Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 459 - 472, Volume 10, Issue 1/2, January/February 2004      doi:10.3934/dcds.2004.10.459

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Tian Ma - Department of Mathematics, Sichuan University, Chengdu, China (email)
Shouhong Wang - Department of Mathematics, Indiana University, Bloomington, IN 47405, United States (email)

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.

Keywords:  Navier-Stokes equations, boundary layer separation, structural bifurcation,location and time of separation, kinematic conditions.
Mathematics Subject Classification:  34D, 35Q35, 58F, 76, 86A10.

Received: March 2003;      Revised: August 2003;      Available Online: October 2003.