Equilibrium entrainment of fine sediment over a coarse immobile bed

Abstract

[1] The transported load in most fluvial systems, including gravel-bedded rivers, includes fine-grained sediment. Models for suspended sediment transport have focused on sandcovered beds, rendering incomplete the theoretical and empirical framework for predicting fine sediment transport and routing. We conducted laboratory experiments involving sand transport over large immobile grains. The experiments were scaled such that immobile particles were much larger than the mobile sediment, but less than 10% of flow depth, and that bed shear stresses, scaled by the size of the mobile sediment, were indicative of transport in suspension. The experiments were conducted in equilibrium transport and included measurements of near-bed sediment concentration and interstitial sand storage for a range of flow and transport rates. Partial filling of grain interstices occurred over a narrow range of flow and transport rates, indicating a sharp threshold between no interstitial sand storage and a sand-covered bed. Less sand coverage on the bed resulted in higher near-bed sand concentrations per unit area of sand than runs with greater sand coverage. As sand bed elevation decreased relative to the coarse grains, turbulent wakes shed by the large grains appeared to enhance grain entrainment more than the corresponding decrease in bed area covered by sand resulted in decreased entrainment. Elevated concentrations were maintained until the bed was depleted of fine sediment. These results are formalized in a proposed sand elevation correction function that scales the entrainment rate for a bed partially covered by sand to the entrainment rate that would be predicted for a sand-covered bed.Citation: Grams, P. E., and P. R. Wilcock (2007), Equilibrium entrainment of fine sediment over a coarse immobile bed, Water Resour. Res., 43, W10420,

Linking morphodynamic response with sediment mass balance on the Colorado River in Marble Canyon: Issues of scale, geomorphic setting, and sampling design

“…Flow strength and grain size are related nonlinearly with concentration while the relation between supply and concentration is linear. Although other measures of sediment supply could be used, we use A s as defined above, because the approximately linear relation between this measure of supply and suspended‐sand concentration has been demonstrated in laboratory flume experiments [ Grams and Wilcock , ]. Rewriting equation in one‐dimensional difference form where X is distance in the streamwise direction, removing the negligible influence of ∂ V s /∂ t , assuming constant bed‐sediment porosity, using equation for sediment flux, and equation for sediment concentration, results in the following proportionality: Taking u * ∝ U then results in the simpler proportionality, …”

Sediment-transport during three controlled-flood experiments on the Colorado River downstream from Glen Canyon Dam, with implications for eddy-sandbar deposition in Grand Canyon National Park

“…This is justified based on the reasoning of Topping and others (2007a), who argued, on the basis of the flume experiments of Grams (2006) and Grams and Wilcock (2007), that the depth-averaged suspended-sand concentration scaled approximately linearly with changes in reach-averaged bedsand area such that, for the same flow and grain-size conditions, a reach-averaged bed-sand area of 50 percent would result in a depth-averaged suspended-sand concentration that is approximately 50 percent of the depth-averaged suspended-sand concentration associated with a reach-averaged bed-sand area of 100 percent. For example, if for a reach-averaged bed-sand area of 100 percent, the concentration term in the numerator of equation 16 were 1,000 mg/L, this concentration term would decrease to 750 mg/L for a reach-averaged bed-sand area of 75 81 percent, 500 mg/L for a bed-sand area of reach-averaged bed-sand area of 50 percent, and 100 mg/L for a reach-averaged bed-sand area of 10 percent.…”

“…By equation 4, the reach-averaged grain-size distribution of the bed sand exerts a nonlinear control on suspended-sand concentration Topping, 2001, 2008), whereas the reach-averaged area of sand on the bed exerts an approximately linear control on suspended-sand concentration (Grams, 2006;Grams and Wilcock, 2007). In the general case, where sand is uniformly distributed on the bed, a factor of 3 decrease in the reach-averaged median grain size of the bed will lead to an approximate factor of 10 increase in suspended-sand concentration (Topping and others, 2000b); a factor of 3 decrease in the reach-averaged area of sand on the bed will lead to an approximate factor of 3 decrease in suspended-sand concentration (Topping and others, 2007a).…”

“…For steady, uniform flow, and an approximately uniform areal distribution of sand on a gravel bed, the fractional area of the bed sand, A b , ranges from 0 to 1 and exerts an approximately linear control on suspended-sand concentration (Topping, 1997;Grams, 2006;Grams and Wilcock, 2007), thus leading to the following form of equation 3:…”

Experimental observation and modelling of roughness variation due to supply-limited sediment transport in uni-directional flow

“…These processes are not described by the presented model concept though. Grams (2006) and Grams and Wilcock (2007) present a study into sand transport over coarse layers that is more appropriate in this regime.…”