Evidence of Nonlogarithmic Behavior of Turbulent Channel and Pipe Flow

Abstract

Employing data of peak position and peak values of Reynolds shear stress provided by canonical channel flow direct numerical simulations and pipe and channel flow experiments, three recent theories predicting the mean-velocity profile of wall-bounded turbulent flows are compared. Based on that analysis it is verified that the mean-velocity profile of such internal flows is logarithmic only to leading order and that the higher-order terms are proportional to reciprocal powers of the Karman number. This finding clearly indicates that higher-order effects with respect to the Karman number and the wall-normal coordinate must be considered. Furthermore, our results show that even the statistics of the flow region closest to the wall are affected by flow phenomena that scale with outer variables.