Variations of von Kármán coefficient in canonical flows

TLDR: In this article, the overlap parameters for the logarithmic law are obtained for available turbulent pipe and channel flow data using composite profiles fitted to the mean velocity, and their resulting behavior with Reynolds number is examined for these flows and compared to results from boundary layers.

Abstract: The overlap parameters for the logarithmic law are obtained for available turbulent pipe and channel flow data using composite profiles fitted to the mean velocity. The composite profile incorporates κ, B, and Π as the varying parameters and their resulting behavior with Reynolds number is examined for these flows and compared to results from boundary layers. The von Karman coefficient in channel flow is smaller than the well-established value for zero pressure gradient turbulent boundary layers of 0.384, while in pipe flows it is consistently higher. In contrast, the estimates of the wake parameter Π are the smallest for channel flows and largest for boundary layers. Further, the Superpipe data are reanalyzed to reveal that κ=0.41 is a better value for the von Karman constant in pipe flow. The collective behavior of κ in boundary layers, pipes, and channels reveals that the von Karman coefficient is not universal and exhibits dependence not only on the pressure gradient but also on the flow geometry.