Streamline topologies near a stationary wall of Stokes flow in a cavity

Two-dimensional Stokes flow in a rectangular single lid-driven cavity with the upper lid moving is considered to investigate streamline topologies near a stationary wall by using both of the qualitative theory and an analytic solution. We consider the velocity field by expanding in a Taylor series at the origin. A systematic use of normal form transformations results in a much simplified system of differential equations for the streamlines encapsulating all features of the original system. Using the simplified system a sequence of possible bifurcations of streamlines is obtained close to a simple linear degeneracy. Then to extract the same streamline topologies by varying a physical parameter, the cavity aspect ratio, we used an eigenfunction solution for the streamfunction.