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G\"{o}rtler vortices in boundary layer flows over concave surfaces are causedby the imbalance between centrifugal effects and radial pressure gradients.Depending on various geometrical and/or freestream flow conditions, vortexbreakdown via secondary instabilities leads to early transition to turbulence.It is desirable, therefore, to reduce vortex energy in an attempt to delay thetransition from laminar to turbulent flow, and thereby achieve a reducedfrictional drag. To this end, we apply a proportional control algorithm aimedat reducing the wall shear stress and the energy of G\"{o}rtler vorticesevolving in high-speed boundary layers. The active control scheme is based onwall transpiration with sensors placed either in the flow or at the wall. Inaddition, we evaluate the effect of wall cooling and heating on G\"{o}rtlervortices evolving in high-speed boundary layers, by reducing or increasing theupstream wall temperature. The numerical results are obtained by solving thefull Navier-Stokes equations in generalized curvilinear coordinates, using ahigh-order numerical algorithm. Our results show that the active control basedon wall transpiration reduces both the wall shear stress and the energy of theG\"{o}rtler vortices; the passive control based on wall cooling or heatingreduces the wall shear stress, but slightly increases the energy of thevortices in both supersonic and hypersonic regimes.

Effect of Wall Transpiration and Heat Transfer on Nonlinear G\"{o}rtler Vortices in High-speed Boundary Layers