Debate Concerning the Mean-Velocity Profile of a Turbulent Boundary Layer

There has been considerable controversy during the past few years concerning the validity of the classical log law that describes the overlap region of the mean-velocity profile in the canonical turbulent boundary layer. Alternative power laws have been proposed by Barenblatt, Chorin, George, and Castillo, to name just a few. Advocates of either law typically have used selected data sets to foster their claims. The experimental and direct numerical simulation data sets from six independent groups are analyzed. For the range of momentum-thickness Reynolds numbers of 5 x 102-2.732 x 104, the best-fit values are determined for the "constants" appearing in either law. Our strategy involves calculating the fractional difference between the measured/computed mean velocity and that calculated using either of the two respective laws. This fractional difference is bracketed in the region +/- 0.5%, so that an accurate, objective measure of the boundary and extent of either law is determined. It is found that, although the extent of the power-law region in outer variables is nearly constant over a wide range of Reynolds numbers, the log-region extent increases monotonically with Reynolds number. The log law and the power law do not cover the same portion of the velocity profile. A very small zone directly above the buffer layer is not represented by the power law. On the other hand, the inner region of the wake zone is covered by it. In the region where both laws show comparable fractional differences, the mean and variance were calculated. From both measures, it is concluded that the examined data do not indicate any statistically significant preference toward either law. [PUBLICATION ABSTRACT]