Streamwise and Vertical Dispersal of Tracer Stones in an Equilibrium Bed

Modeling transport, erosion, and deposition of nonuniform sediment over temporal intervals that are short compared to those characterizing channel bed aggradation and degradation remains an open problem due to the complex quantification of the sediment fluxes between the bed material load and the alluvial deposit. Parker, Paola, and Leclair in 2000 proposed a morphodynamic (PPL) framework to overcome this problem. This framework is used here to model the dispersal of a patch of gravel tracers in three different settings, a laboratory flume, a mountain creek, and a braided river. To simplify the problem, (a) the bed slope, bedload transport rate, and bed configuration are assumed to be constant in space and time (equilibrium), (b) sediment entrainment and deposition are modeled with a constant step length formulation, and (c) the PPL framework is implemented in a one-dimensional (laterally averaged) model. Model validation against laboratory experiments suggests that, as the transport capacity of the flow increases, the maximum elevation-specific density of sediment entrainment may migrate downward in the deposit. The comparison between model results and field data shows that the equilibrium solution can reasonably capture tracer dispersal. The equilibrium model can also reproduce subdiffusion and superdiffusion of a patch of tracers in the streamwise direction, depending on the magnitude of the short-term bed level changes. Finally, the average tracer elevation in a cross-section decreases in time because particles that are buried deep in the deposit are only rarely reentrained into bedload transport.