Topology of vortex breakdown bubbles in a cylinder with a rotating bottom and a free surface

The flow patterns in the steady, viscous flow in a cylinder with a rotating bottom and a free surface are investigated by a combination of topological and numerical methods. Assuming the flow is axisymmetric, we derive a list of possible bifurcations of streamline structures on varying two parameter s, the Reynolds number and the aspect ratio of the cylinder. Using this the ory we systematically perform numerical simulations to obtain the bifurcati on diagram. The stability limit for steady flow is found and established as a Hopf bifurcation. We compare with the experiments by Spohn, Mory & Hopfi nger (1993) and find both similarities and differences.