Three-Layer Ornstein–Uhlenbeck Model for Turbulent Flow Simulation

This study develops a three-layer embedded Lagrangian stochastic (LS) model for simulating suspended sediment transport in open-channel flows. The model describes particle motion at three levels: position, velocity, and acceleration, using multiple Ornstein–Uhlenbeck (OU) processes within a coupled stochastic system. This construction preserves intrinsic stochasticity while allowing the velocity process to be differentiated in time to obtain particle acceleration, enabling a consistent description of particle motion at small time scales.

In conventional LS models, random forcing is typically represented by a Wiener process. Since this process is nowhere differentiable, it limits the interpretation of higher-order kinematic quantities. In this study, an embedded Ornstein–Uhlenbeck formulation is employed, where the random forcing is described by a finite-order system of coupled stochastic ordinary differential equations. Compared with conventional two-layer LS models, the three-layer formulation produces smoother Lagrangian velocity trajectories by improving the differentiability of the velocity process. This formulation reduces abrupt fluctuations in the simulated velocity signal and allows acceleration to remain finite and well-behaved.

As a result, the model provides a clearer basis for describing short-time-scale particle motion and for exploring rapid turbulent effects near the bed. Model parameters are determined based on laboratory experimental data and commonly used turbulence scaling relations reported in the literature.

Overall, the proposed framework provides a stochastic description of particle motion that allows velocity and acceleration to be consistently represented at small time scales and offers a basis for further investigation of near-bed particle behavior and suspended sediment transport processes.