An Eulerian Model For The Transport And Diffusion Of Floating Particles Within Regions Of Emergent Vegetation

Emergent vegetation has a significant impact on floating particle transport and diffusion in open channel flow. The random walk model of a Lagrangian approach has proven more than suitable to describe the rather unpredictable moving trajectory of particles within emergent vegetation. However, compared to the large computational costs of the Lagrangian model, which also requires more input data, a simplified model based on the Eulerian approach can be by far preferable and cost-effective for rapid first-order prediction of particle transport and diffusion within vegetated areas. In this study, we developed a one-dimensional advection-diffusion model to simulate particle transport processes within vegetated areas, and to explore the impacts of vegetation on particles transport, diffusion and removal. The model parameters, including the probability of a particle colliding with a stem, and the probability of it being temporarily trapped or permanently captured by a stem, as well as the mean retention time that govern the random walk model, are introduced to estimate the mean velocity, diffusion coefficient, removal rate of particles of Eulerian model, distinguishing from the standard advection and diffusion parameters. The validity of the parameters is verified through the stochastic model with a large number of realizations. The comparison between the dispersal kernel as well as the spatio-temporal distribution of floating particles predicted by Eulerian model and stochastic model is quite satisfactory and suggests that the Eulerian model we proposed is properly described.