A multilayer shallow water approach for the approximate description of polydisperse sedimentation in a viscous fluid is presented. The fluid is assumed to carry finely dispersed solid particles that belong to a finite number of species that differ in density and size. These species segregate and form areas of different composition. In addition, the settling of particles influences the motion of the ambient fluid. A distinct feature of the new approach is the particular definition of the average velocity of the mixture. It takes into account the densities of the solid particles and the fluid and allows us to recover the global mass conservation and linear momentum balance laws of the mixture. This definition motivates a modification of the Masliyah-Lockett-Bassoon (MLB) settling velocities of each species. The multilayer shallow water model allows one to determine the spatial distribution of the solid particles, the velocity field, and the evolution of the free surface of the mixture. The final model can be written as a multilayer model with variable density where the unknowns are the average velocities and concentrations in each layer, the transfer terms across each interface, and the total mass. An explicit formula of the transfer terms leads to a reduced form of the system. Finally, an explicit bound of the minimum and maximum eigenvalues of the transport matrix of the system is utilized to design a Harten-Lax-van Leer (HLL)-type path-conservative numerical method. Numerical simulations illustrate the coupled polydisperse sedimentation and flow fields in various scenarios, including sedimentation in a type of basin that is used in practice in mining industry and in a basin whose bottom topography gives rise to recirculations of the fluid and high solids concentrations.Mathematics Subject Classification. 65N06, 76T20.

<p>The phenomena associated with global climate variability may lead to more intense extreme events, thus causing an increase in floods and prolonged droughts. In view of this situation, the Chilean Directorate of Hydraulic Works (DOH) has the task of selecting the works to be executed with the highest priority with the annual budget, to control and mitigate the effects of floods. Hence the need for a tool that includes the evaluation of fluvial morphodynamics, which allows the management of hydraulic works compatible with the processes of response and adjustment of the channels. The objective of this study is to characterize the fluvial styles of the Duqueco River based on its geomorphology, to understand the character and behavior of the fluvial corridor in a semi-automatic way applying GIS techniques and Python geoprocessing. The first stage of the River Styles framework is applied through the South Rivers Toolbox program, which characterizes and classifies fluvial styles based on hydromorphological attributes measured at segment scale, implementing a semi-automatic approach that reduces expert judgment. Previously, the disaggregation and aggregation framework is used, which determines channel attributes at a local scale, and then aggregates them with a statistical test in larger reaches. The whole process is performed in a semi-automated way with tools from the South Rivers Toolbox set within the QGIS software. As results, 36 main fluvial styles and 47 complementary styles are classified and characterized, and the river channel is analyzed in 3 zones. The upper zone is characterized by being mostly confined, mono-channel, with a bed of boulders and blocks, being highly intervened by power generation works; the middle zone is still mostly confined and mono-channel, with a change in the type of bed towards boulders. Finally, the lower zone is more diverse in styles, mostly unconfined, with a high presence of geomorphic units that give way to multichannel and transition zones.</p>

We used the lumped rainfall–runoff hydrologic models Génie Rural à 4, 5, 6 paramètres Journalier (GR4J, GR5J and GR6J) to evaluate the most robust model for simulating discharge on four forested small catchments (<40 ha) in south-central Chile. Different evapotranspiration methods were evaluated: Oudin, Hargreaves–Samani and Priestley–Taylor. Oudin’s model allows the achievement of the highest efficiencies in the flow simulation. The more sensitive parameters for each model were identified through a Generalized Probability Uncertainty Estimation (GLUE) model. Our results demonstrate that the three hydrological models were capable of efficiently simulating flow in the four study catchments. However, the GR6J model obtained the most satisfactory results in terms of simulated to measured streamflow closeness. In general, the three models tended to underestimate peak flow, as well as underestimate and overestimate flow events in most of the in situ observations, according to the probability of non-exceedance. We also evaluated the models’ performance in a simulation of summer discharge due to the importance of downstream water supply in the months of greatest scarcity. Again, we found that GR6J obtained the most efficient simulations.

A three-dimensional multilayer shallow water approach to study polydisperse sedimentation and sediment transport in a viscous fluid is presented. The fluid is assumed be loaded with finely dispersed solid particles that belong to a finite number of species that differ in density and size. The model formulation allows one to recover the global mass and linear momentum balance laws of the mixture. The model incorporates compressibility of the sediment and viscosity of the mixture through a viscous stress tensor. As a consequence of a dimensional analysis applied to the global mass conservation and linear momentum balance equations, the horizontal components of the compression term and the horizontal terms of the viscous stress tensor may be neglected. This results in a final model that is vertically consistent with the classical one-dimensional vertical model. Numerical simulations illustrate the coupled solids volume fraction and flow fields in various scenarios and the effect of the compressibility and viscosity terms. Various bottom topographies give rise to recirculation of the fluid and high solids volume fractions on the bottom.