Stochastic-deterministic modeling of bed load transport in shallow water flow over erodible slope: Linear stability analysis and numerical simulation

Bohorquez, Patricio; Ancey, Christophe

doi:10.1016/j.advwatres.2015.05.016

Cited by 35 publications

(61 citation statements)

References 70 publications

(196 reference statements)

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“…The above equations hold for a narrow range of flow conditions: d ≈6mm, F r > 1, 0.1 < u ∗ / w s <0.3,

τ^{*} - τ_{cr}^{*} < 0.25

, and

- 0.2 < \tan θ < 0.1

. In this paper, we took a first step toward closing stochastic and deterministic nonequilibrium bed load models [ Charru , ; Audusse et al , ; Bohorquez and Ancey , , ]. Extending equations (17)–(21) to a wider range of flow conditions requires much more work.…”

Section: Discussionmentioning

confidence: 68%

Entrainment, motion, and deposition of coarse particles transported by water over a sloping mobile bed

Heyman

Bohorquez

Ancey

2016

J. Geophys. Res. Earth Surf.

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International audienceIn gravel bed rivers, bed load transport exhibits considerable variability in time and space. Recently, stochastic bed load transport theories have been developed to address the mechanisms and effects of bed load transport fluctuations. Stochastic models involve parameters such as particle diffusivity, entrainment, and deposition rates. The lack of hard information on how these parameters vary with flow conditions is a clear impediment to their application to real-world scenarios. In this paper, we determined the closure equations for the above parameters from laboratory experiments. We focused on shallow supercritical flow on a sloping mobile bed in straight channels, a setting that was representative of flow conditions in mountain rivers. Experiments were run at low sediment transport rates under steady nonuniform flow conditions (i.e., the water discharge was kept constant, but bed forms developed and migrated upstream, making flow nonuniform). Using image processing, we reconstructed particle paths to deduce the particle velocity and its probability distribution, particle diffusivity, and rates of deposition and entrainment. We found that on average, particle acceleration, velocity, and deposition rate were responsive to local flow conditions, whereas entrainment rate depended strongly on local bed activity. Particle diffusivity varied linearly with the depth-averaged flow velocity. The empirical probability distribution of particle velocity was well approximated by a Gaussian distribution when all particle positions were considered together. In contrast, the particles located in close vicinity to the bed had exponentially distributed velocities. Our experimental results provide closure equations for stochastic or deterministic bed load transport models. ©2016. American Geophysical Union. All Rights Reserved

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“…The above equations hold for a narrow range of flow conditions: d ≈6mm, F r > 1, 0.1 < u ∗ / w s <0.3,

τ^{*} - τ_{cr}^{*} < 0.25

, and

- 0.2 < \tan θ < 0.1

Section: Discussionmentioning

confidence: 68%

Entrainment, motion, and deposition of coarse particles transported by water over a sloping mobile bed

Heyman

Bohorquez

Ancey

2016

J. Geophys. Res. Earth Surf.

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“…Bohorquez and Ancey () describe the motion of unisize sediment based on a stochastic interpretation of sediment transport. We extend their framework to mixed‐size sediment conditions by considering all variables to be grain size dependent.…”

Section: The Silke Modelmentioning

confidence: 99%

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

2019

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The active layer model (Hirano, 1971) is frequently used for modeling mixed‐size sediment river morphodynamic processes. It assumes that all the dynamics of the bed surface are captured by a homogeneous top layer that interacts with the flow. Although successful in reproducing a wide range of phenomena, it has two problems: (1) It may become mathematically ill‐posed, which causes the model to lose its predictive capabilities, and (2) it does not capture dispersion of tracer sediment. We extend the active layer model by accounting for conservation of the sediment in transport and obtain a new model that overcomes the two problems. We analytically assess the model properties and discover an instability mechanism associated with the formation of waves under conditions in which the active layer model is ill‐posed. Numerical simulations using the new model show that it is capable of reproducing two laboratory experiments conducted under conditions in which the active layer model is ill‐posed. The new model captures the formation of waves and mixing due to an increase in active layer thickness. Simulations of tracer dispersion show that the model reproduces reasonably well a laboratory experiment under conditions in which the effect of temporary burial of sediment due to bedforms is negligible. Simulations of a field experiment illustrate that the model does not capture the effect of temporary burial of sediment by bedforms.

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“…Several attempts have been made to include the random behavior of particles moving as bed load into morphodynamic models by introducing probabilistic or stochastic models [e.g., Einstein , ; Nakagawa and Tsujimoto , ; Parker et al ., ; Ancey , ; Furbish et al ., ; Bohorquez and Ancey , ]. For instance, the bed load flux q b can be decomposed into particle advective and diffusive fluxes [ Furbish et al ., ].…”

Section: Tracer Transport Modelmentioning

confidence: 99%

“…For instance, the bed load flux q b can be decomposed into particle advective and diffusive fluxes [ Furbish et al ., ]. The former flux may correspond to the bulk‐averaged bed load transport rate explained above, and the latter flux describes the dispersal of bed load tracers [ Furbish et al ., ; Bohorquez and Ancey , ; Ancey et al ., ]. Such kinds of probabilistic flux‐based models have been proposed relatively recently, most commonly so as to incorporate stochastic variations of bed load transport into a morphodynamic model via an entrainment‐based form for the Exner equation of sediment conservation:

\frac{\partial η}{\partial t} = \frac{1}{1 - λ_{p}} ((), D - E),

where E is the volumetric entrainment rate of sediment per unit bed area into the bed load and D is the volumetric deposition rate of sediment per unit area onto the bed.…”

Section: Tracer Transport Modelmentioning

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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Stochastic-deterministic modeling of bed load transport in shallow water flow over erodible slope: Linear stability analysis and numerical simulation

Cited by 35 publications

References 70 publications

Entrainment, motion, and deposition of coarse particles transported by water over a sloping mobile bed

Entrainment, motion, and deposition of coarse particles transported by water over a sloping mobile bed

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

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

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