Routing of Heterogeneous Sediments over Movable Bed: Model Development

A one‐dimensional numerical model of sediment routing is derived to simulate erosion, transport, and deposition of individual size‐density fractions in the bed material within a relatively straight, nonbifurcating alluvial channel. The reach of interest is subdivided into a number of longitudinal elements of varying width‐averaged properties. During each time step, flow depths and velocities in each element are determined from the gradually varied flow equation using the standard step method for backwater calculations. The bedload transport rate of each size fraction is calculated from a modified Bagnold equation implementing a novel approach that takes into consideration the effects of turbulent fluctuations in the bed shear stress. Critical shear stresses for entrainment of particles from the mixed bed are determined using relationships that treat grain protrusion and hiding. The transport of particles in suspension is modeled using a convection‐diffusion sediment continuity equation, either explicitly solved by the Rouse equation or implicitly solved using a finite difference scheme. Changing vertical geometry is handled using coordinate stretching. The velocity profile in the vertical is calculated at each point using the von Karman‐Prandtl logarithmic velocity distribution, and vertical sediment diffusivities for the suspended sediment are computed assuming a parabolic distribution for diffusion of fluid momentum. Interaction of the transported load and the bed is calculated by a bed‐continuity equation solved for each size‐density fraction in an active layer. Bed composition and elevation are monitored through time, so that simulations produce complete stratigraphic sequences of sediment. The advantages of this model over previous models are a treatment of turbulent fluctuations of bed shear stress, minimization of calibration factors, and explicit consideration of multiple grain densities.