Streamline topology of steady axisymmetric vortex breakdown in a cylinder with co- and counter-rotating end-covers

Using a combination of bifurcation theory for two-dimensional dynamical sys tems and numerical simulations, we systematically determine the possible fl ow topologies of the steady vortex breakdown in axisymmetric flow in a cyli ndrical container with rotating end-covers. For fixed values of the ratio o f the angular velocities of the covers in the range from -0.02 to 0.05, bif urcations of recirculating bubbles under variation of the aspect ratio of t he cylinder and the Reynolds number are found. Bifurcation curves are deter mined by a simple fitting procedure of the data from the simulations. For t he much studied case of zero rotation ratio tone fixed cover) a complete bi furcation diagram is constructed. Very good agreement with experimental res ults is obtained, and hitherto unresolved details are determined in the par ameter region where up to three bubbles exist. For non-zero rotation ratios the bifurcation diagrams are found to change dramatically and give rise to other types of bifurcations.