Analyzing and modeling sub-diffusive transport of bedload along a heterogeneous gravel bed using stochastic and statistical methods

Li, ZhiPeng; Chen, Dong; Sun, HongGuang; Meng, Zhenzhu; Zhang, Yong; Sibatov, Renat T.

doi:10.1016/j.jhydrol.2020.125697

Cited by 12 publications

(10 citation statements)

References 62 publications

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“…This is due to the first moment of the hyperexponential distribution being convergent, which is different from the studies conducted by Martin et al (2012) and Z. Li et al (2020). In the literature (Z.…”

Section: Numerical Simulationscontrasting

confidence: 60%

Dynamics of Dual‐Mode Bedload Transport With Three‐Dimensional Alternate Bars Migration in Subcritical Flow: Experiments and Model Analysis

Oshtorjani

Chen

et al. 2023

JGR Earth Surface

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Bedload transport often exhibits dual-mode behavior due to interactions of spatiotemporal controlling factors with the migrating three-dimensional bedforms (characterized by the fully developed patterns in the bed, such as alternate bars, pools, and clusters). This study explores dual-mode bedload transport based on experimental measurements and develops Einstein's exponential-based model to characterize large fluctuations of bedload sediment discharge. The particle waiting time, particle flux, and bed elevation are measured in a series of well-controlled laboratory experiments. Flume experiments show that the waiting time distribution of sediments gives a bimodal characteristic, two distinct modes can be identified from the measured data. This study encapsulates this dual-mode bedload transport behavior in a hyperexponential distribution of sediment resting times and introduces it into the continuous time random walk (CTRW) framework. Considering the scaling limit of the thin/heavy-tailed CTRW processes, a single-rate mass transfer (SRMT) and fractional-derivative SRMT (F-SRMT) models are obtained, and the model parameters are determined from the hyperexponential distribution. Further analyses reveal that the dual-mode bedload transport behavior is controlled by mass exchange between the mobile and immobile zones, and a dimensionless index η can quantify the intensity of dual-mode behavior. Applications show that the dual-mode bedload transport models are much more accurate in characterizing bedload transport in a mixed-size gravel bed than the traditional exponential-based model, and the nonlocal movement of bedload sediments is significant in the mixed-size gravel bed. Further investigations will focus on the applicability test of the dual-mode models to other flow regimes and conditions.

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Section: Numerical Simulationscontrasting

confidence: 60%

Dynamics of Dual‐Mode Bedload Transport With Three‐Dimensional Alternate Bars Migration in Subcritical Flow: Experiments and Model Analysis

Oshtorjani

Chen

et al. 2023

JGR Earth Surface

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“…Alternatives such as the time-fractional deposition process (Li et al. 2021) may also be considered.…”

Section: Discussionmentioning

confidence: 99%

“…Recently, Wu et al (2021, (2.29)) applied a 'bulk' absorption term to the FP equation to account for the deposition, which means that bedload particles may have an equal chance of ceasing their motions at any velocity (Ancey et al 2008;Ma et al 2014;Wu et al 2021;Pierce et al 2022). Alternatives such as the time-fractional deposition process (Li et al 2021) may also be considered.…”

Section: Discussionmentioning

confidence: 99%

Theoretical analysis for bedload particle deposition and hop statistics

Jiang

Zeng

et al. 2023

J. Fluid Mech.

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Understanding the statistics of bedload particle motions is of great importance. To model the hop events which are defined as trajectories of particles moving successively from the start to the end of their motions, recently, Wu et al. (Water Resour. Res., vol. 56, 2020, p. e2019WR025116) have successfully performed individual-based simulations according to the Fokker–Planck equation for particle velocities. However, analytical solutions are still not available due to (i) difficulties in treating the velocity-dependent diffusivity, and (ii) a knowledge gap in incorporating the termination of particle motions for the equation. To tackle the above-mentioned challenges, we first specify a Robin boundary condition representing the deposition of particles. Second, for analytical solutions of hop statistics, a variable transformation is devised to deal with the velocity-dependent diffusivity. The original bedload transport problem is thus found to be governed by the classic equation for the solute transport in tube flows with a constant diffusivity after the transformation. Finally, through solving the spatial and temporal moments of the governing equation, we investigate the influence of the deposition rate on three key characteristics of particle hops. Importantly, we have related the deposition rate to the mean travel times and hop distances, enabling a direct determination of this physical parameter based on measured particle motion statistics. The analytical solutions are validated by experimental observations with different bedload particle diameters and transport conditions. Based on the limited experimental datasets, the deposition frequency is shown to decrease as the shear stress increases when the flow rate is not small.

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“…In works [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], a fractional-differential approach is accomplished, which, in contrast to others, allows describing the normal and dispersive transport within a unified formalism. Within the fractional approach, many results of the diffusional decomposition theory of supersaturated solid solutions can be generalized to the case of dispersive self-similar transport in disordered solids.…”

Section: Introductionmentioning

confidence: 99%

Nucleation Controlled by Non-Fickian Fractional Diffusion

Светухин

2021

Mathematics

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Kinetic models of aggregation and dissolution of clusters in disordered heterogeneous materials based on subdiffusive equations containing fractional derivatives are studied. Using the generalized fractional Fick law and fractional Fokker–Planck equation for impurity diffusion with localization, we consider modifications of the classical models of Ham, Aaron–Kotler, and Lifshitz–Slezov for nucleation and decomposition of solid solutions. The asymptotic time dependencies of supersaturation degree, average cluster size, and other characteristics at the stages of subdiffusion-limited nucleation and coalescence are calculated and analyzed.

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Analyzing and modeling sub-diffusive transport of bedload along a heterogeneous gravel bed using stochastic and statistical methods

Cited by 12 publications

References 62 publications

Dynamics of Dual‐Mode Bedload Transport With Three‐Dimensional Alternate Bars Migration in Subcritical Flow: Experiments and Model Analysis

Dynamics of Dual‐Mode Bedload Transport With Three‐Dimensional Alternate Bars Migration in Subcritical Flow: Experiments and Model Analysis

Theoretical analysis for bedload particle deposition and hop statistics

Nucleation Controlled by Non-Fickian Fractional Diffusion

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