Reynolds shear stress distributions in a gradually varied flow in a roughened channel

The Reynolds shear stress distribution in non-uniform flows has been investigated. The theoretical results show that the wall-normal velocity causes the deviation of Reynolds shear stress from the standard linear distribution, i.e. , but the sum of Reynolds shear stress and the momentum flux, i.e. remains a linear distribution. By connecting the velocity gradient with Reynolds shear stress, the study demonstrates theoretically that the linear distribution of Reynolds shear stress and semi-logarithmic distribution of velocity (i.e., log-law) can be observed when and only when the wall-normal velocity is zero; the concave distribution of Reynolds shear stress and dip-phenomenon can be observed when and only when the wall-normal velocity is downward; the convex distribution of Reynolds shear stress can be observed and the wake-law correction is needed when and only when the upflow occurs. The theoretical results are in good agreement with experimental data