The erodibility of a grain on a rough bed is controlled by, among other factors, its relative projection above the mean bed, its exposure relative to upstream grains, and its friction angle. Here we report direct measurements of friction angles, grain projection and exposure, and small‐scale topographic structure on a variety of water‐worked mixed‐grain sediment surfaces. Using a simple analytical model of the force balance on individual grains, we calculate the distribution of critical shear stress for idealized spherical grains on the measured bed topography. The friction angle, projection, and exposure of single grain sizes vary widely from point to point within a given bed surface; the variability within a single surface often exceeds the difference between the mean values of disparate surfaces. As a result, the critical shear stress for a given grain size on a sediment surface is characterized by a probability distribution, rather than a single value. On a given bed, the crtitical shear stress distributions of different grain sizes have similar lower bounds, but above their lower tails they diverge rapidly, with smaller grains having substantially higher median critical shear stresses. Large numbers of fines, trapp.ed within pockets on the bed or shielded by upstream grains, are effectively lost to the flow. Our calculations suggest that critical shear stress, as conventionally measured, is defined by the most erodible grains, entrained during transient shear stress excursions associated with the turbulent flow; this implies a physical basis for the indeterminacy of initial motion. These observations suggest that transport rate/shear stress relationships may be controlled, in part, by the increasing numbers of grains that become available for entrainment as mean shear stress increases. They also suggest that bed textures and grain size distributions may be controlled, within the constraints of an imposed shear stress and sediment supply regime, by the influence of each size fraction on the erodibility of other grain sizes present on the bed.
[1] River beds are often arranged into patches of similar grain size and sorting. Patches can be distinguished into ''free patches,'' which are zones of sorted material that move freely, such as bed load sheets; ''forced patches,'' which are areas of sorting forced by topographic controls; and ''fixed patches'' of bed material rendered immobile through localized coarsening that remain fairly persistent through time. Two sets of flume experiments (one using bimodal, sand-rich sediment and the other using unimodal, sand-free sediment) are used to explore how fixed and free patches respond to stepwise reductions in sediment supply. At high sediment supply, migrating bed load sheets formed even in unimodal, sand-free sediment, yet grain interactions visibly played a central role in their formation. In both sets of experiments, reductions in supply led to the development of fixed coarse patches, which expanded at the expense of finer, more mobile patches, narrowing the zone of active bed load transport and leading to the eventual disappearance of migrating bed load sheets. Reductions in sediment supply decreased the migration rate of bed load sheets and increased the spacing between successive sheets. One-dimensional morphodynamic models of river channel beds generally are not designed to capture the observed variability, but should be capable of capturing the time-averaged character of the channel. When applied to our experiments, a 1-D morphodynamic model (RTe-bookAgDegNormGravMixPW.xls) predicted the bed load flux well, but overpredicted slope changes and was unable to predict the substantial variability in bed load flux (and load grain size) because of the migration of mobile patches. Our results suggest that (1) the distribution of free and fixed patches is primarily a function of sediment supply, (2) the dynamics of bed load sheets are primarily scaled by sediment supply, (3) channels with reduced sediment supply may inherently be unable to transport sediment uniformly across their width, and (4) cross-stream variability in shear stress and grain size can produce potentially large errors in width-averaged sediment flux calculations.
Abstract. The routing of bed material through channels is poorly understood. We approach the problem by observing and modeling the fate of a low-amplitude sediment wave of poorly sorted sand that we introduced into an experimental channel transporting sediment identical to that of the introduced wave. The wave essentially dispersed upstream and downstream without translation, although there was inconclusive evidence of translation late in the experiment when the wave was only 10-20 grain diameters high. Alternate bars migrated through zones of differing bed load transport rate without varying systematically in volume, celerity, or transport rate. Sediment that overpassed migrating bars was apparently responsible for dispersion of the wave. The evolution of the wave was well predicted by a one-dimensional model that contains no adjusted empirical constants. Numerical experiments demonstrate, however, that the theory does not predict sediment waves that migrate long distances downstream. Such waves can only be explained by the following processes not represented by the theory: selective bed load transport, spatial variations in bar and other form roughness, the mechanics of mobile armor, and perhaps other mechanisms.
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