Two-Particle Stochastic Model for Suspended Sediment Transport Using Spatial Relationship with Particles

This study aims to develop a Lagrangian stochastic model for simulating suspended sediment transport in open channel flows. The model focuses on a pair of particles, describing the trajectories of paired particles, which are dependent on the Reynolds number. It uses relative particle velocity as a foundation for tracking sediment motion, with key factors such as separation distance and relative velocity being critical in defining particle interactions and their role in separation processes. This model captures non-Gaussian turbulence features in Eulerian statistics to construct a relative velocity probability density function. A structure-function approach is employed to derive Eulerian velocity moments from velocity increments, ensuring stable dispersion by considering relevant scale properties. The model incorporates the Langevin equation for relative velocity, consisting a drift term defined by conditional acceleration and a Eulerian probability density function, and a random term defined by a scale-dependent diffusion coefficient influenced by viscous effects, exhibiting Brownian motion properties.

The model extends the fluid particle framework to sediment particles through the principles of force balance and accounts for the resuspension mechanism for sediment particles. In sediment transport, the influence of the resuspension mechanism on the two particles must be considered. This mechanism is different from those in fluid particle models and single-particle sediment models. Additionally, the relative velocity model is transformed into an absolute velocity model, and two-particle coefficients are introduced to determine particle motion. The Ornstein-Uhlenbeck (OU) process is employed to simulate velocity fluctuations for individual particles.

Compared to single-particle models, this two-particle stochastic model investigates turbulent sediment transport in terms of relative velocity and separation distance variations. We analyze the variation of the diffusion coefficient across scales by tuning specific parameters. Results are compared with direct numerical simulation (DNS) data across different Reynolds numbers to calibrate the model coefficients effectively. The initial findings provide valuable insights into the influence of turbulence characteristics on sediment behavior, particularly in relation to relative velocity and separation distance variations. This work contributes to a deeper understanding of the complex interactions governing sediment transport in turbulent open channel flows.