Prediction of velocity profiles and Reynolds stress distributions in turbulent open-channel flows with adverse pressure gradient

Abstract

Turbulence measurements in open-channel flows with adverse pressure gradient were conducted with an X-type hot-film anemometer. The velocity profiles in whole depth are described well by the log-wake law which involves a wake strength parameter π. The wake strength parameter π is controlled only by the pressure gradient parameter β in the equilibrium region, i.e., normalized velocity profiles are similar at all streamwise distances. A new relationship formula between the wake strength parameter π and the pressure gradient parameter β is suggested on the basis of experimental data. The equation of motion and continuity equation are transformed to predict the velocity profiles and also the Reynolds stress distributions under the conditions that the flow is in equilibrium and the coefficient of velocity is constant in the streamwise direction. The wake strength parameter π can be predicted with high accuracy from the obtained equations. The predicted Reynolds stress distributions correspond to the experimental data when the pressure gradient parameter β is low. On the other hand, the predicted ones do not correspond to the experimental data when the pressure gradient parameter β is high.