# A stochastic multivariate framework for modeling movement of discrete sediment particles in open channel flows

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## Abstract

A stochastic multivariate framework was utilized to characterize the random properties associated with discrete sediment particle movement in an open channel flow. Difficulties in modeling sediment transport with a high degree of accuracy are mainly attributed to the complexity associated with flow randomness and interactions between the flow and sediment particles. In particular, flow turbulence is the major factor in assessing sediment particle movement. To analyze the random properties of particle movement, we adopted a stochastic particle-tracking approach (i.e., the Lagrangian approach) that is effective for tracking discrete, randomly moving particles as a function of time. A set of stochastic differential equations that reflects the effect of forces exerted on fluid and sediment particles on average and the randomly fluctuating motion by turbulence was formulated. The fluctuation motion is described by the Wiener process. The proposed stochastic multivariate model is expected to present a more comprehensive evaluation of fluid velocity, particle velocity and position under the influence of flow turbulence, as opposed to the stochastic univariate model that focuses primarily on the sediment particle position. The outcome of the stochastic multivariate particle tracking model can provide a probabilistic description for fluid and discrete suspended sediment particles through ensemble statistics of kinematic variables in a random system (e.g., the ensemble mean and ensemble variance of particle trajectories and velocity). The proposed multivariate model was validated by comparing the results with available experimental flume data. The applicability of the proposed stochastic multivariate particle tracking model was also evaluated.

## Keywords

Stochastic multivariate particle tracking models Sediment transport Particle trajectory Particle velocity Wiener process Markovian assumption## Notes

### Acknowledgements

The authors gratefully acknowledge the financial support from National Science Foundation under grant contract number EAR-0748787. Funding was provided by Ministry of Science and Technology, Taiwan (Grant No. 104-2628-E-002-011-MY3).

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