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 rotation rate 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 rate 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 rates the bifurcation
diagrams are found to change dramatically and give rise to other
types of bifurcations.

Publication status | Published - 1998 |
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