Bed load transport for a mixture of particle sizes: Downstream sorting rather than anomalous diffusion

Fan, Niannian; Xie, Yushu; Nie, Ruihua

doi:10.1016/j.jhydrol.2017.07.012

Cited by 8 publications

(10 citation statements)

References 49 publications

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“…Recognition of the importance of the size of the detection window is recently new to the study of particle motion in laboratory experiments (Ballio et al, ; Bialik & Karpiński, ; Fan et al, ). The uncensored database collected with the annular flume was used to clarify to which extent results from B tests are to be considered reliable.…”

Section: Resultsmentioning

confidence: 99%

“…As argued by Fan et al (), areal limitations, particularly along the longitudinal direction, affect the proper assessment of the variance of particle locations. The global range consists of time periods when particles are in motion alternated by rest periods.…”

Section: Discussion: Temporal and Spatial Scales Of Diffusive Regimesmentioning

confidence: 99%

“…Field studies inherently lack of a continuous record of particle locations that is needed to evaluate the diffusive character at different stages of particle motion. Even if this has now been made possible at the laboratory scale, the areal extent of the observed bed surface is usually restrained to a scale of tens of centimeters due to equipment constraints for image acquisition (Heays et al, ; Lajeunesse et al, ; Nikora et al, ; Tregnaghi, Bottacin‐Busolin, Tait, et al, ), thus the motions of particles that enter or leave the video sampling area are spatially censored (Fan et al, ; Fathel et al, ). Accurate reconstruction of particle trajectories is dependent on the frequency of the image acquisition, as a higher frame rate can support more accurate measurement of grain trajectories.…”

Section: Introductionmentioning

confidence: 99%

“…Following Nikora et al (),

\overset{X'^{2}}{true}

and

\overset{Y'^{2}}{true}

are expressed as a function of the shear velocity, the particle diameter d and the elapsed time t (= total time spent in motion or at rest from the beginning of the observation period):

\begin{matrix} centertrue \\ \overset{true¯}{X'^{2}} \\ \overset{true¯}{d^{2}} \end{matrix}, \begin{matrix} centertrue \\ \overset{true¯}{Y'^{2}} \\ \overset{true¯}{d^{2}} \end{matrix} \propto {(\frac{{italictu}^{*}}{d})}^{2 γ}

equation has been applied in several studies, all confirming the anomalous nature of bed load transport, but with scaling diffusive coefficients falling within a relatively wide range (Bialik et al, , ; Campagnol et al, ; Furbish, Ball, & Schmeeckle, ; Martin et al, ). According to Fan et al (), discrepancies may emerge as a consequence of selected experimental conditions, with major inconsistency resulting from defining the accurate boundaries of the local range (because of the high frame rate required) and of the global range (because of the large temporal and spatial observation windows required; Bialik & Karpiński, ). Campagnol et al () revisited the original theoretical framework to attempt to explain evidence that superballistic diffusion (1 < γ < 2) was observed in the local range during the early unsteady stage of particle entrainment (the so called near‐field subrange influenced by particle acceleration as reported in Bialik et al, ).…”

Section: Introductionmentioning

confidence: 99%

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Diffusive Regimes of the Motion of Bed Load Particles in Open Channel Flows at Low Transport Stages

Cecchetto

Tregnaghi

Bottacin‐Busolin

et al. 2018

Water Resources Research

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The stochasticity of fluid and sediment parameters has been identified as a source of diffusion, particularly anomalous diffusion at different temporal and spatial scales of bed load particle trajectories. Data from two sets of flume experiments are presented, one data set has gravel particle trajectories tracked over a limited area and was used in identifying the influence of different shear stress conditions on diffusive processes. A new experiment was performed using spherical particles moving as bed load in an annular flume in order to address concerns about censorship effects caused by the size of the detection window. An annular flume allowed collection of practically uncensored particle trajectories over longer time period than has been previously possible in the laboratory. Three diffusive regimes were observed at distinct stages of particle motion: (i) ballistic regime at the local range; (ii) Fickian diffusion at the intermediate range; (iii) subdiffusion at the global range. Characteristic time scales separate the regimes and correlate with the mean traveling and resting times of particles. Fickian diffusion in the intermediate range is first recognized as a result of the balance between intermittent weak transport and near‐bed turbulence, as first predicted by Nikora et al. (2002, https://doi.org/10.1029/2001WR000513). In the global range, extreme values were observed in the distribution of particle resting times, suggesting that two types of distributions (related to surface motion and vertical mixing) were responsible for the subdiffusion at longer time scales. Diffusion was found to be anisotropic at all stages of particle motion.

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Section: Resultsmentioning

confidence: 99%

Section: Discussion: Temporal and Spatial Scales Of Diffusive Regimesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Following Nikora et al (),

\overset{X'^{2}}{true}

and

\overset{Y'^{2}}{true}

are expressed as a function of the shear velocity, the particle diameter d and the elapsed time t (= total time spent in motion or at rest from the beginning of the observation period):

\begin{matrix} centertrue \\ \overset{true¯}{X'^{2}} \\ \overset{true¯}{d^{2}} \end{matrix}, \begin{matrix} centertrue \\ \overset{true¯}{Y'^{2}} \\ \overset{true¯}{d^{2}} \end{matrix} \propto {(\frac{{italictu}^{*}}{d})}^{2 γ}

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Diffusive Regimes of the Motion of Bed Load Particles in Open Channel Flows at Low Transport Stages

Cecchetto

Tregnaghi

Bottacin‐Busolin

et al. 2018

Water Resources Research

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show abstract

“…The existence of large rest times is related to the manner in which sediment disperses. Laboratory and field data suggest that tracer sediment diffuses anomalously (Bradley, ; Bradley et al, ; Fan et al, ; Ferguson et al, ; Haschenburger, , ; Nikora et al, ), whereas the model predicts normal (i.e., Fickian) diffusion. The propagation of tracer sediment is best represented by means of a fractional advection‐diffusion equation (Ancey, ; Martin et al, ; Schumer & Jerolmack, ), which originates, for instance, from heavy‐tail resting times under unisize sediment conditions (Fan et al, ), as well as from a relation between the travel distance and grain size under mixed‐size sediment conditions (Ganti et al, ; Hill et al, ).…”

Section: Discussionmentioning

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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Continuous time random walk model for non-uniform bed-load transport with heavy-tailed hop distances and waiting times

Sun

Zhang

et al. 2019

Journal of Hydrology

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Bed load transport for a mixture of particle sizes: Downstream sorting rather than anomalous diffusion

Cited by 8 publications

References 49 publications

Diffusive Regimes of the Motion of Bed Load Particles in Open Channel Flows at Low Transport Stages

Diffusive Regimes of the Motion of Bed Load Particles in Open Channel Flows at Low Transport Stages

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

Continuous time random walk model for non-uniform bed-load transport with heavy-tailed hop distances and waiting times

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