Estimate of Zero-Plane Displacement for Open-Channel Flows with Submerged Rigid Vegetation

Abstract

Zero-plane is an important reference level included in the logarithmic velocity profile. The prediction of the zero-plane displacement remains challenging, especially in open-channel flows with submerged vegetation. In this study, we first review the existing formulas for estimating the zero-plane displacement. Then, we conducted a series of laboratory experiments of open-channel flows with submerged rigid vegetation, by varying flow rate, water depth, vegetation density, and stem diameter. By utilizing particle image velocimetry (PIV) technique, the spatio-temporal averaged (double-averaged) flow velocity and Reynolds shear stress profiles were obtained. The data analysis shows that the zero-plane displacement is almost proportional to the surface layer depth for the shallow flow cases. As the flow depth increases, the zero-plane displacement tends to be constant and increases with decreasing vegetation density. This result substantiates the hypothesis that the zero-plane displacement is related to large-scale eddies. Lastly, a heuristic model is developed to explain possible variations of the large-scale eddies, which yields a formula for predicting the zero-plane displacement for flows subjected to submerged rigid vegetation.