Boundary layer separation and structural bifurcation for 2-D incompressible fluid flows

Abstract

The main objective of this article and the previous articles [2, 3, 7] is to provide a rigorous characterization of the boundary layer separation of 2-D incompressible viscous fluids. First we establish a simple equation linking the separation location and time with the Reynolds number, the external forcing the boundary curvature, and the initial velocity field. Second, we show that external forcing with reverse orientation to the initial velocity field leads to structural bifurcation at a degenerate singular point with integer index of the velocity field at the critical bifurcation time. Necessary and sufficient kinematic conditions are given to identify the case for boundary layer separation.