The late start of the mean velocity overlap log law at-a generic feature of turbulent wall layers in ducts

Abstract

One of the key observations in the Princeton Superpipe was the late start of the logarithmic mean velocity overlap layer at a wall distance of the order of inner units. Between, the start of the overlap layer in zero pressure gradient turbulent boundary layers, and, the Superpipe profile is modelled equally well by a power law or a log law with a larger slope than in the overlap layer. This paper demonstrates, that the asymptotic mean velocity profile in turbulent plane channel flow exhibits analogous characteristics, namely a rather sudden decrease of logarithmic slope (increase of) at a of approximately, which marks the start of the actual overlap layer. The demonstration results from the first construction of the complete mean velocity inner and outer asymptotic expansions up to order from direct numerical simulations (DNS) at moderate Reynolds numbers. The contribution to the indicator function is found to be important and to prevent the direct determination of from currently available channel DNS. A preliminary, leading-order analysis of a Couette flow DNS, on the other hand, yields an increase of logarithmic slope (decrease of) at a. The correlation between the sign of the slope change and the flow symmetry motivates the hypothesis that the breakpoint between the possibly universal short inner logarithmic region and the actual overlap log-law corresponds to the penetration depth of large-scale turbulent structures originating from the opposite wall.