Advection and diffusion characteristics for uniform bed load particles from a semi-mechanistic model accounting for forces exerted on individual particles

An episodic Langevin equation, which could account for forces exerted on individual particles and simulate stochastic and episodic motion characteristics of particles, is developed in order to reveal the control factor of normal or anomalous advection and diffusion characteristics for uniform particles. Using a model embedded with different distributed resting times, we study advection and diffusion characteristics by analyzing the statistical data of a large number of simulated particle trajectories. The results reveal that for uniform particles, because of the constraint of thin-tailed velocities of active particles, super-diffusion does not necessarily occur, even if their step lengths are heavy tailed. Diffusion characteristics are determined by the tail of resting times; for heavy-tailed resting times, sub-, normal, and super diffusion could all occur. The proposed semi-mechanistic model is further compared with other stochastic models, and the step time is ignored as it could result in right advection but wrong diffusion characteristics, which could be generalized for studying stochastic variables, i. e., the higher the moment of the studied stochastic variables, the more complex the model.