Linear sandbanks are located globally in areas where there are strong currents and an abundance of sand. In recent years, these sandbanks have become a strategic interest as a potential source of marine aggregates (sand and gravel) and mineral deposits. They also commonly reach the sea surface and thus pose a threat to navigation. Headland-associated linear sandbanks are a specific type of sandbank, which are located in the lee of coastal topographic features such as headlands and islands. Interaction between tidal currents and topographic features generate complex three-dimensional circulation patterns that significantly influence the distribution of sediments in the vicinity of the feature. Field and numerical model investigations of the three-dimensional flow structure have been undertaken on the Levillain Shoal, a headland-associated linear sandbank present in the lee of Cape Levillain (Shark Bay, Western Australia). The field data indicated the presence of secondary flows near the tip of the Cape and around the bank, which were reproduced in the numerical simulations. Sediment transport paths near the Cape and the bank indicate that the sandbank is part of a sand circulation cell where the sand is circulating around the bank with exchanges between the sandbank and the headland. A morphological model (MTM) has been developed to understand processes responsible for the formation of the headland associated linear sandbanks. With an “idealized” Gaussian shaped headland, the formation of two symmetrical sandbanks on each side of the headland is observed. It is shown that sandbanks are formed in regions where there is a net accumulation of sand over a tidal cycle, due to the acceleration/⁄deceleration effects of the flow in the presence of the headland. Initially, sandbanks develop in a circular shape and grow vertically. As the sandbanks interact with the tidal flow, they evolve into elongated linear deposits (as observed in nature). The sandbank growth is dependent on the tidal regime, secondary flow, sand availability, and sediment grain size

A program for selecting the optimal wave conditions for morphodynamically accelerated simulations of coastal evolution (‘OPTIWAVE’) has been constructed using a novel Genetic Algorithm approach. The optimization routine iteratively reduces the complexity of an incident wave climate by removing the events that contribute least to a target sediment transport pattern, and then ‘evolving’ a new set of weights for the remaining wave conditions such that the target sediment transport pattern (and magnitude) is optimally maintained. The efficacy of OPTIWAVE to satisfactorily reduce the incident wave climate is tested against three coastal modeling paradigms of increasing complexity: (a) A simple 1-D beach profile model (no tides); (b) A 2-D micro-tidal beach; (c) A tidal inlet, where the interaction between waves, tides, and wave-current interaction, adds significant complexity. The simple test case for a beach profile shows that OPTIWAVE is successfully capable of maintaining a target profile-integrated long-shore sediment transport rate. The calculated skill and RMSE of the reduced wave climate is a good indicator of its ability to reproduce the target sediment transport pattern. The optimal number of wave conditions is identified by an ‘inflection point’ at a critical number of wave conditions, where less complex a wave climate results in substantially reduced skill (increased error). The assumption that the ability of OPTIWAVE to reproduce a target sediment transport field is a valid proxy for the potential skill of a morphologically accelerated simulation is assessed for the case of a 2D micro-tidal beach. The skill of the accelerated models, which use a state-of-the-art ‘event-parallel’ method of simulating bed evolution from multiple wave conditions in parallel, is tested against a ‘brute force’ reference simulation that considers the full wave forcing. A strong positive correlation is found between the skill of the reduced wave climate to reproduce a target sediment transport pattern, and the resultant skill of the accelerated morphodynamic model against the ‘brute force’ reference simulation. Finally, the ability to combine reduced wave and tide climates for simulations that must consider both wave and tidal forcing, is assessed against a ‘brute force’ reference simulation of the seasonal evolution Ancao inlet, Algarve, Portugal. The reference simulation is validated against a comprehensive field dataset collected in 1999, and is shown to qualitatively reproduce key features of inlet behavior over a seasonal period. The combination of reduced wave and tidal climates in accelerated ‘event-parallel’ models did not successfully reproduce the reference seasonal morphological evolution of Ancao inlet. Assessing the model Brier Skill Score showed that the model was more successful in reproducing the reference morphology in areas dominated by tidal forcing, but did not have any predictive power in regions where morphological evolution is due to some combination of both wave and tidal processes.

Dans ce travail réalisé au Centre de Morphologie Mathématique and IFPEN, on s'intéresse à la microstructure et aux propriétés physiques d'alumines mésoporeuses. Il s'agit d'un supporte de catalyseur utilisés notamment dans les processus industriels de raffinage du pétrole. Fortement poreux, ce matériau est formé de ''plaquettes'' distribuées de manière désordonnée à l'échelle de la dizaine de nanomètres. Les propriétés de transport de masse du support de catalyseur sont fortement influencées par la morphologie de la microstructure poreuse. Ce travail porte sur la modélisation de la microstructure et des propriétés de transport des alumines mésoporeuses, à l'aide d'outils numériques et théoriques dérivés de l'analyse d'image et de la théorie des ensembles aléatoires. D'une part, on met en place des méthodes de caractérisation et de modélisation des microstructures, qui s'appuient sur, entre autre, des images obtenues par microscopie électronique en transmission (MET) et des courbes de porosimétrie azote. D'autre part, on utilise des méthodes d'homogénéisation numérique à champs complets par transformées de Fourier rapide (FFT).Dans un premier temps, le matériau est caractérisé expérimentalement par porosimétrie azote et résonance magnétique nucléaire à gradient de champ pulsé (RMN-GCP). Les images MET sont obtenus sur des échantillons d'épaisseur variable, filtrées et caractérisés par des fonctions de corrélation, notamment. Le bruit à haute fréquence issu de la membrane de carbone est identifié et pris en compte dans la modélisation de l'imagerie MET. À partir des images MET 2D, un modèle aléatoire à deux échelles est proposé pour représenter la microstructure 3D. Il prend en compte la forme des plaquettes d'alumines, leurs tailles, les effets d'alignement locaux et d'agrégation, qui sont identifiés numériquement. La procédure est validée à l'aide de comparaisons entre modèle et images expérimentales, en terme notamment de fonctions de corrélation et de surface spécifique, mesurées par porosimétrie azote.Dans un deuxième temps, une méthode de simulation des courbes d'isothermes de porosimétrie dans des milieux poreux périodiques ou aléatoires est développée. Basée sur des opérations morphologiques simples, elle étend un travail antérieur sur la porosimétrie au mercure. L'adsorption multicouche à basse pression est simulée à l'aide d'une dilatation tandis que les ménisques de l'interface vapeur-liquide intervenant pendant l'adsorption sont simulés à l'aide de fermetures de la phase solide par des éléments structurants sphériques. Pour simuler la désorption, une combinaison de fermetures et de bouchages de trou est utilisée. Le seuil de désorption est obtenu par une analyse de la percolation de la phase gazeuse. La méthode, d'abord validée sur des géométries simples, est comparée à des résultats antérieurs. Elle prédit une hystérésis et les distributions de pores associées à la porosimétrie. Nous l'appliquons aux modèles de microstructures 3D d'alumines mésoporeuses et proposons un modèle à trois échelles afin de rendre compte du seuil de pression pendant la désorption. En plus de la courbe de désorption, ce modèle reproduit les fonctions de corrélation mesurées sur les images MET.Dans un troisième temps, la diffusion de Fick, la perméabilité de Darcy, et les propriétés élastiques sont prédits à l'aide de calculs de champs complets par FFT sur des réalisations des modèles d'alumines mésoporeuses à deux et trois échelles. Les coefficients de diffusion effectifs et les facteurs de tortuosité sont prédits à partir de l'estimation du flux. Sont étudiés les effets de forme, d'alignement et d'agrégation des plaquettes sur les propriétés de diffusion à grande échelle. Les prédictions numériques sont validées au moyen des résultats expérimentaux obtenus par méthode RMN-GCP. / In a work made at Centre de Morphologie Mathématique and IFPEN, we study the microstructure and physical properties of mesoporous alumina. This is a catalyst carrier used in the petroleum refining industry. Highly porous, it contains disordered ''platelets'' at the nanoscale. The mass transport properties of the catalyst carrier are strongly influenced by the morphology of the porous microstructure. We focus on the modeling of the microstructure and of transport properties of mesoporous alumina, using numerical and theoretical tools derived from image analysis and random sets models. On the one hand, methods are developed to characterize and model the microstructure, by extracting and combining information from transmission electron microscope (TEM) images and nitrogen porosimetry curves, among others. On the other hand, the numerical homogenization relies on full-field Fourier transform computations (FFT).The material is first characterized experimentally by nitrogen porosimetry and pulse-field gradient nuclear magnetic resonance (PFG-NMR). TEM images, obtained on samples of various thicknesses are filtered and measured in terms of correlation function. The high-frequency noise caused by carbon membrane support is identified and integrated in the TEM image model. Based on the 2D TEM images, a two-scale random set model of 3D microstructure is developed. It takes into account the platelet shape, platelet size, local alignments and aggregations effects which are numerically identified. The procedure is validated by comparing the model and experimental images in terms of correlation function and specific surface area estimated by nitrogen porosimetry.Next, a procedure is proposed to simulate porosimetry isotherms in general porous media, including random microstructures. Based on simple morphological operations, it extends an earlier approach of mercury porosimetry. Multilayer adsorption at low pressure is simulated by a dilation operation whereas the menisci of the vapor-liquid interface occurring during adsorption are simulated by closing the solid phase with spherical structuring elements. To simulate desorption, a combination of closing and hole-filling operations is used. The desorption threshold is obtained from a percolation analysis of the gaseous phase. The method, validated first on simple geometries, is compared to previous results of the literature, allowing us to predict the hysteresis and pore size distribution associated to porosimetry. It is applied on 3D microstructures of mesoporous alumina. To account for the pressure threshold during desorption, we propose a refined three-scale model for mesoporous alumina, that reproduces the correlation function and the desorption branch of porosimetry isotherms.Finally, Fick diffusion, Darcy permeability, and elastic moduli are numerically predicted using the FFT method and the two-scale and three-scale models of mesoporous alumina. The hindering effects in diffusion are estimated by the Renkin's equation. The effective diffusion coefficients and the tortuosity factors are estimated from the flux field, taking into account hindering effects. The effects of platelet shape, alignment and aggregation on the diffusion property are studied. The numerical estimation is validated from experimental PFG-NMR results.