Bifurcations of streamline patterns in a lid-driven cavity with an embedded cylinder

We study numerically the streamline patterns in the incompressible, two-dimensional flow in a rectangular lid-driven cavity with an embedded cylinder. The problem is characterized by two parameters, the dimensionless cylinder radius and the Reynolds number. With the aid of bifurcation theory we identify 17 topologically distinct streamline patterns as well as bifurcation curves in the parameter plane, separating the realms of the patterns. The introduction of a small cylinder affects the streamline pattern significantly and gives rise to a complex sequence of bifurcations. For larger cylinders, the bifurcations become simpler, and the size of a corner-crossing recirculation zone decreases, such that the cylinder improves the overall circulation in the cavity.