A probabilistic description of suspended sediment transport: advection, diffusion and random movement

Sediment transport is an important issue for human. It is closely related to human society, such as bridge scour and water quality. A sediment particle in flow not only follows the flow direction, but also diffuses through the surrounding water due to turbulence. Markov chain is used to approach the movement of sediment particles. From this perspective, particle movement is regarded as a stochastic process in our study; moreover, the proposed models simulate particle trajectories based on stochastic methodologies and physical mechanisms, underscoring mechanics in the stochastic differential equation. To simulate sediment particle movement, the stochastic diffusion particle tracking model (SD-PTM) has been derived from the Langevin equation, which is able to show the random characteristics of sediment movement. SD-PTM has two basic elements, the mean drift term and the turbulence term. One of the particle characteristics, the mean drift term, is that particles follow the flow direction; another one is called the turbulence term that describes random behaviors caused by turbulence diffusion. This movement is known as Brownian motion. In general, the diffusion movement is modeled by the Wiener process. The aim of this study is to simulate sediment particle trajectories under the normal flow condition by the SD-PTMs, one-particle PTM and two-particle PTM. The difference between the single particle model and the paired particle model is that the paired particle model accounts for large eddy turbulence. In other words, the paired particles may have similar random movement if the locations of particles are in the immediate vicinity of each other. Besides, to observe assemblage of particles’ motion in the macroscopic manner, the sediment concentrations can be estimated. Moreover, sediment concentrations involve the property of uncertainty on account of sediment particles’ stochastic trajectories. Therefore, to demonstrate such uncertainty of sediment particles, the ensemble means and ensemble standard deviations of sediment trajectory as well as concentrations are presented in the study respectively. The proposed models are validated against experimental data by ensemble mean velocity and sediment concentrations. Moreover, this study also discussed the random movement of sediment particles under various flow conditions, laminar cavity flow and fully developed turbulent open channel flow. Results show that the random movement of sediment particles is significant in turbulent flow. Thus, it is appropriate to consider the fluctuation of sediment concentrations under high Reynolds number flow conditions. Besides, the Markovian property of the PTMs is validated in our study. However, the variance of particle displacement and time are not a linear proportion as the result. Resuspension of sediment particles may cause particle movement to be anomalous diffusion.