  The axisymmetric flow in an aspect-ratio-one cylinder whose upper and lower
bounding disks are maintained at different temperatures and rotate at equal and
opposite velocities is investigated. In this combined Rayleigh-Benard/von
Karman problem, the imposed temperature gradient is measured by the Rayleigh
number Ra and the angular velocity by the Reynolds number Re. Although fluid
motion is present as soon as Re is non-zero, a symmetry-breaking transition
analogous to the onset of convection takes place at a finite Rayleigh number
higher than that for Re=0. For Re<95, the transition is a pitchfork bifurcation
to a pair of steady states, while for Re>95, it is a Hopf bifurcation to a
limit cycle. The steady states and limit cycle are connected via a pair of
SNIPER bifurcations except very near the Takens-Bogdanov codimension-two point,
where the scenario includes global bifurcations. Detailed phase portraits and
bifurcation diagrams are presented, as well as the evolution of the leading
part of the spectrum, over the parameter ranges 0<Re<120 and 0<Ra<30,000.
