Mean-Velocity Profile of Turbulent Boundary Layers Approaching Separation

Turbulent boundary layers approaching separation are a common flow situation in many technical applications. Numerous theoretical, experimental and numerical attempts have been made to find the proper scaling for the mean-velocity profile of this type of wall-bounded flow. However, none of these approaches seems to be completely satisfactory. In this paper, we present new water-tunnel experiments of adverse pressure gradient turbulent boundary layers that clearly show the breakdown of the logarithmic law. Using this data and experimental results from several independent research groups, we analyze the classical scaling for zero pressure gradient turbulent boundary layer, the scaling by George & Castillo and the scaling by Zagarola & Smits for adverse pressure gradient turbulent boundary layer. Only the latter can be applied successfully for the outer region of the mean-velocity profile close to separation. It is shown that Zagarola & Smits' scaling is consistent with the classical two-layer approach, and can be applied to collapse the different data. Analyzing the Reynolds shear stress, the George & Castillo's scaling shows a reasonably good collapse of the data in the outer region