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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. [ABSTRACT FROM AUTHOR]

Nonuniform-unsteady flow in open channels with streamwise sloping beds having uniform upward seepage is theoretically analyzed. Expressions for the Reynolds stress and bed shear stress are developed, assuming a modified logarithmic law of velocity profile due to upward seepage, and using the Reynolds and continuity equations of two-dimensional open channel flow. The computed Reynolds stress profiles are in agreement with the experimental data. DOI: 10.1061/(ASCE)0733-9399(2005)131:4(451) CE Database subject headings: Reynolds stress: Shear stress: Open channel flow: Streamflow; Nonuniform flow: Unsteady flow; Seepage; Hydraulics.

In this study, we investigated a vertical dilute sediment-laden jet both experimentally and theoretically. First, an instantaneous whole-field velocimetry tool, particle image velocimetry, was applied to measure the sediment and fluid mean and fluctuating velocities of a downward sediment-laden jet at the same time. Subsequently, an analysis was performed based on two-phase conservation equations for both downward and upward jets. The analysis shows that the mean sediment velocity can be taken as the sum of fluid velocity and the settling velocity in both cases. For the downward jets, the decay rate of the centerline sediment concentration increases with the sediment settling velocity while decreases with the initial discharge velocity. The zone of flow establishment for the sediment velocity is found to be longer than that of the fluid. For the upward jets, the maximum rise of the sediment particles and their deposition distribution on the ground were derived theoretically. The predicted results compare well to the experimental data in the literature. CE Database subject headings: Sediment transport; Submerged jets; Velocity; Two-phase flow; Pipe flow.

With the assumption that the bed shear stress fluctuates in a lognormal fashion, the probability density function (PDF) of the standardized bed shear stress is derived as a function of the relative shear stress intensity. The PDF is more skewed with larger relative intensities, but approaches a Gaussian function when the relative intensity is small. The computed PDF agrees well with the reported experimental data for flows over a smooth boundary. The higher-order moments of the bed shear stress, skewness, and kurtosis, are shown analytically to be also dependent on the relative intensity. The theoretical dependencies are then compared to a number of measurements available in the literature. The Reynolds number effect on the relative intensity is also discussed. DOI: 10.1061/(ASCE)0733-9399(2003) 129:1(126) CE Database keywords: Shear stress; Skewness; Reynolds number; Beds.