The movement of translatory waves over an erodible stream has a critical influence on the time of rise of the hydrograph which, in turn, affects the stability of the stream channel. In the present study, the movement of these flood waves is described by the one-dimensional equations of continuity and motion which are obtained by the space integration of the three-dimensional equation of continuity and Reynolds equations. The flow of suspended sediment is described by a one-dimensional dispersion equation which is derived from a three-dimensional equation of conservation of solid mass in the flow. With some modifications the one-dimensional dispersion equation is used to describe the scouring of the stream bed. Then the suspended sediment model is connected to the bed scouring model by a stochastic model which describes the bed load and the sediment transfer between the suspended sediment state and the immobile bed state. The stochastic model consists of a set of nine Kolmogorov differential equations for the probabilities of sediment transfer between different states in which a sediment particle may be. To obtain a high-accuracy approximation in the solution of the one-dimensional equations of continuity and motion, the one-step Lax-Wendroff numerical scheme is adopted. The Kolmogrov differential equations are solved directly by means of an analog computer. An analytical investigation of the stability of the approximation scheme is performed. The simulation of the model is done on a hybrid computer by incorporating into the entire model various model components and testing the effects of each component on the whole model and on the other components to see its behavior.

L’érosion éolienne des matières granulaires (minerais, charbons,. . . ) est un des facteurs influençant grandement la qualité de l’air dans l’environnement proche de nombreux sites industriels. L’objectif principal de ce travail est l’amélioration des méthodologies de quantification des émissions des sources diffuses, notamment à partir d’une meilleure prise en compte de l’exposition éolienne des sources que sont les tas de stockage et des répartitions granulométriques des matières présentes sur les sites de stockage. Les observations sur sites industriels montrent que les régions proches des tas de stockage de matières granulaires sont chargées de particules de granulométries plutôt fines. Celles-ci sont susceptibles d’être remises en suspension par les structures tourbillonnaires générées par le vent incident. Ainsi, ces zones d’envol potentiel ont fait l’objet d’analyses afin de quantifier leur contribution aux émissions globales. Une technique de visualisation d’écoulement pariétal, associée à des simulations numériques tridimensionnelles, ont été mises en oeuvre pour mieux comprendre ces structures de l’écoulement. Les matières granulaires sont un mélange de particules érodibles et non-érodibles. Le caractère érodible étant lié aux propriétés des particules (principalement granulométrie et masse volumique), ainsi qu’à la vitesse du vent incident. Dans ce cadre, deux types d’études ont été menées: des essais expérimentaux d’envol de particules dans une soufflerie et des simulations numériques tridimensionnelles avec un logiciel open-source de mécanique des fluides (Code_Saturne). Une technique originale a ainsi été développée pour quantifier, par une pesée en continue, l’influence des particules non-érodibles sur le flux massique envolé. En parallèle, le comportement des particules sur la surface est analysé à l’aide de clichés photographiques. L’analyse de l’effet des particules non-érodibles au niveau local est réalisée grâce à des simulations numériques pour des configurations polydispersées. Les résultats présentés dans ce mémoire constituent de premiers éléments pouvant possiblement contribuer à l’amélioration des modèles actuels de quantification des émissions de particules par une meilleure intégration et pris en compte de la présence de particules non-érodibles pour les matières présentant de larges spectres granulométriques. / Wind erosion of granular materials (ores, coal, ...) is one of the factors that greatly influence the quality of the air in the immediate vicinity of many industrial sites. The main objective of this work is the improvement of methodologies for quantifying emissions from diffuse sources. It may be carried out by a better consideration of wind exposure on the sources (storage piles) and larger size distributions of granular materials present at the storage sites. Observations show that areas near storage piles of granular materials on industrial sites are loaded with silt particles. These particles may be re-emitted by vortex structures. Thus, these areas of potential particles take-off were analyzed to quantify their contribution to global emissions. A wall flow visualization technique associated with three-dimensional numerical simulations have been implemented. Granular material is a mixture of erodible and non-erodible particle. The erodible character may be associated to particle properties (mainly size and density), as well as the ambient wind speed. In this context, two types of studies were conducted: experimental tests of particles take-off in a wind-tunnel and numerical simulations with a three-dimensional open-source fluid dynamics code (Code_Saturne). An original technique has been developed to quantify, by a continuous weighing, the influence of non-erodible particles of the mass flow. In parallel, the behaviour of particles on the surface is analyzed using photographs. The analysis of the effect of nonerodible particles at local level is achieved through numerical simulations for poly-dispersed configurations. The results presented in this thesis are the first elements that can potentially contribute to the improvement of current models of quantification of particulate emissions through a better integration of the presence of non-erodible particles for materials with large particle size spectra.

Geophysical research has long been interdisciplinary, with many phenomena on the Earth's surface involving multiple, linked processes that are best understood using a combination of techniques. This is particularly true in the case of grain flows on sand dunes, in which the sedimentary stratification with which geologists are concerned arises from the granular processes investigated by physicists and engineers, and the water permeation that interests hydrologists and soil scientists determines the seismic velocities of concern to exploration geophysicists. In this dissertation, I describe four projects conducted for the degree of Doctor of Philosophy, using a combination of laboratory experimentation, fieldwork, numerical simulation, and mathematical modelling to link avalanching on dunes to its effects on stratification, on the permeation of water, and on seismic surveys. Firstly, I describe experiments on erodible, unbounded, grain piles in a channel, slowly supplied with additional grains, and I demonstrate that the behaviour of the consequent, discrete avalanches alternates between two regimes, typified by their size statistics. Reconciling the `self-organised criticality' that several authors have predicted for such a system with the hysteretic behaviour that others have observed, the system exhibits quasi-periodic, system-spanning avalanches in one regime, while in the other avalanches pass at irregular intervals and have a power-law size distribution. Secondly, I link this power-law size distribution to the strata emplaced by avalanches on bounded grain piles. A low inflow rate of grains into an experimental channel develops a pile, composed of strata in which blue-dyed, coarser grains overlie finer grains. Associating stopped avalanche fronts with the `trapped kinks' described by previous authors, I show that, in sufficiently large grain piles, mean stratum width increases linearly with distance downslope. This implies the possibility of interpreting paleodune height from the strata of aeolian sandstones, and makes predictions for the structure of avalanche-associated strata within active dunes. Thirdly, I discuss investigations of these strata within active, Qatari barchan dunes, using dye-infiltration to image strata in the field and extracting samples across individual strata with sub-centimetre resolution. Downslope increases in mean stratum width are evident, while measurements of particle size distributions demonstrate preferential permeation of water along substrata composed of finer particles, explaining the strata-associated, localised regions of high water content discovered by other work on the same dunes. Finally, I consider the effect of these within-dune variations in water content on seismic surveys for oil and gas. Having used high performance computing to simulate elastic wave propagation in the vicinity of an isolated, barchan sand dune, I demonstrate that such a dune acts as a resonator, absorbing energy from Rayleigh waves and reemitting it over an extensive period of time. I derive and validate a mathematical framework that uses bulk properties of the dune to predict quantitative properties of the emitted waves, and I demonstrate the importance of internal variations in seismic velocity, resulting from variations in water content.

Bien que répandus dans l'environnement et dans l'industrie, les écoulements granulaires possèdent des caractéristiques particulières qui sont différentes de celles des écoulements de liquides ordinaires comme l'eau (fluides newtoniens). L'une de ces caractéristiques est de présenter un seuil d'écoulement, il est donc fréquent qu'une des frontières de l'écoulement soit constituée de grains au repos (frontière érodable). L'échange entre les deux états solide et liquide d'un écoulement granulaire est à l'origine du phénomène d'érosion et de déposition et constitue le cœur de cette thèse. Nous y effectuons à la fois des études expérimentales et des études théoriques en nous basant sur les modèles phénoménologiques concernant le taux d'échange proposés par Bouchaud, Cates, Ravi Prakash et Edwards et modifiés par Boutreux et de Gennes. A l'aide d'un dispositif expérimental permettant de lâcher sans vitesse initiale une colonne de grains sur une pente granulaire, nous avons quantifié l'importance relative des phénomènes d'érosion et de déposition notamment en déterminant l'angle neutre qui définit la pente critique pour laquelle ces deux processus s'équilibrent. Dans un deuxième temps nous avons appliqué le modèle proposé par Boutreux et de Gennes au cas de l'étalement d'une « marche » granulaire (marche du Sinaï). / Granular flows, which are common in nature and industry, have particular characteristics that are different from the ordinary flow of liquid (eg. water, oil, etc.) and are not yet well understood in the literature. This case underlines the lack of knowledge on the exchange rate between solid and liquid states of granular flows which is the origin of the erosion - deposition phenomenon and constitutes the core of this thesis. To address the issue of the exchange rate solid - liquid, this work is based mainly in two subjects. The first subject is to study the processes of erosion and deposition of a flow generated by the grains stocked in a reservoir. By releasing naturally with zero-velocity the grains to generate the granular flow, we quantified the relation between the erosion and deposition for determining the neutral angle which defines the slope where these two processes balance. The second subject is to analyze the fall of grains in Sinai step problem by studying the spread of the march. For both works, we conduct not only the experimental but also theoretical studies based on the phenomenological models of the exchange rate proposed by BCRE (Bouchaud, Cates, Ravi Prakash and Edwards) and BDG (Boutreux and de Gennes) with some modifications.