Materials can flow down a slope in a wide range of geophysical and industrial contexts, including lava flows on volcanoes and thin films on coated surfaces. The aim of my research is to provide quantitative insight into these forms of motion and their dependence on effects of the topography, the volume and the rheology of the flowing structure. Numerous different problems are investigated through mathematical models, which are developed analytically and confirmed by laboratory experiments. The initial advance of long lava flows is studied by considering the flow of viscous fluid released on sloping channels. A scaling analysis, in agreement with analog experiments and field data, offers a practical tool for predicting the advance of lava flows and conducting hazard analysis. A simple and powerful theory predicts the structure of flows resulting from any time-dependent release of fluid down a slope. Results obtained by the method of characteristics reveal how the speed of the advancing front depends importantly on the rate of fluid supplied at an earlier time. Viscous flows on surfaces with different shapes are described by similarity solutions to address problems motivated by engineering as well as geophysical applications. Pouring viscous fluid out of a container can be a frustratingly slow process depending on the shape and the degree of tipping of the container. The discharge rate of the fluid is analysed in simple cases, shedding light on how containers can be emptied most quickly in cosmetic and food industries. In a separate study motivated by coating industries, thin films are shown to evolve with uniform thickness as they drain near the top of a horizontal cylinder or sphere. The leading edge eventually splits into rivulets as predicted theoretically and confirmed by experiments. Debris flows can develop levees and trigger avalanches which are studied by considering dense granular flows down a rough inclined plane. Granular materials released down a slope can produce a flowing structure confined by levees or trigger avalanches at regular intervals, depending on the steady rate of supply. The experimental results are discussed using theoretical ideas of shallow granular flows. Finally, materials flowing in long and slender ducts are investigated theoretically to better understand the digestive and urinary systems in biology. The materials are pumped in an elastic tube by translating waves of muscular contraction and relaxation. The deformation of the tube is predicted by solving a free-boundary problem, a similar mathematical exercise to predicting the moving boundaries of materials spreading on slopes.

Turbulent bedload transport represents the main contribution to the riverbed morphological evolution, and associates the non-trivial collective granular behavior with a turbulent fluid flow. Therefore, its description is both a scientific challenge and a societal issue. The present numerical approach focuses on the granular phase characterization, and considers idealized steady uniform bedload transport, with monodisperse spherical beads and a unidirectional fluid flow. This simplified configuration allows to study the underlying physical mechanisms.A minimal coupled numerical model is proposed, associating a three dimensional discrete element method with a one-dimensional volume-averaged fluid momentum balance resolution. The model is compared with classical experimental results of dimensionless sediment transport rate as a function of the Shields number. The comparison is extended to granular depth profiles of solid volume fraction, solid velocity and sediment transport rate density in quasi-2D bedload transport configurations. Parameter sensitivity analysis evidenced the importance of the fluid-particle phase coupling, and showed a robust agreement of the model with the experiments. The validated model is further used to analyze the granular depth structure in bedload transport. Varying the channel inclination angle and the specific density, it is shown that the classical Shields number and dimensionless sediment transport rate formulations do not take appropriately into account the effects of these two parameters. Analyzing the solid depth profiles and the continuous two-phase flow equations, the neglected fluid flow inside the granular bed is identified as the missing contribution. Its importance is enhanced near the transition to debris flow. A rescaling of the Shields number is proposed and is shown to make all the data collapse onto a master curve when considering the dimensionless sediment transport rate as a function of the modified Shields number. Lastly, the bedload transport granular rheology is characterized by computing locally the stress tensor as a function of the depth. The lowermost part is shown to follow a creeping regime and exhibits signature of non-local effects. The dense granular flow on the top of it, is well described by the mu(I) rheology and is observed to persist up to unexpectedly high inertial numbers. It is characterized by the co-existence of frictional and collisional contributions. The transition from dense to dilute granular flow is controlled by the Shields number, the slope and the specific density. Saltation is observed in the uppermost granular layer. These findings improve the understanding of bedload transport granular mechanisms and challenge the existing granular rheologies. / Turbulent bedload transport represents the main contribution to the riverbed morphological evolution, and associates the non-trivial collective granular behavior with a turbulent fluid flow. Therefore, its description is both a scientific challenge and a societal issue. The present numerical approach focuses on the granular phase characterization, and considers idealized steady uniform bedload transport, with monodisperse spherical beads and a unidirectional fluid flow. This simplified configuration allows to study the underlying physical mechanisms.A minimal coupled numerical model is proposed, associating a three dimensional discrete element method with a one-dimensional volume-averaged fluid momentum balance resolution. The model is compared with classical experimental results of dimensionless sediment transport rate as a function of the Shields number. The comparison is extended to granular depth profiles of solid volume fraction, solid velocity and sediment transport rate density in quasi-2D bedload transport configurations. Parameter sensitivity analysis evidenced the importance of the fluid-particle phase coupling, and showed a robust agreement of the model with the experiments. The validated model is further used to analyze the granular depth structure in bedload transport. Varying the channel inclination angle and the specific density, it is shown that the classical Shields number and dimensionless sediment transport rate formulations do not take appropriately into account the effects of these two parameters. Analyzing the solid depth profiles and the continuous two-phase flow equations, the neglected fluid flow inside the granular bed is identified as the missing contribution. Its importance is enhanced near the transition to debris flow. A rescaling of the Shields number is proposed and is shown to make all the data collapse onto a master curve when considering the dimensionless sediment transport rate as a function of the modified Shields number. Lastly, the bedload transport granular rheology is characterized by computing locally the stress tensor as a function of the depth. The lowermost part is shown to follow a creeping regime and exhibits signature of non-local effects. The dense granular flow on the top of it, is well described by the mu(I) rheology and is observed to persist up to unexpectedly high inertial numbers. It is characterized by the co-existence of frictional and collisional contributions. The transition from dense to dilute granular flow is controlled by the Shields number, the slope and the specific density. Saltation is observed in the uppermost granular layer. These findings improve the understanding of bedload transport granular mechanisms and challenge the existing granular rheologies.

Le transport sédimentaire contrôle l'évolution morphologique des rivières, l'érosion du littoral et l'équilibre des écosystèmes. Il constitue également un facteur de risque pour les populations et les infrastructures. Le sheet-flow, ou charriage intense, est un régime de transport sédimentaire qui s'établi lors de crues dans les fleuves et les rivières ou lors du déferlement des vagues littorales sur les plages sableuses. Le fort taux de transport associé à ce régime le rend très morphogène et une bonne compréhension des processus physiques impliqués est fondamentale pour prédire la morphodynamique. Cependant, les interactions granulaires et les fluctuations turbulentes, qui sont les principaux mécanismes à l'œuvre dans ce phénomène, constituent des verrous scientifiques pour la modélisation du régime de sheet-flow. Cette déficience s'explique essentiellement par le manque de données expérimentales haute résolution. Partant de ce constat, l'objectif de la thèse est de proposer un modèle diphasique et un dispositif expérimental haute résolution permettant de mieux caractériser les mécanismes impliqués. indent Dans un premier temps, le modèle diphasique est présenté et les résultats obtenus sont confrontés aux données de la littérature. L'analyse des résultats montre que la rhéologie des écoulements granulaires denses ($mu(I)/phi(I)$) et l'approche de longueur de mélange utilisées sont des fermetures appropriées pour reproduire les principales caractéristiques du régime de sheet-flow pour une large gamme d'écoulements et de propriétés sédimentaires. La deuxième partie de la thèse est consacrée à la mise en place d'un dispositif expérimental capable de fournir des mesures instantanées de vitesse et de concentration en régime de sheet-flow uniforme. Dans la troisième partie les grandeurs moyennes sont analysées pour décrire la structure verticale de l'écoulement. Les résultats obtenus montrent qu'une formulation en longueur de mélange et un profil de Rouse permettent de décrire la contrainte turbulente et le profil de concentration dans la suspension à condition de fortement modifier le paramètre de von Karman ($kappa approx 0.2$) et le nombre de Schmidt ($sigma_s=0.44$). La rhéologie frictionnelle ($mu(I)/phi(I)$) et la théorie cinétique des écoulements granulaires prédisent qualitativement le comportement observé, mais échoue à reproduire quantitativement les mesures. Le lien étroit existant entre les structures cohérentes turbulentes et la dynamique du lit sédimentaire illustre l'importance des fluctuations et de l'intermittence de l'écoulement. Ce couplage pourrait expliquer l'écart observé entre le comportement prédit par les modèles de contraintes inter-granulaires et les mesures expérimentales. Finalement, la comparaison des analyses statistiques en régime de sheet-flow et en écoulement sur fond fixe rugueux permet de montrer que l'énergie cinétique turbulente est peu affectée par la présence des sédiments mais que le niveau de corrélation entre fluctuations horizontales et verticales est sensiblement diminué, impliquant une diminution de la longueur de mélange et de la viscosité turbulente. Une augmentation significative de la rugosité équivalente induite par le lit mobile est aussi observée. / Sediment transport controls river morphological evolution, coastal erosion and ecosystem equilibrium. It represents a risk factor for populations and infrastructures. The sheet-flow, or intense bed-load, is a regime of sediment transport occurring during river floods or in the coastal wave breaking region above sandy beaches. The large amount of sediment transported in this regime is the main source for morphological evolution in our natural systemswater bodies. A good understanding of the underlying physical processes is a pre-requisite for accurate morphodynamic predictions. However, particle-particle interactions and turbulent flow interactions, which are the main driving mechanisms in this problem, constitute the scientific bottlenecks for sheet-flow modelling. This deficiency is mainly caused by the lack of high resolution experimental data. Based on this observation, the objective of the present thesis is to propose a novel two-phase model and to generate a new set of high resolution experiment data to improve process based sheet-flow modelling. indent First, the two-phase flow model is presented and the obtained results are compared with data from the literature. The result analysis has shown that the dense granular flow rheology ($mu(I)/phi(I)$) combined with a turbulent mixing length concept predicts the main sheet flow characteristics over a wide range of flow and sediment properties. Secondly, the experimental set up providing high-rate measurements of velocity and concentration under a uniform sheet-flow regime is presented. Third, the measured mean flow quantities are analysed to describe the vertical structure of the flow. The obtained results show that a mixing length formulation and a Rouse profile allow to describe the turbulent stress and the concentration profiles in the turbulent suspension layer, provided that the von Karman parameter and the Schmidt number are modified ($kappa approx 0.2$ and $sigma_s=0.44$). The frictional rheology ($mu(I)/phi(I)$) and the kinetic theory of granular flows predict qualitatively the observed behaviour but fail to reproduce measurements quantitatively. The observed link between the turbulent coherent structures and the bed dynamic illustrates the importance of flow fluctuations and intermittency. This coupling could be responsible for the discrepancy found between the predictions from the intergranular stresses models and the measurements. Finally, the comparison between the statistical analysis performed for a sheet-flow regime and for a clear water flow over a rough fixed bed demonstrates that the turbulent kinetic energy is weakly affected by the presence of sediments whereas the turbulent correlation level between horizontal and vertical fluctuations is significantly reduced, leading to a decrease of both the mixing length and the turbulent eddy viscosity. An increase of the equivalent roughness height induced by the moving bed is also observed.