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.