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Numerical simulation of large‐scale bed load particle tracer advection‐dispersion in rivers with free bars
Author(s) -
Iwasaki Toshiki,
Nelson Jonathan,
Shimizu Yasuyuki,
Parker Gary
Publication year - 2017
Publication title -
journal of geophysical research: earth surface
Language(s) - English
Resource type - Journals
eISSN - 2169-9011
pISSN - 2169-9003
DOI - 10.1002/2016jf003951
Subject(s) - advection , mechanics , tracer , dispersion (optics) , entrainment (biomusicology) , randomness , turbulence , particle (ecology) , mass flux , physics , geology , mathematics , statistics , optics , oceanography , rhythm , nuclear physics , acoustics , thermodynamics
Asymptotic 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.