Momentum Transport in Sharp Open-Channel Bends

Abstract

Flow in open-channel bends is characterized by cross-stream circulation, which redistributes the velocity and the boundary shear stress and thereby shapes the characteristic bed topography. Besides a center-region cell, classical helical motion, a weaker counterrotating outer-bank cell often exists. In spite of its engineering importance, the mechanisms underlying distributions of the velocity and the boundary shear stress in open-channel bends, and especially the role of both circulation cells, are not yet fully understood. In order to investigate these mechanisms, an evaluation is made of the various terms in the momentum equations based on the data measured, which gave the following results. The outer-bank cell forms a buffer layer that protects the outer bank from any influence of the center-region cell and keeps the core of maximum velocity a distance from the bank. Advective momentum transport by the center-region cell is a dominant mechanism; it significantly contributes to the observed outward shift of the downstream velocity and the bed shear stress and to flattening of the vertical profiles of the velocity. This important advective momentum redistribution has to be included in the depth-integrated flow models often used in engineering practice. Commonly used linear models overpredict the effects of the center-region cell. Based on results of the analysis of experimental data, these models are extended by accounting for the feedback between the center-region cell and the downstream velocity. The nonlinear model obtained clearly reveals the mechanisms of the center-region cell and its advective momentum transport. An analysis of nonlinear model results confirms and complements the analysis of experimental data. A true quasithree-dimensional flow model is obtained by coupling this nonlinear model to depth-integrated flow models, thus providing an engineering tool for morphodynamical investigations.