Using a combination of bifurcation theory for two-dimensional dynamical systems
and numerical simulations, we systematically determine the possible flow topologies
of the steady vortex breakdown in axisymmetric flow in a cylindrical container with
rotating end-covers. For fixed values of the ratio of the angular velocities of the
covers in the range from −0.02 to 0.05, bifurcations of recirculating bubbles under
variation of the aspect ratio of the cylinder and the Reynolds number are found.
Bifurcation curves are determined by a simple fitting procedure of the data from
the simulations. For the much studied case of zero rotation ratio (one fixed cover) a
complete bifurcation diagram is constructed. Very good agreement with experimental
results is obtained, and hitherto unresolved details are determined in the parameter
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.