Department of

# Mathematics

Seminar Calendar
for events the day of Monday, November 28, 2005.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, November 28, 2005

3:00 pm in 2005 MEL,Monday, November 28, 2005

#### Nonlinear Dynamics of Aerodynamic Separation

###### George Haller   [email] (Dept. of Mechanical Engineering, MIT)

Abstract: Flow separation (the detachment of fluid from a no-slip boundary) is a major cause of performance loss in engineering devices, including diffusers, airfoils and jet engines. In a landmark 1904 paper on boundary layers, L. Prandtl derived a criterion for flow separation in steady two-dimensional incompressible flows. Despite widespread effort, no generally applicable extension of this result has emerged for unsteady flows or even three-dimensional steady flows. In this talk, I describe an analytic criterion that predicts the location of flow separation in two-dimensional unsteady fluid flows. Based on nonlinear dynamical systems techniques, the criterion identifies separation by locating nonhyperbolic unstable manifolds that collect and eject fluid particles from the wall. I show numerical and experimental results confirming the above criterion, as well as applications of the new separation criterion to flow control. I also describe recent three-dimensional extensions of the theory.