| A theoretical model of sediment motion in the bedload layer, derived herein, yields detailed information about bedload mechanics for a large range of sediment types and flow conditions. The model, based on the equations of motion for a sediment grain near a non-cohesive bed, includes drag, lift, gravity, and relative acceleration. Solved numerically, these equations give the path of a saltating grain, from which saltation height, length, and particle velocity can be computed; the initial conditions are determined as part of the model. Heights of calculated trajectories are significantly lower and more symmetrical than available measurements would suggest unless the collisions with the bed are included in the model, in which case the calculated trajectories agree well with experimental measurements.; Bedload sediment flux is the product of particle velocity and sediment concentration integrated over the bedload layer. Concentration is set by the momentum extracted from the flow by the accelerating grains, and can be found using the model. Predicted curves of bedload transport vs. boundary shear stress agree will with data from Gilbert, Meyer-Peter, et al., and the Waterways Experimental Station; measured shear stress is corrected for pressure drag in cases where bedforms were present. Comparison of predicted bedload transport with common bedload equations reveals considerable similarity among the relationships. The best agreement with the data is produced by relationships in which the transport rate vanishes as the shear stress approaches the critical value, as in our model and Yalin's equation. An algebraic equation for bedload flux, constructed from approximate expressions for saltation height, particle velocity, and sediment concentration, provides a good representation of the calculated values and has the same asymptotic form at high transport stage as the Yalin and Meyer-Peter and Muller equations.; As transport stage increases, the conditions are reached for either incipient suspension or a high-concentration grain flow at the bed surface. The former is more likely for quartz-density grains less than 0.08 cm in diameter, and the latter for larger sizes. In either case, a transition is reached by a transport stage of twenty, providing the upper limit for purely bedload transport of well sorted sediment. |
