On turbulent marginal boundary layer separation: how the half-power law supersedes the logarithmic law of the wall

As the authors have demonstrated recently, application of the method of matched asymptotic expansions allows for a self-consistent description of a Turbulent Boundary Layer (TBL) under the action of an adverse pressure gradient, where the latter is controlled such that it may undergo marginal separation. In that new theory, the basic limit process considered is provided by the experimentally observed slenderness of a turbulent shear layer, hence giving rise to an intrinsic perturbation parameter, say alpha, aside from the sufficiently high global Reynolds number Re. Physically motivated reasoning, supported by experimental evidence and the existing turbulence closures, then strongly suggests that is indeed independent of Re as Re -> infinity. Here, we show how the inclusion of effects due to high but finite values of Re clarifies a long-standing important question in hydrodynamics, namely, the gradual transformation of the asymptotic behaviour of the so-called wall functions, which characterises the flow in the overlap regime of its fully turbulent part and the viscous sublayer (and, consequently, its scaling in the whole shear layer), as separation is approached.