Laminar boundary-layer separation control by Görtler-scale blowing

Recent experimental work has succeeded in retarding or removing boundary-layer separation by means of blowing supersonic microjets transversely through the wall. To provide some theoretical context for such work, the current study examines the removal of separation by transverse blowing within the framework of the standard Prandtl scalings for incompressible boundary layers. One key result, obtained using asymptotic analysis, is that such removal is not possible for two-dimensional flow. Neither is removal of separation possible by three-dimensional blowing in an initially two-dimensional separated boundary layer if the blowing distribution has a finite-scale spanwise variation. The second key result obtained is that the previous conclusion is no longer valid when there is nontrivial short-scale spanwise variation of the blowing distribution. This result is obtained by providing a numerical counter-example in which blowing, with a Görtler scale spanwise variation, creates an attached boundary layer flow where none existed before the blowing. One consequence is that there are at least some flows in which transverse Görtler-scale blowing can turn a separated flow into an attached flow, with a vanishingly small drag that is inversely proportional to the square root of the Reynolds number. The flow physics of the computed example is analyzed to obtain a better understanding of how the Görtler-scale blowing affects the flow.