ratio of 0.5 and Reynolds number (based
on cylinder radius and base rotation) of 1000, rotating waves with
azimuthal wavenumbers 4 and 5 co-exist and are stable over an
extensive range of the ratio of top to base rotation. Mixed-modes and
period doublings are also found, and a bifurcation diagram is
determined. The agreement between the Navier-Stokes computations and
the experimental measurements is excellent. The simulations not only
capture the qualitative features of the multiple states observed in
the laboratory, but also quantitatively replicate the parameter values
over which they are stable, and produce accurate precession
frequencies of the various rotating waves.