Exploring a semimechanistic episodic Langevin model for bed load transport: Emergence of normal and anomalous advection and diffusion regimes

Abstract

Bed load transport is a highly stochastic, multiscale process, where particle advection and diffusion regimes are governed by the dynamics of each sediment grain during its motion and resting states. Having a quantitative understanding of the macroscale behavior emerging from the microscale interactions is important for proper model selection in the absence of individual grain-scale observations. Here we develop a semimechanistic sediment transport model based on individual particle dynamics, which incorporates the episodic movement (steps separated by rests) of sediment particles and study their macroscale behavior. By incorporating different types of probability distribution functions (PDFs) of particle resting times T r , under the assumption of thin-tailed PDF of particle velocities, we study the emergent behavior of particle advection and diffusion regimes across a wide range of spatial and temporal scales. For exponential PDFs of resting times T r , we observe normal advection and diffusion at long time scales. For a power-law PDF of resting times (i.e., f T r ð Þ$T 2m r ), the tail thickness parameter m is observed to affect the advection regimes (both sub and normal advective), and the diffusion regimes (both subdiffusive and superdiffusive). By comparing our semimechanistic model with two random walk models in the literature, we further suggest that in order to reproduce accurately the emerging diffusive regimes, the resting time model has to be coupled with a particle motion model able to produce finite particle velocities during steps, as the episodic model discussed here.

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

“…Making an analogy with Brownian motion in a potential well, Ancey and Heyman [] assumed that behaves like white noise and 〈 F 〉 relaxes to its steady state value over a certain characteristic time, and thereby they deduced that P ( u p ) was a truncated Gaussian distribution, a form supported by experimental evidence [ Martin et al , ]. Assuming that 〈 F 〉 was constant and particles move sporadically, Fan et al [] found that particles may exhibit subdiffusive, normal, or superdiffusive behavior depending on the resting time. While particle diffusion and more specifically the determination of particle diffusivity have been addressed experimentally [ Heyman et al , ; Seizilles et al , ], there is scarce information on how D u varies with the flow conditions.…”

“…The first family follows the Lagrangian framework, in which particles are tracked individually. To deduce the bulk properties, such as particle flux and activity (i.e., the number of moving particles per unit streambed area), recent studies have focused on the statistical properties of particle trajectories in their random walks [Ganti et al, 2010;Furbish et al, 2012bFurbish et al, , 2012cArmanini et al, 2014;Pelosi et al, 2016;Fan et al, 2016]. An alternative is the Eulerian framework, which derives the bulk properties by averaging particle behavior over a control volume [Ancey et al, 2008;Ancey and Heyman, 2014].…”

Lagrangian and Eulerian Description of Bed Load Transport

“…The approach taken in this section is an alternative way to account for the intermittence of the bed load process. It is closely related to an entrainment‐disentrainment form of the Exner equation (e.g., Ancey, ; Ancey & Heyman, ; Ballio et al, ; Charru et al, ; Lajeunesse et al, ), as well as to modeling the particle trajectories as random walks (e.g., Fan et al, ; Lisle et al, ). From a phenomenological point of view, the persistence of motion is also obviously related to the characteristics of particle hops (e.g., Campagnol et al, ; Fathel et al, ; Hu & Hui, ; Lee et al, ; Ramesh et al, ).…”

A Statistical Description of Particle Motion and Rest Regimes in Open‐Channel Flows Under Low Bedload Transport

“…Bedload is a common mechanism of sediment transport for sand particles in natural flow, characterized by cyclic sequences of particles moving and resting on the sediment bed (e.g., Fan et al, , ; Furbish et al, ; González et al, ; Lajeunesse et al, ; Roseberry et al, ). The physical mechanisms governing bedload transport are highly complex due to (i) the turbulent fluctuations of the flow and (ii) random interactions of grains with each other and with the bed, over a wide range of bed topography and corresponding flow scales, from the grain size to the reach (e.g., Bagnold, ; Church, ; Furbish et al, ).…”

“…Another potential source of variability is the effect of sediment‐mixture heterogeneity (Houssais & Lajeunesse, ), which could be related to the different waiting‐time distributions proposed in the literature. All of these issues are important for the physical understanding of sediment‐transport mechanisms, for the correct prediction of particle trajectories (microscale), and for the advection and diffusion properties of the particle ensemble (macroscale), as discussed above (Han & He, , Nikora et al, ; Fan et al, , Weeks et al, , Schumer et al, b, and Fan et al, ).…”