River dynamic behaviour is affected by variations both in the water phase and in the transported sediment phase. A change in the water regime may lead to significant morphological changes in the bed profile, which in turn may strongly influence the flow conditions. Transcritical flows over mobile beds are particularly challenging to model due to the rapid variation in space and time of the solid transport, and to the specific treatment required for boundary conditions. The one-dimensional numerical model presented in this dissertation divides the flow in two fully coupled layers: a water layer and a water-sediment transport layer. This model was initially designed to depict dam-break flows, which does not require a specific treatment of boundary conditions. An extension of the two-layer approach is proposed in order to properly take into account boundary conditions. The treatment of boundary conditions commonly relies on characteristics. Within a two-layer model, which embodies five governing equations, an appropriate eigenstructure analysis is developed based on numerical estimations. This novel approach results in a new characterization of the critical stage by defining a specific two-layer Froude number. The model is compared to the classical Saint-Venant – Exner approach and favourably applied to several typical situations: uniform flow, which allows a straightforward calibration of the model parameters; regressive erosion around a mild-to-steep slope transition; evolution of a mobile bed under a hydraulic jump; and scour hole formation downstream of a fixed bed.

The dynamics of the world's oceans occur at a vast range of length scales. Although there are theories that aid in understanding the dynamics at planetary scales and microscales, the motions in between are still not yet well understood. This work discusses a numerical model to study barotropic wind-driven gyre flow that is capable of resolving dynamics at the synoptic, O(1000 km), mesoscale, O(100 km) and submesoscales O(10 km). The Quasi-Geostrophic (QG) model has been used predominantly to study ocean circulations but it is limited as it can only describe motions at synoptic scales and mesoscales. The Rotating Shallow Water (SW) model that can describe dynamics at a wider range of horizontal length scales and can better describe motions at the submesoscales. Numerical methods that are capable of high-resolution simulations are discussed for both QG and SW models and the numerical results are compared. To achieve high accuracy and resolve an optimal range of length scales, spectral methods are applied to solve the governing equations and a third-order Adams-Bashforth method is used for the temporal discretization. Several simulations of both models are computed by varying the strength of dissipation. The simulations either tend to a laminar steady state, or a turbulent flow with dynamics occurring at a wide range of length and time scales. The laminar results show similar behaviours in both models, thus QG and SW tend to agree when describing slow, large-scale flows. The turbulent simulations begin to differ as QG breaks down when faster and smaller scale motions occur. Essential differences in the underlying assumptions between the QG and SW models are highlighted using the results from the numerical simulations.

The dynamics of the world's oceans occur at a vast range of length scales. Although there are theories that aid in understanding the dynamics at planetary scales and microscales, the motions in between are still not yet well understood. This work discusses a numerical model to study barotropic wind-driven gyre flow that is capable of resolving dynamics at the synoptic, O(1000 km), mesoscale, O(100 km) and submesoscales O(10 km). The Quasi-Geostrophic (QG) model has been used predominantly to study ocean circulations but it is limited as it can only describe motions at synoptic scales and mesoscales. The Rotating Shallow Water (SW) model that can describe dynamics at a wider range of horizontal length scales and can better describe motions at the submesoscales. Numerical methods that are capable of high-resolution simulations are discussed for both QG and SW models and the numerical results are compared. To achieve high accuracy and resolve an optimal range of length scales, spectral methods are applied to solve the governing equations and a third-order Adams-Bashforth method is used for the temporal discretization. Several simulations of both models are computed by varying the strength of dissipation. The simulations either tend to a laminar steady state, or a turbulent flow with dynamics occurring at a wide range of length and time scales. The laminar results show similar behaviours in both models, thus QG and SW tend to agree when describing slow, large-scale flows. The turbulent simulations begin to differ as QG breaks down when faster and smaller scale motions occur. Essential differences in the underlying assumptions between the QG and SW models are highlighted using the results from the numerical simulations.

No / Nazarbayev University Seed Grant, entitled “Environmental assessment of sediment pollution impact on hydropower plants”.

Un des mécanismes proposés pour expliquer l'origine de la variabilité climatique sur des périodes décennales à multidécennales est une oscillation propre de la circulation océanique thermohaline. Son mécanisme s'apparente aux modes de bassin basse fréquence et grande échelle qui résultent de l'interaction entre les ondes lentes planétaires et les ondes rapides de bord au cours du processus d'ajustement du bassin. Toutefois, la plupart des études de ce prototype oscillation décennale ont été menées dans des contextes simplifiés quasi-géostrophiques, à gravité réduite ou à fond plat. On se propose dans ce travail de thèse d'étudier l'effet de la topographie du fond et de la circulation moyenne sur les caractéristiques des modes de bassin baroclines. On utilise un modèle shallow water à deux couches verticales avec surface libre. Différentes bathymétries analytiques type fond plat, dorsale médio-océanique et pentes continentales sont étudiées.L'obtention des vecteurs propres du modèle linéarisé par analyse de stabilité linéaire autour d'un état au repos révèle que (1) la sélection de ces modes à basse résolution s'établit par la dissipation explicite introduite dans le modèle, (2) la période décennale et l'amortissement du mode le moins amorti sont faiblement sensibles à la topographie. Les budgets d'énergie et de vorticité de ces modes sont calculés dans le but de rationaliser le rôle amortisseur de la topographie via la conversion d'énergie qui a lieu entre les modes barotrope et barocline. En effet, une circulation barotrope, absente à fond plat, émerge à travers l'interaction entre le mode barocline à fond plat et la topographie. Toutefois, cette conversion d'énergie sous l'effet JEBAR demeure faible comparée aux processus visqueux.En présence d'une circulation stationnaire forcée par le vent et les flux de chaleur, les intégrations temporelles du modèle nonlinéaire perturbé par des structures baroclines cohérentes type tourbillons gaussiens montrent la forte interaction entre le vortex et la topographie. Cette interaction se manisfeste par : (1) une accélération de la vitesse de phase vers l'ouest par rapport au résultat à fond plat, (2) une circulation barotrope construite par la conversion de l'énergie barocline en barotrope, et (3) un déplacement méridien de l'anomalie dépendant de son signe même en l'absence d'advection nonlinéaire.Par ailleurs, le mode majeur de variabilité barocline, fortement amorti par la topographie et la dissipation dans la configuration non forcée paraît renforcé par l'écoulement stationnaire qui diminue son taux d'amortissement. Sa période d'oscillation développe une dépendance à la migration méridienne de l'advection zonale par l'écoulement moyen: elle est raccourcie (T ̴ 16 ans) pour le forçage par le vent et rallongée (T ̴ 22 ans) pour le forçage par les flux de chaleur. / One of the potential mechanisms at the origin of climatic variability on decadal to multidecadal timescales is the thermohaline oscillation corresponding to large-scale and low frequency basin modes that result from the interaction between long planetary waves and fast inertia-gravity waves during the adjustment process. However, most of the studies dealing with this decadal oscillation were carried out in a simplified flat bottom or reduced-gravity quasigeostrophic context.This dissertation aims to study the effect of bottom topography and mean flow on the characteristics of the gravest baroclinic basin modes in a mid-latitude idealized ocean basin. To that end, we make use of a two-layer shallow water (SW) model. Different bathymetries such as a flat bottom, a mid-ocean ridge and continental slopes are studied. Getting the eigenvectors from the linearized model through linear stability analysis around a state of rest reveals that (1) the selection of these modes is set by the explicit dissipation introduced in the model, (2) the oscillation period and decay rate are weakly sensitive to the form and height of the topography. Vorticity and energy budgets are computed in order to give a rationale for the decaying role of the topography via energy conversion from the baroclinic to the barotropic mode. Indeed, the barotropic flow absent in a flat bottom, results accurately from the interaction of the flat-bottomed baroclinic motion with the topographic height. However, the energy conversion under the JEBAR effect remains weaker with respect to the frictional processes.A stationary circulation is now included through wind or thermal forcing. Temporal integrations of the nonlinear model perturbed by coherent baroclinic structures with a gaussian eddy form show the strong interaction between the vortex and the topography. This interaction implies: (1) a westward acceleration of the zonal phase speed (with respect to the classic flat-bottom result), (2) a barotropic circulation built up by the conversion of the baroclinic energy into a barotropic one, and (3) an eddy sign-dependent meridional migration, even in the absence of nonlinear advection. Moreover, the decadal basin mode strongly damped by the topography and the dissipation shows a decrease of its decay rate by the large scale stationary forcing. Its oscillation period is found to be a strong function of the meridional migration of the eastward advection by the mean flow: it is shortened (T ̴ 16 yrs) in the wind-forced experiment and lengthened (T ̴ 22 yrs) with a thermal forcing.

Cette thèse est consacrée à l’étude théorique ainsi qu’au traitement numérique de fluides incompressibles à surface libre. La première partie concerne un système d’équations appelé le système de Green–Naghdi. Comme le système de Saint-Venant, il s’agit d’une approximation d’eaux peu-profondes du problème de Zakharov. La différence est que le système de Green–Naghdi est d’un degré plus élevé en ordre d’approximation. C’est pourquoi il contient tous les termes du système de Saint-Venant plus de termes d’ordre trois non-linéairement dispersives. Autrement dit, le système de Green–Naghdi peut être vu comme une perturbation dispersive du système de Saint-Venant. Ce dernier système étant hyperbolique, il entre dans le cadre classique développé pour des systèmes hyperboliques. En particulier, il est entropique (au sense de Lax) et symétrique. On peut donc lui appliquer les résultats d’existence et d’unicité bien connus pour des systèmes hyperboliques. Dans la première partie de ce travail, on généralise la notion de symétrie à une classe plus générale de systèmes contenant le système de Green–Naghdi. Ceci nous permet de symétriser les équations de Green–Naghdi et d’utiliser la symétrie obtenue pour déduire un résultat d’existence globale après avoir ajouté un terme dissipative d’ordre 2 au système. Ceci est fait en adaptant l’approche utilisée dans la littérature pour des systèmes hyperboliques. La deuxième partie de ce travail concerne le traitement numérique des équations de Navier–Stokes à surface libre avec un terme de tension de surface. Ici, la surface libre est modélisée en utilisant la formulation des lignes de niveaux. C’est pourquoi la condition cinématique (condition de l’évolution de surface libre) s’écrit sous la forme d’une équation d’advection satisfaite par la fonction de ligne de niveaux. Cette équation est résolue sur une domaine de calcul contenant strictement le domaine de fluide, sur de petits sous-intervalles du temps. Chaque itération de l’algorithme global correspond donc à l’advection du domaine du fluide sur le sous-intervalle du temps associé et ensuite de résoudre le système de Navier–Stokes discrétisé en temps sur le domaine du fluide. Cette discrétisation en temps est faite par la méthode des caractéristiques. L’outil clé qui nous permet de résoudre ce système uniquement sur le domaine du fluide est l’adaptation de maillage anisotrope. Plus précisément, à chaque itération le maillage est adapté au domaine du fluide tel que l’erreur d’approximation et l’erreur géométrique soient raisonnablement petites au voisinage du domaine du fluide. La résolution du problème discrétisé en temps sur le domaine du fluide est faite par l’algorithme d’Uzawa utilisé dans la cadre de la méthode des éléments finis. Par ailleurs, la condition de glissement de Navier est traité ici en ajoutant un terme de pénalisation à la formulation variationnelle associée. / This thesis is about theoretical study and numerical treatment of some problems raised in incompressible free-surface fluid dynamics. The first part concerns a model called the Green–Naghdi (GN) equations. Similarly to the non linear shallow water system (called also Saint-Venant system), the Green–Naghdi equations is a shallow water approximation of water waves problem. Indeed, GN equation is one order higher in approximation compared to Saint-Venant system. For this reason, it contains all the terms of Saint-Venant system in addition to some non linear third order dispersive terms. In other words, the GN equations is a dispersive perturbation of the Saint-Venant system. The latter system is hyperbolic and fits the general framework developed in the literature for hyperbolic systems. Particularly, it is entropic (in the sense of Lax) and symmertizable. Therefore, we can apply the well-posedness results known for symmetric hyperbolic system. During the first part of this work, we generalize the notion of symmetry to a more general type of equations including the GN system. This lets us to symmetrize the GN equation. Then, we use the suggested symmetric structure to obtain a global existence result for the system with a second order dissipative term by adapting the approach classically used for hyperbolic systems. The second part of this thesis concerns the numerical treatment of the free surface incompressible Navier–Stokes equation with surface tension. We use the level set formulation to represent the fluid free-surface. Thanks to this formulation, the kinematic boundary condition is treated by solving an advection equation satisfied by the level set function. This equation is solved on a computational domain containing the fluid domain over small time subintervals. Each iteration of the algorithm corresponds to the adevction of the fluid domain on a small time subinterval and to solve the time-discretized Navier–Stokes equations only on the fluid domain. The time discretization of the Navier–Stokes equation is done by the characteristic method. Then, the key tool which lets us solve this equation on the fluid domain is the anisotropic mesh adaptation. Indeed, at each iteration the mesh is adapted to the fluid domain such that we get convenient approximation and geometric errors in the vicinity of the fluid domain. This resolution is done using the Uzawa algorithm for a convenient finite element method. The slip boundary conditions are considered by adding a penalization term to the variational formulation associated to the problem.

Dans ce manuscrit, nous parlons des matériaux composites à matrice céramiques (CMCs) qui sont envisagés pour intégrer les chambres de combustion de futurs moteurs aéronautiques civils. Pour faire face des conditions extrêmes, ces matériaux possèdent la particularité de s’auto-protéger vis-à-vis de l’oxydation par la formation d’un oxyde passivant qui limite la diffusion des espèces oxydantes au sein des fissures matricielles. Nous modélisons l’écoulement d’un oxyde dans une fissure par l’équation de Navier-Stokes, puis les mettons sous forme non dimensionnelles, et les dérivations de deux types de modèles sont intéressantes : les modèles de Saint-Venant et les modèles de lubrification. Ensuit nous nous engageons à chercher l’existence de solution faible de l’approximation de lubrification d’ordre 4 obtenue précédent dans le cas uni-dimensionnel. Enfin nous précisons la limite entre les équations de Saint-Venant et l’équation de lubrification. / In this work, we are interested in the ceramic matrix composite materials(CMCs) who will be used to integrate the combustion chambers of future civil aeronautical engines. To face extreme conditions, these materials possess the peculiarity to auto-protect itself towards the oxidation by the formation of an oxide passivate which limits the distribution of the oxidizing species within the matrix cracks. We model the flow of an oxide in a crack by the Navier-Stokes equation, then put them under an asymptotic analysis in order to get two types of asymptotic models : models of Saint-Venant (Shallow water model) and lubrication models. Next we are interested in looking for the existence of weak solution to the one-dimensional approximated lubrication equation of order 4 obtained before. Finally we talk about the limit between the Saint-Venant equations and the lubrication equation.

Cette thèse traite de la modélisation des tsunamis, des grandes échelles de propagation aux impacts sur desstructures côtières. Un inventaire des phénomènes physiques associés est établi et des modèles adéquats sontprésentés. Une étude numérique avec le modèle de Saint-Venant est effectuée avec le développement d’uneméthode de raffinement de maillage à seuil automatique. La simplicité et les performances de l’approche sontdémontrées. Pour améliorer la précision des prévisions, un système original approchant le modèle Serre-Green-Nahgdi est investigué. Une méthode pour prendre en compte la dissipation d’énergie au déferlement estproposée. Ce modèle permet d’envisager la modélisation fine de la propagation et de l’arrivée à la côte destsunamis dispersifs et non linéaires en des temps de calcul acceptables. Les différents types d’impact sur desstructures sont modélisés grâce à un modèle diphasique compressible permettant de considérer les écoulementsà phases séparées et les milieux aérés. Pour envisager une résolution à tous les régimes, des schémas TousMach sont investigués. Un schéma Tous Mach à variation totale limitée est proposé. Grâce à cette approche,des impacts incompressibles et compressibles sont investigués avec le même modèle. Les impactsd’écoulements aérés induisent des pressions moins élevées mais sur des temps plus longs que leurshomologues en phases pures. Bien que le schéma Tous Mach proposé soit moins sujet aux oscillationsnumériques que les préconditionnements classiques de la littérature, des oscillations non physiques à basnombre de Mach sont mises en évidence sur certains cas tests. Pour finir, une méthode de couplage entremodèles de propagation et d’impact est proposée, afin de pouvoir simuler un tsunami finement avec desmodèles appropriés à chacune de ces phases. / This thesis deals with tsunami modeling, from the large propagation scales to impacts on coastal structures. Aninventory of the associated physical phenomena is given and some adequat models are presented. A numericalstudy is carried out with the Saint-Venant model with the devellopment of an automatic refinment adaptivemesh method. The resolution efficiency and simplicity is justified. To increase the accuracy forecasts, anoriginal system which approximates the Serre-Green-Naghdi model is investigated. A breaking wave methodassociated with this model is proposed. This dissipative model allows thinking about accurate dispersive nonlinear tsunamis simulations up to the coast. Several wave impacts on stuctures are investigated with a generaltwo-phase model allowing separate phases as well as aerated impact studies. The all Mach regime numericaldifficulties are investigated. A new all Mach scheme with limited total variation bound is proposed. Thanks tothis approach, incompressible and compressible impacts are investigated with the same model. Aerated impactsare shown to give smaller impact pressure but on longer time than pure fluid impacts. In spite that the all Machscheme proposed reduces the numerical oscillations of classical literature preconditionning, some unphysicaloscillations are highlighted on some test cases. At the end, a coupling method is proposed in order to accuratlymodel the propagation and the impact of a tsunami with appropriated models for each phases.

Yes / Based on the common approach, the adaptation length in sediment transport is normally estimated in the temporal independence. However, this approach might not be theoretically justified as the process of reaching of the sediment transport equilibrium stage is affected by the flow conditions in time, especially for those fast sediment moving flows, such as scour-hole developing flow. In this study, the 2D shallow water formulation together with a sediment continuity-concentration (SCC) model were applied to flow with mobile sediment boundary. A time-varying approach was proposed to determine the sediment transport adaptation length to treat the flow sediment erosion-deposition rate. The proposed computational model was based on the Finite Volume (FV) method. The Monotone Upwind Scheme of Conservative Laws (MUSCL)-Hancock scheme was used with the Harten Lax van Leer-contact (HLLC) approximate Riemann solver to discretize the FV model. In the flow applications of this paper, a highly discontinuous dam-break fast sediment transport flow was used to calibrate the proposed time-varying sediment adaptation length model. Then the calibrated model was further applied to two separate experimental sediment transport flow applications documented in literature, i.e. a highly concentrated sediment transport flow in a wide alluvial channel and a sediment aggradation flow. Good agreements with the experimental data were presented by the proposed model simulations. The tests prove that the proposed model, which was calibrated by the discontinuous dam-break bed scouring flow, also performed well to represent the rapid bed change and the steady sediment mobility conditions. / The National Natural Science Foundation of China NSFC (Grant Number 20101311246), Major State Basic Research Development Program (973 program) of China (Grant Number 2013CB036402) and Open Fund of the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University of China (Grant Number SKLH-OF-1103).

In this thesis we study the properties of exoplanetary atmospheres. The first part describes methods for searching exoplanets, statistics of discovered exoplanets and the sampling factors. The second part describes the properties of chosen planets and moons in the Solar system (Venus, Mars and Titan) and also possible properties of the exoplanetary atmospheres that are only briefly understood. The third part describes the atmospheric models which incorporate a full 3D model of the atmosphere, and a shallow- water model. We also show the results of exoplanetary atmospheric models published in the scientific journals. This part also describes the icosahedral geodetic grid that is advantageous for the global climatic models, and also discretisation on sphere and the application of the operators (gradient, divergence, vorticity) on geodetic grid. The last part is about creating program for global shallow water model in divergence-vorticity variables with forcing system with using icosahedral geodetic grid - we describe technical properties connected with model creating, parameters which the model uses during time integration, geographic system for results display and we show results for various kinds of extrasolar planets and planets in the Solar system. We used several numerical tests for testing model...