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

Toshiki Iwasaki, Jonathan Nelson, Yasuyuki Shimizu, Gary Parker

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)847-874
Number of pages28
JournalJournal of Geophysical Research: Earth Surface
Issue number4
StatePublished - Apr 1 2017


  • advection-dispersion
  • anomalous dispersion
  • bed load tracers
  • free single-row alternate bars
  • normal dispersion

ASJC Scopus subject areas

  • Earth-Surface Processes
  • Geophysics


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