A bed-load transport model for rough turbulent open-channel flows on plane beds

Data from flume studies are used to develop a model for predicting bed-load transport rates in rough turbulent two-dimensional open-channel flows moving well sorted non-cohesive sediments over plane mobile beds. The object is not to predict transport rates in natural channel flows but rather to provide a standard against which measured bed-load transport rates influenced by factors such as bed forms, bed armouring, or limited sediment availability may be compared in order to assess the impact of these factors on bed-load transport rates. The model is based on a revised version of Bagnold's basic energy equation i(b)s(b) = e(b)omega, where i(b) is the immersed bed-load transport rate, omega is flow power per unit area, e(b) is the efficiency coefficient, and s(b) is the stress coefficient defined as the ratio of the tangential bed shear stress caused by grain collisions and fluid drag to the immersed weight of the bed load. Expressions are developed for s(b) and e(b) in terms of G, a normalized measure of sediment transport stage, and these expressions are substituted into the revised energy equation to obtain the bed-load transport equation i(b) = omega G(3.4). This equation applies regardless of the mode of bed-load transport (i.e. saltation or sheet flow) and reduces to i(b) = omega where G approaches 1 in the sheet-flow regime. That i(b) = omega does not mean that all the available power is dissipated in transporting the bed load. Rather, it reflects the fact that i(b) is a transport rate that must be multiplied by s(b) to become a work rate before it can be compared with omega It follows that the proportion of omega that is dissipated in the transport of bed load is i(b)s(b)/omega, which is approximately 0.6 when i(b) = omega It is suggested that this remarkably high transport efficiency is achieved in sheet flow (1) because the ratio of grain-to-grain to grain-to-bed collisions increases with bed shear stress, and (2) because on average much more momentum is lost in a grain-to-bed collision than in a grain-to-grain one. Copyright (c) 2006 John Wiley & Sons, Ltd.