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 MTL wind tunnel at KTH and the NDF wind tunnel at 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 2,500 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 Re θ value where a significant logarithmic overlap region exists is about 6,000. 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 B 1 = 3.6 (δ = δ 95 ).In the classical theory, the overall description of a turbulent boundary layer is dependent on two separate inner and outer length scales. The outer length scale is commonly taken as the thickness of the boundary layer δ, and the inner length scale as the viscous length l * = ν/u τ , where u τ = τ w /ρ is the friction velocity, τ w is the skin friction and ρ is the density of the air. Dimensional analysis of the dynamic equations with boundary conditions leads to a scaling of the mean velocity profile in the inner and the outer parts of the boundary 29
New scaling laws for turbulent boundary layers recently derived (see Oberlack 2000) using Lie group symmetry methods have been tested against experimental data from the KTH database for zero-pressure-gradient turbulent boundary layers. The most significant new law predicts an exponential variation of the mean velocity defect in the outer (wake) region. It was shown to fit the experimental data very well over a large part of the boundary layer, from the outer part of the overlap region to about half the boundary layer thickness (δ 99 ). In the outermost part of the boundary layer the velocity defect falls more rapidly than predicted by the exponential law. This can partly be attributed to intermittency in that region but the main cause stems from non-parallel effects that are not accounted for in the derivation of the exponential law. The two-point correlation function behaviour in the outer region, where an exponential velocity defect law is observed, was found to be very different from that derived under the assumption of parallel flow. It is found to be plausible that this indeed can be attributed to non-parallel effects. A small modification of the innermost part of the log-layer in the form of an additive constant within the log-function is predicted by the Lie group symmetry method. A qualitative agreement with such a behaviour just below the overlap region was found. The derived scaling law behaviour in the overlap region for the two-point correlation functions was also verified by the experimental data.
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