Streamline topology near non-simple degenerate critical points in two-dimensional flow with symmetry about an axis

Abstract

The local flow patterns and their bifurcations associated with non-simple degenerate critical points appearing away from boundaries are investigated under the symmetric condition about a straight line in two-dimensional incompressible flow. These flow patterns are determined via a bifurcation analysis of polynomial expansions of the streamfunction in the proximity of the degenerate critical points. The normal form transformation is used in order to construct a simple streamfunction family, which classifies all possible local streamline topologies for given order of degeneracy (degeneracies of order three and four are considered). The relation between local and global flow patterns is exemplified by a cavity flow.