Turbulent marginal separation

Asymptotic methods have contributed significantly to the understanding of high-Reynolds-number wall-bounded, i.e. boundary layer flows. However, while satisfactory and powerful theories exist for both attached as well as separated laminar flows, only attached boundary layers have been analysed successfully in the case of turbulent flows. No self-consistent asymptotic description capable of turbulent separation seems to be available at present. In the classical asymptotic approach to the study of turbulent boundary layer flow the inverse of the Reynolds number is taken to be the only small perturbation parameter. Reynolds number asymptotics then predicts that the boundary layer exhibits a two layer structure and that the flow in the outer predominant inviscid layer, which comprises most of the boundary layer, has the form of an asymptotically small velocity defect. As a consequence, the flow withstands separation from a smooth surface due to an externally imposed adverse pressure gradient in the high-Reynolds-number limit. It has, therefore, been argued more recently that the description of the large velocity defect of a turbulent boundary layer close to and at separation requires the inclusion of an additional perturbation parameter which measures the slenderness of the outer almost Reynolds number independent wake-type flow. It is the aim of the proposed research project to show that such a strategy indeed allows the construction of an asymptotic theory based on first principles which is capable describing turbulent separation, provided that the separated flow region is small, i.e. that the flow is marginally separated. Needless to say that the development of a theory of turbulent separation represents a task which is of importance in its own but also from the viewpoint of practical engineering applications.