The Mean Velocity Profile of Two-Dimensional Fully Developed Turbulent Plane-Channel Flows

This work is concerned with the reliable determination of the value of the von Karman constant for the logarithmic law of the wall. For this purpose, direct measurements of the mean velocity distribution in two-dimensional fully developed turbulent plane-channel flows were carried out. The results obtained were also employed to explain the wide scatter and the discrepancies in the von Karman constant found in the literature. In addition, the entire set of the current data provides a good basis for assessing questions regarding the scaling of the mean velocity profiles in turbulent channel flows and also to make contributions to answer the question of whether a logarithmic or a power law exists in the overlap region. Data obtained in channel flow, over a wide range of Reynolds numbers, unequivocally support a Reynolds number-independent logarithmic law to describe the overlap region with κ = 0.37 which is very close to κ = 1/e = 0.368 and B = 3.7 for Reτ>2 × 103.