A note on the overlap region in turbulent boundary layers

Two independent experimental investigations of the behavior of turbulent boundary layers with increasing Reynolds number were recently completed. The experiments were performed in two facilities, the Minimum Turbulence Level (MTL) wind tunnel at Royal Institute of Technology (KTH) and the National Diagnostic Facility (NDF) wind tunnel at Illinois Institute of Technology (IIT). Both experiments utilized oil-film interferometry to obtain an independent measure of the wall-shear stress. A collaborative study by the principals of the two experiments, aimed at understanding the characteristics of the overlap region between the inner and outer parts of the boundary layer, has just been completed. The results are summarized here, utilizing the profiles of the mean velocity, for Reynolds numbers based on the momentum thickness ranging from 2500 to 27 000. Contrary to the conclusions of some earlier publications, careful analysis of the data reveals no significant Reynolds number dependence for the parameters describing the overlap region using the classical logarithmic relation. However, the data analysis demonstrates that the viscous influence extends within the buffer region to y+≈200, compared to the previously assumed limit of y+≈50. Therefore, the lowest Reθ value where a significant logarithmic overlap region exists is about 6000. This probably explains why a Reynolds number dependence had been found from the data analysis of many previous experiments. The parameters of the logarithmic overlap region are found to be constant and are estimated to be κ=0.38, B=4.1 and B1=3.6 (δ=δ95).