Finite-Reynolds-number asymptotics of wall-turbulence fluctuations

As a generalization of our earlier work (Chen and Sreenivasan, JFM 2021 and 2022---hereafter referred to as CS), we present a perspective on finite-Reynolds-number asymptotics for turbulence mean profiles (including the variance of fluctuations of streamwise and spanwise velocities as well as pressure) in turbulent channels, pipes and flat-plate boundary layers. When normalized by the peak values, the near-wall turbulence profiles are characterized by single point functions independent of the friction Reynolds number. Utilizing the defect power-law given in CS, it is shown that all the data share the same inner scaling form. Using a matching scheme between the above inner scaling and the celebrated outer flow similarity, it is shown that bounded decay is in very good agreement with all current data in the three wall flows, and more importantly, that it leads to a finite plateau in the bulk for asymptotically high friction Reynolds numbers.