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This article is concerned with the mean velocity distributions of two-dimensional fully developed turbulent plane-channel flows. To yield reliable information, the authors performed detailed hot-wire measurements for more than 12 Reynolds numbers. The experimental investigations covered a wide range of the Reynolds numbers up to Reτ≈5×103, where Reτ is based on the wall friction velocity and the channel half-height. From the distribution of the mean velocity gradient (dU+/dy+)=f(y+) the entire flow field was analyzed, resulting in a logarithmic region for the mean velocity profile in the inertial sublayer, extending almost up to the center of the channel at higher Reynolds numbers. The analysis of the experimental results yield a value of the von Kármán constant, κ, close to 0.37(≈1/e) independent of the Reynolds number and the additive constant B=3.70, which is close to 10/e, i.e., U+=e ln y++10/e=(1/0.37)ln y++3.70.
Zanoun et al. (Fri,) studied this question.