The cause of advective slowdown of tracer pebbles in rivers: Implementation of Exner‐Based Master Equation for coevolving streamwise and vertical dispersion

Pelosi, Anna; Schumer, R.; Parker, Gary; Ferguson, R.

doi:10.1002/2015jf003497

Cited by 53 publications

(79 citation statements)

References 32 publications

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“…The same effect was assumed by Einstein (1950) from the more intense hiding of the smaller grains. Models have been developed to simulate the slowdown process Pelosi et al, 2016). However, in contrast, the derived thresholds to motion for the two grain sizes suggest that the bedload transport at the Mur River occurs independently from the gradation of the surrounding sediment.…”

Section: Discussionmentioning

confidence: 99%

Deriving formulas for an unsteady virtual velocity of bedload tracers

Klösch

Habersack

2018

Earth Surf Processes Landf

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In a flume experiment with steady flow conditions, H. A. Einstein recognised the transport of bedload particles as consisting of steps of rolling, sliding, or saltation with intermittent rest periods, and introduced the concept of an average, ‘virtual’ transport velocity. This virtual velocity then has also been derived from tracer studies in the field by dividing the travelled distance of a tracer by the duration of competent flow. As a consequence, the virtual velocity in the field is represented by one single value only, despite the unsteady flow variables. Tracer measurements in a river have not been yet used to express transport velocity as a direct function of these actual variables, and insights from tracer measurements into the processes of sediment transport remain limited. In particular, the unsteady conditions for bedload in the field have impeded the derivation of sediment transport characteristics as determined from laboratory experiments, as well as the transfer of laboratory insights to a field setting. We introduce a method of data regression for the derivation of an ‘unsteady’ virtual velocity from repeated surveys of tracer positions. The regression program called graVel (provided as supplementary material) relates the integral of an excess flow variable term to measured travel distances, yielding the most probable threshold value for entrainment and the coefficient of linear and non‐linear formulas. An extended regression allows additional fitting of the exponent in non‐linear formulas. Application to published tracer data from the Mameyes River, Puerto Rico, shows that the unsteady virtual velocity is more likely governed by non‐linear relations to excess Shields stress, similar to bedload transport, than by relations linking the particle velocity linearly to excess shear velocity. Partial agreements with non‐dimensional results derived from the larger, non‐wadeable Mur River encourage the establishment of a generalised formula for the unsteady virtual velocity. Copyright © 2017 John Wiley & Sons, Ltd.

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Section: Discussionmentioning

confidence: 99%

Deriving formulas for an unsteady virtual velocity of bedload tracers

Klösch

Habersack

2018

Earth Surf Processes Landf

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“…This formulation considers conservation of tracer particles (of uniform size) in an active layer with a constant thickness under the idealized case of mobile bed equilibrium (no net bed aggradation or degradation; Ganti et al, ; Parker et al, ; Pelosi et al, ; Pelosi et al, ):

L_{a} \frac{\partial f_{a} ((), x, t)}{\partial t} = - D_{p} J f_{a} ((), x, t) + D_{p} \int_{0}^{\infty} J f_{a} ((), x - r, t) p ((), r) normald r,

where f a is the fraction of tracer particles in the active layer, x is the streamwise location (L), t is time (T), D p is particle size (L), J is the particle entrainment frequency (1/T), and p ( r ) is the PDF of the streamwise step length. Equation is straightforward as it considers mass conservation of the tracers and demonstrates that the variation of tracer concentration (left‐hand side of equation ) is under the combined action of particle entrainment and deposition.…”

Section: Formulationmentioning

confidence: 99%

Transient Anomalous Diffusion and Advective Slowdown of Bedload Tracers by Particle Burial and Exhumation

Singh

et al. 2019

Water Resources Research

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The process of burial and exhumation of bedload particles within a certain depth of the riverbed leads to vertical exchange of particles, which significantly affects the characteristics of streamwise bedload transport. In this paper, we revisit the classic active layer formulation and extend it by incorporating the burial and exhumation through conceptualizing the fluctuations of bed surface as the relative vertical movement of buried tracer particles in the substrate layer (i.e., we change the static reference system to the fluctuating riverbed surface). We theoretically demonstrate, for the first time, the emergence of the transient anomalous diffusion (both superdiffusion and subdiffusion) and power‐law advective slowdown at the intermediate timescales, which are induced by the nonequilibrium transport as characterized by the inhomogeneous vertical mixing of tracers due to particle burial and exhumation. Neglecting the ballistic regime at extremely short times, at small and large timescales, the transport regimes show normal diffusion. This result further implies that for the most typical fluvial riverbed with finite vertical exchange depth (i.e. nonaggrading or nondegrading bed), the subdiffusion of bedload tracers for large timescale transport may still be transient, which will eventually converge to the normal diffusion as time increases. Comparing the obtained analytical solutions with available numerical results as well as field observations, we show that the proposed formulation can capture well anomalous diffusion and the power‐law slowdown of the advective velocity of bedload tracers at intermediate timescales, and more importantly the transition from anomalous to normal diffusion at large timescales.

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“…g . Pelosi et al ., , ], are future challenges in the pursuit of a comprehensive understanding of bed load tracer advection‐dispersion in nature. This study contributes to a better understanding of tracer advection‐dispersion in the global regime [ Nikora et al ., ].…”

Section: Discussionmentioning

confidence: 99%

“…Because bed load tracer transport can be treated as a random process, simple stochastic models (e.g., Markov process and random walk model) have been proposed to capture the horizontal and vertical mixing of tracers [ Sayre and Hubbell , ; Yang and Sayre , ; Hassan and Church , ; Ferguson and Hoey , ; Schumer et al ., ]. Physically based models that include the origin of this stochasticity, for instance, the probability of bed surface fluctuation, entrainment, and deposition [ Parker et al ., ; Ancey , ; Pelosi et al ., , ]; the irregularity of bed form dimensions [ Blom and Parker , ]; and the velocity variability of bed load particles [ Furbish et al ., ], have led to the derivation of master equations describing tracer dispersal. A key question for each of these approaches is how to model the stochasticity of bed load motion under the influence of physical phenomena such as bed forms and planform variation.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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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.

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The cause of advective slowdown of tracer pebbles in rivers: Implementation of Exner‐Based Master Equation for coevolving streamwise and vertical dispersion

Cited by 53 publications

References 32 publications

Deriving formulas for an unsteady virtual velocity of bedload tracers

Deriving formulas for an unsteady virtual velocity of bedload tracers

Transient Anomalous Diffusion and Advective Slowdown of Bedload Tracers by Particle Burial and Exhumation

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

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