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

Abstract

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. −u v /u 2 * = 1 − y/ h, but the sum of Reynolds shear stress and the momentum flux, i.e. −(u v + u v)/u 2 * 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. RÉSUMÉLa distribution du cisaillement de Reynolds dans des écoulements non uniformes a été étudiée. Les résultats théoriques montrent que la vitesse normale à la partoi produit une déviation du cisaillement de Reynolds par rapport à la distribution linéaire standard, i.e. −u v /u 2 * = 1 − y/ h, mais la somme du cisaillement de Reynolds et du débit de quantité de mouvement, i.e −(u v + u v)/u 2 * demeure une distribution linéaire. En reliant le gradient de vitesse au cisaillement de Reynolds, l'étude démontre que le phénomène de chute est provoqué par la vitesse normale à la paroi de haut en bas. Les résultats théoriques sont en bon accord avec des données expérimentales.

Turbulence structures in non-uniform flows

“…In decelerating flow ðo u=ox < 0Þ, a positive wall-normal velocity exists. The wall-normal velocity at the free surface can be expressed by Yang and Lee [18] …”

“…The decelerating flow generates the upward wall-normal velocity whereas the accelerating flow yields the downward velocity [17,18]. The socalled ''wall-normal velocity" refers to the time-averaged velocity in the wall-normal direction, which is zero at a solid wall but becomes non-zero in the main flow region under non-uniform flow.…”

“…The separation between data points implies that the mechanism for the deviation of turbulence intensities could be identical to the deviation of Reynolds shear stress. The mechanism for the deviation of Reynolds shear stress has been discussed by Yang and Lee [18]. As a continuous effort to investigate the effect of non-uniformity, this study concentrates on the turbulence intensities in non-uniform flow.…”

Dominant features in three-dimensional turbulence structure: comparison of non-uniform accelerating and decelerating flows

“…The strategy adopted for the analysis of non-uniform time-averaged velocity and turbulence characteristics was usually based on comparison to the uniform flow profiles [9,33]. Nezu et al [18] first suggested the representation of nonuniform flow characteristics using the indication of streamwise pressure gradient.…”

Distribution of Reynolds Shear Stress in Steady and Unsteady Flows

“…Based on his theoretical distribution, Song investigated that a good agreement between the measured and predicted Reynolds shear stress can be observed when the bed slope is not very large, for example, the theoretical distributions match well with his measurements when the bed slope =-0.15% and 0.30%, which is better than when the slope =-0.60% . [10] investigated theoretically the deviation of Reynolds shear stress distribution in accelerating/decelerating non-uniform flow. They reported that this deviation is related to the presence of upward/downward vertical velocity.…”