A Lagrangian Stochastic Approach with Embedded Ornstein-Uhlenbeck Processes for Suspended Sediment Transport

Abstract

This study aims to develop a Lagrangian stochastic (LS) model for simulating suspended sediment transport in open channels. The model incorporates three physical levels, namely, position, velocity, and acceleration, to describe sediment movement precisely. Without using any approximations, this approach is intrinsically stochastic and differentiable. It can reproduce different scale motions in turbulent flow for any Reynolds number. We will introduce the Lagrangian turbulent velocity theory into the random term of the sediment transport force balance equation. The random term, describing random particle movements, is usually represented by the Weiner process (i.e., Brownian motion), which is nowhere differentiable. Building upon prior research on stochastic turbulence models, we adopt an 'embedded' Ornstein-Uhlenbeck process to replace the Weiner process in this study. This embedded structure is defined through a set of coupled stochastic ordinary differential equations (ODEs), resulting in a multi-layered equation system. These different levels are interconnected through differentials and integrals. We introduce specific time scales and parameters tailored to different flow conditions to enhance their applicability to sediment transport scenarios. After we build these LS models, we have to validate with data or even calibrate the parameters in the model. We usually use two types of data: DNS data and experimental data. We will extract the details of isotropic turbulent flow in DNS data (such as the Kolmogorov time scale and Lagrangian velocity). The mean flow velocity profile will be determined from the experimental data. One-way coupling might be a reasonable assumption for the suspended sediment transport. However, when the gravitational force acts on the particles, the inter-particle interactions dominate the bed region due to the high particle concentration. A more appropriate resuspension mechanism must be identified so the particle concentrations can be more accurately quantified.