Non-unique self-similar turbulent boundary layers in the limit of large Reynolds numbers

As pointed out in the pioneering experimental work of Clauser [1], self-similar or, equivalently, equilibrium turbulent boundary layer flows may be non-unique in a certain range of the controlling parameters: Specifically, Clauser observed that if the imposed (adverse) pressure gradient varies as a power of the streamwise distance in order to maintain equilibrium and if the associated exponent m falls below a certain limit, the boundary layer forming initially rapidly approaches a different state (most probably due to instabilities). The initial flow is seen to resemble a classical turbulent boundary layer, characterized by an essentially inviscid outer part having a small velocity defect and the logarithmic law of the wall. In contrast, the second state exhibits a much larger defect and momentum thickness reflecting a wake-type velocity profile and possibly approaches separation.