| Abstract: | Modeling of suspended sediment particle movement in surface water can be achieved by stochastic particle tracking model approaches.In this paper,different mathematical forms of particle tracking models are introduced to describe particle movement under various flow conditions,i.e.,the stochastic diffusion process,stochastic jump process,and stochastic jump diffusion process.While the stochastic diffusion process can be used to represent the stochastic movement of suspended particles in turbulent flows,the stochastic jump and the stochastic jump diffusion processes can be used to describe suspended particle movement in the occurrences of a sequence of extreme flows.An extreme flow herein is defined as a hydrologic flow event or a hydrodynamic flow phenomenon with a low probability of occurrence and a high impact on its ambient flow environment.In this paper,the suspended sediment particle is assumed to immediately follow the extreme flows in the jump process(i.e.the time lag between the flow particle and the sediment particle in extreme flows is considered negligible).In the proposed particle tracking models,a random term mainly caused by fluid eddy motions is modeled as a Wiener process,while the random occurrences of a sequence of extreme flows can be modeled as a Poisson process.The frequency of occurrence of the extreme flows in the proposed particle tracking model can be explicitly accounted for by the Poisson process when evaluating particle movement.The ensemble mean and variance of particle trajectory can be obtained from the proposed stochastic models via simulations.The ensemble mean and variance of particle velocity are verified with available data.Applicability of the proposed stochastic particle tracking models for sediment transport modeling is also discussed. |
