This study introduces the fractional stochastic diffusion particle tracking model (FSD-PTM), a novel Lagrangian particle tracking model (PTM) designed to simulate stochastic suspended sediment transport by incorporating fractional Brownian motion (FBM). This FBM-based approach introduces memory into particle movements, particularly when particles are influenced by coherent turbulent structures near boundaries, such as ejection and sweep events. These coherent structures exhibit consistent motion over time, leading to correlated increments in particle movements. In scenarios unaffected by coherent structures, the FBM reverts to the Wiener process, preserving the independent increments. The FSD-PTM is applied to a steady, incompressible, fully developed two-dimensional open channel flow, and Monte Carlo simulations yield ensemble statistics results, including mean, variance, skewness of particle positions, particle velocity, and concentrations. These simulation results validate the FSD-PTM against experimental data, demonstrating its superior performance when considering correlated increments. Without such consideration, concentration profiles generated by previous PTMs fail to reach long-term equilibrium. A key innovation of the FSD-PTM is its integration of correlated motion directly within the governing stochastic differential equation (SDE), eliminating the need for additional terms. This model's flexibility also allows for the incorporation of various particle dynamic models, enhancing its utility for sediment transport analysis. The FSD-PTM represents a substantial advancement in modeling stochastic suspended sediment transport, particularly when particles' movements exhibit correlations due to surrounding turbulence.
