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The accuracy estimate is important for equations (8) and (9) since the degree of their agreement with the available experimental data is up to now a point of controversy. Experimental studies of near-wall turbulent flows continue to be popular and recently several such investigations claiming to be quite accurate were carried out but this did not clarify the situation. Here we will only mention often cited recent papers by Zagarola and Smits [85] ¨ and Osterlund et al. [86] which both stated that their data confirm the validity of the logarithmic law (1) and both gave rise to a controversy.

Recall that the first violations of the “classical similarity laws” for the “overlap layer” of near-wall turbulence which were detected by Townsend [70] and Bradshaw [71] (and confirmed by Perry and Li [74]) concerned not the mean-velocity profile but profiles of the second-order moments u2 and v 2 . Since the mentioned here similarity laws were based on the same seemingly obvious dimensional arguments which imply the logarithmic velocity-profile law, the discovery of their violations is very important for future studies of real properties of near-wall turbulence.

The arguments presented above imply that the classical logarithmic mean-velocity (and mean-temperature) laws of wall turbulent flows possibly represent only some reasonable approximations the accuracy of which must be thoroughly checked. Barenblatt, Chorin and Prostokishin, who are apparently the most energetic modern opponents of logarithmic laws, reasonably noted (in [76] and a number of other publications) that the description of the mean velocity U (z) of wall turbulent flows by power laws U (z) ∝ z k was widely used long enough by scientists and engineers and, if the power k was properly chosen for all values of Re of interest, usually led to satisfactory agreement with the data over a wide range of z-values (in this respect usually Schlichting’s book [77] is referred).

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