Abstract:
A stochastic diffusion jump model in response to extreme flows is proposed herein to describe the movement of sediment particles in surface waters. The proposed particle tracking model classifies the movement of particles into three categories—a drift motion, a Brownian type motion due to turbulence in the flow field for example, and jumps due to the occurrence of extreme events. In the proposed model, a random term mainly caused by the fluid eddy motions is modeled as a Wiener process. In addition, the occurrence of the extreme flow event is modeled as a Poisson process. The magnitude of particle movement in response to extreme flow events, characterized as the Poisson jump, depends on the characteristics of the extreme events and the properties of sediment particles. The frequency of occurrence of the extreme events in the proposed model can be explicitly accounted for when evaluating the movement of sediment particles. As such, the proposed particle tracking model, when coupled with an appropriate hydrodynamic model, can assist in developing a forecast model to predict the movement of particles in the presence of extreme flows. The mean and variance of particle trajectory can be obtained from the proposed stochastic model via simulations.
