The logarithmic velocity region is considered in zero-pressure gradient turbulent boundary layers. We propose a new definition of the log-law region using the probability profiles of stream-wise velocity fluctuation. The log-law profile is extracted readily from the experimental data as well as from the pdf equation. The measure called Kullback Leibler divergence is applied for distinguishing the probability profiles. If the logarithmic profile is a good representation of experimental data, our results show that the slope is independent of Reynolds number but the additive constant depends on it. The ratio of boundary layer thickness to the upper end of log-law extent is not constant but approaches a constant as Reynolds number increases.
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