In this paper we present numerical simulations of large-scale tracer particle advection-dispersion in alluvial rivers. We specifically focus on conditions for which bedload is the dominant mode of sediment transport, and for which the river is subject to the formation of free, migrating alternate bars. We apply two formulations of the Exner equation of sediment conservation; a standard flux form, in which bed elevation change is related to the divergence of the vector of sediment transport rate, and a stochastic entrainment form, in which bed elevation change is related to the net entrainment rate of particles into bedload. In modeling tracer advection-dispersion, we use a single grain size, as well as an active layer formulation in which active layer thickness scales with grain size. We specifically consider conditions so that no be aggradation or degradation occurs when averaged over the bars. We find that the presence of bars has a dramatic effect on streamwise advection-dispersion of tracer particles. When the flux form of Exner equation is used for the case of a flat bed (no bars), tracer particles advect without dispersing. When the entrainment formulation is applied to the same condition, the particles also disperse, in response to the stochasticity associated with the PDF of particle step length. The effect of bars is to substantially increase the streamwise dispersion rate. The statistics of the pattern of advection-dispersion seen in the presence of bars are to a large degree independent of whether the flux or entrainment forms of Exner equation are used, indicating that dispersion is dominated by the bars themselves. The simulated asymptotic pattern of streamwise tracer advection-dispersion under the influence of free bars is either normal or weakly superdiffusive. The numerical model self-generates stochasticity in bar properties, including wavelength, wave height, and celerity. This in turn imparts a randomness to tracer behavior, resulting in large-scale dispersion. More specifically, the randomness of the alternate bar dimensions renders local bed surface elevation a stochastic quantity. In some cases, the probability distribution of trough elevation is such that it results in a heavy-tailed waiting time distribution; a deeply-buried particle must wait an anomalously long time before it is re-entrained. Migrating bars strongly constrain the length-scale of tracer transport, likely causing a thin-tailed distribution of travel distance. The combination of thin-tailed travel distance and heavy-tailed waiting time may be the cause of the simulated superdiffusive dispersion when it occurs. The morphological evolution of bed surface we consider in the simulation is that of alternate bars only, in the absence of bed aggradation or degradation when averaged over the bars. However, the coexistence of several static and dynamic morphological elements might make the waiting time distribution more complex, perhaps causing other dispersion behavior (e.g., subdiffusive dispersion) and perhaps affecting advection (e.g., advective slowdown), which are not illustrated in this paper. The effects of different bed morphologies (e.g., multiple-row bars, braiding and 3D dunes) and channel planform (e.g., meandering, systematic width variation, and interacting channel and floodplain) on tracer advection-dispersion invite further investigation. In addition, model extensions including e.g. sediment size mixtures, and also describing the bed in terms of a continuous vertical structure rather than the active layer formulation so as to better simulate vertical mixing of tracers in the bed [e.g. Pelosi et al., 2014, 2016], are future challenges in the pursuit of a comprehensive understanding of bedload tracer advection-dispersion in nature. This study contributes to a better understanding of tracer advection-dispersion in the global regime [Nikora et al., 2002].
- PI: Gary Parker
- PI Institution: University of Illinois
- August 16, 2015 – August 15, 2016