Blow-up and control of marginally separated boundary layers. (English) Zbl 1152.76371

Summary: Interactive solutions for steady two-dimensional laminar marginally separated boundary layers are known to exist up to a critical value \(\Gamma _{c}\) of the controlling parameter (e.g. the angle of attack of a slender airfoil) \(\Gamma \) only. Here, we investigate three-dimensional unsteady perturbations of such boundary layers, assuming that the basic flow is almost critical, i.e. in the limit \(\Gamma _{c} - \Gamma \rightarrow 0\). It is then shown that the interactive equations governing such perturbations simplify significantly, allowing, among others, a systematic study of the blow-up phenomenon observed in earlier investigations and the optimization of devices used in boundary-layer control.


76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76D55 Flow control and optimization for incompressible viscous fluids
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