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

Abstract

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.

Lagrangian and Eulerian Description of Bed Load Transport

“…Different bed conditions and transport intensities (particularly those higher than described here) may change the active processes and, in turn, the correlation terms. For example, processes such as sediment burial and reappearance in a mobile layer (possibly, in the presence of bedforms) may strongly alter the temporal fluctuations with respect to those for continuously exposed particles (see, e.g., Ghilardi et al, , ; Iwasaki et al, ; Voepel et al, ). Threshold sizes to consider spatial and temporal scales large enough to achieve process uniformity/stationarity are expected to be more demanding than in the present case.…”

Experimental Censorship of Bed Load Particle Motions and Bias Correction of the Associated Frequency Distributions

“…Example 2 explores the effects of censorship and truncation with a thick‐tailed distribution. Rest time, R , is a suitable quantity that may present a heavy tail resulting from particle burial and reappearance (e.g., Ferguson et al, ; Iwasaki et al, ; Voepel et al, ); we here assume a power law distribution for R . In this case the length of the observation window, L w , has no effect on the variable and censorship or truncation effects are only due to the time window; as in example 1 we assume a perfect correction to the censorship bias to be achievable by equation .…”

“…Four are particularly relevant to the description of bed load sediment transport and the behavior of tracer particles, namely, the instantaneous velocities and accelerations of the particles, and their hop distances and associated travel times (Ancey & Heyman, ; Campagnol et al, , ; Einstein, ; Fathel, ; Fathel et al, ; Furbish et al, , ; Heyman, ; Wilcock, ). In addition, particle rest times between motions are essential for understanding the residence time of particles on and within the streambed and the spreading behavior of tracer particles (Bradley et al, ; Iwasaki et al, ; Lajeunesse et al, ; Martin et al, ; Sayre & Hubbell, ; Voepel et al, ).…”

“…While the concept of censorship of particle hops is, in the end, straightforward, its impact on measured statistics cannot be assessed a priori, since it depends on both operational parameters (first of all, the size of an observation window) and phenomenological properties (typical size of particle hops or rests) that, in turn, are linked to hydrodynamic and morphologic conditions. For example, the task of estimating the distribution of rest time and its moments may be particularly problematic if these times follow a power law distribution whose moments are undefined or emerge only after long times in relation to particle burial and exhumation (e.g., Ferguson et al, ; Iwasaki et al, ; Voepel et al, ). The scientific literature on sediment transport mechanics offers limited examples of studies where the censorship problem has been recognized and addressed.…”

A Well‐Posed Alternative to the Hirano Active Layer Model for Rivers With Mixed‐Size Sediment

“…The second limitation of the active layer model is related to sediment dispersion. Under dynamic equilibrium conditions, the active layer model predicts tracer sediment to be advected downstream at a mean speed inversely proportional to the active layer thickness without dispersing (Iwasaki et al, 2017). However, traced sediment particles are observed to disperse as they move downstream both in the field (e.g., Bradley & Tucker, 2012;Bradley, 2017;Drake et al, 1988;Hassan et al, 1991;Nikora et al, 2002;Rathbun et al, 1971;Sayre & Hubbell, 1965) and in the laboratory (e.g., Hill et al, 2010;Martin et al, 2012;Roseberry et al, 2012).…”