Diffusion of bedload particles in open-channel flows: distribution of travel times and second-order statistics of particle trajectories

Abstract

The motion of bedload particles is diffusive and occurs within at least three scale ranges: local, intermediate and global, each of which with a distinctly different diffusion regime. However, these regimes, extensions of the scale ranges and boundaries between them remain to be better defined and quantified. These issues are explored using a Lagrangian model of saltating grains over the uniform fixed bed. The model combines deterministic particle motion dynamics with stochastic characteristics such as probability distributions of step lengths and resting times. Specifically, it is proposed that a memoryless exponential distribution is an appropriate model for the distribution of rest periods while the probability that a particle stops after a current jump follows a binomial distribution, which is a distribution with lack of memory as well. These distributions are incorporated in the deterministic Lagrangian model of saltating grains and extensive numerical simulations are conducted for the identification of the diffusive behavior of particles at different time scales. Based on the simulations and physical considerations, the local, intermediate, and global scale ranges are quantified and the transitions from one range to another are studied for a spectrum of motion parameters. The obtained results demonstrate that two different time scales should be considered for parameterization of diffusive behavior within intermediate and global scale ranges and for defining the localintermediate and intermediate-global boundaries. The simulations highlight the importance of the distributions of the step lengths and resting times for the identification of the boundaries (or transition intervals) between the scale ranges.

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

“…The mismatch between MSD and AC estimates result from different working assumptions: MSD considers particle motion on long times, whereas AC is computed on short times. In numerous systems driven by fluctuations, particle motion is ballistic at short times (typically, for times shorter than the flight time between two collisions), resulting in superdiffusion [ Pusey , ], and this behavior is also observed for bed load transport [ Martin et al , ; Heyman , ; Bialik et al , ]. As a result, apparent diffusivity is smaller at short timescales.…”

Lagrangian Modelling of Saltating Sediment Transport: A Review

“…However, only the combination of experimental studies (e.g., Habersack 2001;Nikora et al 2002;Campagnol et al 2013) and Lagrangian models of saltation (e.g., Nikora et al 2001;Lukerchenko et al 2009a, b;Bialik 2011b;Bialik et al 2012Bialik et al , 2015Moreno and Bombardelli 2012) have allowed for the improvement of our knowledge on this issue and the building of the theory of particles' diffusion in bedload. Figure 16.3 shows examples of temporal changes of the particles' positions based on the simulations carried out using the Bialik et al (2012) model.…”

“…Moreno and Bombardelli (2012) showed that sudden changes in the particles' velocity and acceleration which appear due to particle-particle collisions introduce additional transverse diffusion, while in the streamwise direction diffusive behaviour due to this process does not exist. On the other hand, in the paper by Bialik et al (2015) it was shown that two different time scales for defining the local-intermediate and intermediate-global boundaries should be considered. The first one is controlled by turbulence, as suggested by Niño (1995), Nikora et al (2002) or Bialik et al (2012), and the second one depends on the duration of the resting period of the particles, which is the most important factor controlling the spread of particles in the global range of diffusion.…”

Grain Size Distribution of Bedload Transport in a Glaciated Catchment (Baranowski Glacier, King George Island, Western Antarctica)

“…Although a substantial amount of progress has been made in this field because of research conducted in laboratory channels (e.g., [19][20][21]) and field studies (e.g., [22][23][24][25][26]) and with the use of bedload transport models (e.g., [1,2,[27][28][29][30]), the relationships among the factors associated with bedload transport are poorly understood in natural gravel-bed channels in general and in those located in polar regions in particular [31]. 30]), the relationships among the factors associated with bedload transport are poorly understood in natural gravel-bed channels in general and in those located in polar regions in particular [31].…”