Relation Between Width, Water Discharge and Bed Load Concentration

In alluvial rivers, the width of the channel that conveys the majority of the water should also convey the majority of the bed load. Channel width thus scales with both water discharge and sediment discharge. Interactions among the different variables controlling channel width are examined here by coupling the equations for discharge, Q, and total bed load transport rate, Qb, using width as a common variable. A relation for bed load concentration, Qb/Q, is formulated from a set of variables linking excess shear stress, grain size and flow depth. Downstream trends in Qb/Q are then computed for a gravel-bed channel characterized by an exponential profile and an arbitrary but plausible downstream fining relation. The results suggest that the downstream trends in Qb/Q are strongly dependent on the assumed relation for excess shear stress: If the difference between bankfull Shields stress and critical Shields stress is constant, as field data indicate, then bed load concentration decreases slowly downstream. This scenario could reflect conditions where the supply of coarse sediment is decreasing downstream due to lower overall relief, and/or the bed load is being milled into finer sizes that are transported in suspension. If the difference between bankfull shear stress and critical shear stress is allowed to decrease, then bed load concentration decreases very rapidly downstream. This scenario is not particularly realistic but could reflect conditions where sediment supply is diminishing and the bed is becoming increasingly armored downstream. If the difference between bankfull Shields stress and critical Shields stress is allowed to increase downstream, then Qb increases almost in proportion to Q, and thus bed load concentration is nearly constant. This last result suggests that the observed hydraulic geometry relations for width, depth, and velocity may reflect a hidden relation to sediment load, which under conditions of increasing excess shear stress appears to scale almost linearly with discharge.