In 1904, Prandtl derived a criterion for separation on
no-slip boundaries of two-dimensional steady flows. Despite intense research, efforts to extend Prandtl's criterion to unsteady fluid flows have been unsuccessful. In this talk, we discuss a new exact criterion for unsteady separation. This criterion is based on time-dependent nonhyperbolic invariant manifolds, predicting both the location and the shape of the separation profile. We describe applications to two- and three-dimensional unsteady flows, and show initial results on unsteady separation control.
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