ar X iv : m at h - ph / 0 00 20 29 v 2 1 6 Fe b 20 00 A Note on the Intermediate Region in Turbulent Boundary Layers

We demonstrate that the processing of the experimental data for the average velocity profiles obtained by J. M. ¨ Osterlund (www.mesh.kth.se/∼jens/zpg/) presented in [ 1 ] was incorrect. Properly processed these data lead to the opposite conclusion: they confirm the Reynolds-number-dependent scaling law and disprove the conclusion that the flow in the intermediate ('overlap') region is Reynolds-number-independent. 1 In a recent issue of the Physics of Fluids¨Osterlund et al. [ 1 ] presented results of the processing of experimental data for the average velocity field in the zero-pressure-gradient turbulent boundary layer, published by the first author of [ 1 ] on the Internet 1 ] is very definite (p. 1): 'Con-trary 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'. In the present note we show that the processing of the experimental data in [ 1 ] is incorrect. A correct processing is performed, and the result is the opposite: there is significant Reynolds number dependence for the parameters describing the intermediate region and the scaling (power) law is valid. We also show where the authors of [ 1 ] went wrong. The correct processing of thë Osterlund data. If a scaling (power) law relates the dimensionless velocity ¯ U + and dimensionless distance from the wall y + (in the notations of [ 1 ]): (I) ¯ U + = A(y +) α (1) then in the coordinates lg y + , lg ¯ U + the experimental points should lie within experimental accuracy along a straight line: lg ¯ U + = lg A + α lg y +. Therefore our first step was to plot the data from all 70 runs available on the Internet in these coordinates. All 70 runs corresponding to different Re θ yield the same pattern: in the intermediate region between the viscous sublayer and free stream the average velocity distribution consists of two straight lines. Three examples are presented in Figure 1 and the Table, all the remaining ones are similar and can be found in our detailed report [ 2 ]. Thus the intermediate structure (between the viscous sublayer and free stream) consists of two self-similar layers: the scaling law (I) is valid for the layer adjacent to the viscous sublayer, and the scaling law (II) ¯ U + = …