Turbulent Marginal Separation and the Turbulent Goldstein Problem

A new rational theory of incompressible turbulent boundary layer flows having a large velocity defect is presented on basis of the Reynolds-averaged Navier–Stokes equations in the limit of infinite Reynolds number. This wake-type formulation allows for, among others, the prediction of singular solutions of the boundary layer equations under the action of a suitably controlled adverse pressure gradient which are associated with the onset of marginally separated flows. Increasing the pressure gradient locally then transforms the marginal-separation singularity into a weak Goldstein-type singularity occurring in the slip velocity at the base of the outer wake layer. Interestingly, this behavior is seen to be closely related to (but differing in detail from) the counterpart of laminar marginal separation where the skin friction replaces the surface slip velocity. Most important, adopting the concept of locally interacting boundary layers gives rise to a closure-free and uniformly valid asymptotic description of boundary layers which exhibit small closed reverse-flow regimes. Numerical solutions of the underlying triple-deck problem are discussed.