On higher order effects in marginally separated flows

If the angle of attack α of a slender airfoil reaches a critical value α_s flow separation is known to occur at the upper s surface. Further increase of α initially leads to the formation of a short laminar separation bubble which has an extremely weak influence on the external flow field – a phenomenon known as marginal separation – but then rather rapidly causes a severe change of the flow behaviour, leading to leading edge stall. According to the asymptotic theory of marginal separation holding in the limit of large Reynolds numbers Re, the flow in the neighbourhood of the separation bubble is governed by an integro-differential equation. This so-called interaction equation contains a single controlling parameter which relates the angle of attack to the Reynolds number, with a value Γ_s corresponding to α_s. Some recent results concerning higher order s s corrections to this theory and their effect on the stability of steady solutions will be presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)