Interior structural bifurcation and separation of 2D incompressible flows

We study transitions in the topological structure of a family of divergence-free vector fields u(,t) near an interior point. It is shown that structural bifurcation occurs at t(0) if u(.,t(0)) has an isolated degenerate singular point x(0)is an element ofM with zero index and nonzero Jacobian at x(0), and with nonzero acceleration in the direction normal to the (unique) eigenspace of the Jacobian. This result is carried out by analyzing the orbit structure of u near such an isolated degenerate interior singular point of u(.,t(0)). Applications to typical interior separation phenomena in two-dimensional fluid flows are addressed as well. (C) 2004 American Institute of Physics.