Comparison of mean flow similarity laws in zero pressure gradient turbulent boundary layers

The paper presents an in depth assessment of different similarity laws for the mean velocity profile in zero pressure gradient (ZPG) turbulent boundary layers (TBL's) in comparison with mostly experimental and few computational data. The emphasis is on the descriptions which are complete in the sense that a full representation of the mean velocity profile, its streamwise evolution and all integral parameters, including the friction factor and the shape factor, are provided as a function of Reynolds number. The first such complete description is the classical two-layer theory with its characteristic logarithmic mean velocity profile in the region where the two layers overlap, henceforth referred to as the “log law.” The main alternative scalings which have been proposed over the last decade have led to power law descriptions of the turbulent mean velocity profile. Since the different descriptions were calibrated with different data sets, the controversy over the relative merits of the different approaches has lingered on. The purpose of the present paper is to measure the principal competing theories against the same vast data set of more than 300 mean velocity profiles from more than twenty different sources. The results confirm the conclusions of numerous authors that the log law provides a fully self-consistent and accurate description of all the mean quantities and demonstrates conclusively that the same cannot be achieved by the competing power law theories. Along the way, it is also argued that the traditional description of the outer velocity profile in terms of a wall-normal coordinate normalized to unity at a hypothetical boundary layer “edge” $δ$ and a “wake parameter” $Π$ is not robust with respect to the fit of the outer velicity profile and should therefore not be used in theoretical arguments.