Numerical simulation of large‐scale bed load particle tracer advection‐dispersion in rivers with free bars

Abstract

AbstractAsymptotic characteristics of the transport of bed load tracer particles in rivers have been described by advection‐dispersion equations. Here we perform numerical simulations designed to study the role of free bars, and more specifically single‐row alternate bars, on streamwise tracer particle dispersion. In treating the conservation of tracer particle mass, we use two alternative formulations for the Exner equation of sediment mass conservation: the flux‐based formulation, in which bed elevation varies with the divergence of the bed load transport rate, and the entrainment‐based formulation, in which bed elevation changes with the net deposition rate. Under the condition of no net bed aggradation/degradation, a 1‐D flux‐based deterministic model that does not describe free bars yields no streamwise dispersion. The entrainment‐based 1‐D formulation, on the other hand, models stochasticity via the probability density function (PDF) of particle step length, and as a result does show tracer dispersion. When the formulation is generalized to 2‐D to include free alternate bars, however, both models yield almost identical asymptotic advection‐dispersion characteristics, in which streamwise dispersion is dominated by randomness inherent in free bar morphodynamics. This randomness can result in a heavy‐tailed PDF of waiting time. In addition, migrating bars may constrain the travel distance through temporary burial, causing a thin‐tailed PDF of travel distance. The superdiffusive character of streamwise particle dispersion predicted by the model is attributable to the interaction of these two effects.