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

Influence of counter-rotating von Kármán flow on cylindrical Rayleigh-Bénard convection