Validation and implications of an energy-based bedload transport equation

A recently developed bedload equation (Abrahams & Gao, 2006) has the form i _b=ωG ^3̇4, where i _b is the immersed bedload transport rate, ω is the stream power per unit area, G=1-θ _c/θ, θ is the dimensionless shear stress and θ _c is the associated threshold value for the incipient motion of bed grains. This equation has a parsimonious form and provides good predictions of transport rate in both the saltation and sheetflow regimes (i.e. flows with low and high θ values, respectively). In this study, the equation was validated using data independent of those used for developing it. The data represent bedload of identical sizes transported in various steady, uniform, fully rough and turbulent flows over plane, mobile beds. The equation predicted i _b quite well over five orders of magnitude. This equation was further compared with six classic bedload equations and showed the best performance. Its theoretical significance was subsequently examined in two ways. First, based on collision theory, the parameter G was related to the ratio of grain-to-grain collisions to the total collisions including both grain-to-grain and grain-to-bed collisions, P _g by P _g=G ², suggesting that G characterizes the dynamic processes of bedload transport from the perspective of granular flow, which partly accounts for the good performance of the equation. Moreover, examining the ability of two common equations to predict bedload in gravel-bed rivers revealed that G can also be used to simplify equations for predicting transport capacities in such rivers. Second, a simple dimensionless form of the equation was created by introducing B=i _b/ω. The theoretical nature of the term B was subsequently revealed by comparing this equation with both the Bagnold model and two commonly used parameters representing dimensionless bedload transport rates.