Il trasporto, la diffusione e la ritenzione di particelle galleggianti all'interno della vegetazione emergente

Emergent vegetation has a significant impact on dispersion of floating particles in open channel flow. In this thesis, we study the transport, diffusion and retention of floating particles by capillarity within emergent vegetation through an analytical model, laboratory experiments, and a numerical analysis. We first develop a one-dimensional advection-diffusion model to analytically simulate particle transport processes within vegetated areas, and to explore the impacts of vegetation on particle transport, diffusion and removal. 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 far preferable and cost-effective for rapid first-order prediction of particle transport and diffusion within vegetated areas. Three key parameters of the standard Eulerian model of advection and diffusion with a first order decay process, namely, the mean transport velocity of floating particles, the diffusion coefficient, and removal rate of particles, are estimated from the parameters of a Lagrangian model, previously proposed for the same purpose. The validity of the parameters of the Eulerian scheme is then verified through performing a large number of realizations with the Lagrangian model. 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 proposed Eulerian approach is properly described. The model results indicate the large impact of temporary trapping events on the advection and diffusion of floating particles, which dramatically reduce the transport velocity compared to the bulk flow velocity, and largely increase the diffusion coefficient. As such, we then conduct laboratory experiments to provide a better understanding of the propagation of floating seeds and propagules through capillarity in areas of emergent vegetation, mainly focusing on the temporary trapping events. The experimental data are also used to verify our proposed Eulerian model. In the experiments, the vegetation is simulated as an array of cylinders, randomly arranged, and seeds are simulated with small wooden spheres having almost the same diameter of the cylinders. The temporary trapping process is found to strictly depend on the stem density and the ratio between the flow velocity and the escape velocity; the latter, representing the scale-velocity of the problem, and at least as a first approximation, can account for the main particle and stem properties needed to estimate particle propagation. Finally, we perform a numerical analysis to gain further insight into how the mean retention time of temporary trapping process varies with the stem density and flow velocity. We speculate that the oscillation frequency of flow velocity component is strictly related to the mean retention time. We decompose the signal of time-depending flow velocity near a stem into a series of frequencies by means of the Fast Fourier transform analysis. We observe two main oscillation frequencies of the velocity. The first is the frequency of vortex shedding of the cylinder, whereas the second is the frequency of the velocity component produced by the interference of the neighbour cylinders. The numerical model results indicate that both frequencies depend on the bulk velocity and stem density; and the mean retention time of temporary trapping process is inversely proportional to the frequency of the velocity component produced by the interference of the neighbour cylinders.