Marginal turbulent separation due to an imposed adverse pressure gradient

The development of an asymptotic theory of turbulent separation has been ha mpered severely by the fact that a pressure increase of O(1) appears to be necessary to separate an initially firmly attached turbulent boundary-layer even in the limit Re --> infinity. A different situation arises if one con siders boundary-layers subjected to adverse pressure gradients such that th e wall shear stress vanishes eventually but immediately recovers. Similar t o the case of laminar marginally separated pouts the pressure changes in th e vicinity of the point of vanishing wall shear then are small. This allows for further analytical progress which among others suggests a self-consist ent description of the separation process by means of how the classical log arithmic law of the wall is gradually transformed into the square-root law that holds at the point of zero skin friction.