As ondas de Rossby são o mecanismo de ajuste às perturbações de grande escala dos fluidos geofísicos. Elas podem ser geradas localmente, forçadas pelo rotacional da tensão de cisalhamento do vento, ou remotamente, devido às perturbações na altura da picnoclina na borda leste. Medidas altimétricas da anomalia da altura do mar tem fornecido evidências robustas da existência destas ondas. Estudos recentes mostram que vórtices não lineares de mesoescala são responsáveis por uma grande parte da variabilidade dos registros altimétricos, tendo sido observados propagando juntamente com as ondas de Rossby. Os objetivos deste estudo são identificar (1) as regiões onde as ondas de Rossby longas lineares explicam as observações, (2) qual mecanismo de geração é dominante e (3) se as ondas propagam-se de forma contínua em condições de não linearidade. Um modelo linear de 1½ camada de ondas de Rossby forçado por dados de tensão de cisalhamento do vento de escaterômetros é utilizado para reproduzir as anomalia da altura do mar. As correlações entre os resultados do modelo linear e os dados altimétricos são de até 0,88. Os resultados sugerem que a dinâmica linear de ondas de Rossby longas explica uma parte significativa da variabilidade anual da anomalia da altura do mar nas regiões tropicais. A oscilação da picnoclina na borda leste é o principal mecanismo gerador de ondas de Rossby nos oceanos Atlântico e Índico, enquanto no Pacífico a fonte dominante das ondas é a forçante atmosférica local. Um modelo quase-geostrófico não linear é utilizado para analisar como as ondas de Rossby geradas na borda leste propagam-se e dissipam-se em condições idealizadas. Em latitudes mais baixas que 32°S, as ondas atravessam toda a bacia oceânica até adentrar a região de meandramento da corrente de borda oeste. Nesta região, a energia é espalhada em todas as bandas de frequência. As ondas de Rossby que estão na latitude crítica tem um papel intermediário na cascata de energia. Em latitudes mais altas que 32°S, as ondas de Rossby não cruzam a totalidade da bacia oceânica, tendo sua energia transferida para outros períodos em uma distância de pelo menos 1000 km da borda oeste. / Rossby waves are the large scale mechanism of adjustment to perturbations of geophysical fluids. They can be generated locally, due to forcing by wind stress curl, or remotely, due to perturbations in the pycnocline level at the eastern boundary. Altimetric measurements of sea level anomaly have been providing sturdy evidences of the existence of these waves. Recent studies argue that mesoscale eddies are responsible for a substantial amount of the variability of the altimeter records. Eddies have been shown to propagate along with Rossby waves. The purposes of this study are (1) to identify the regions where linear long Rossby waves explain the observations, (2) to determine which generation mechanism is dominant, and (3) to verify if these waves can continuously propagate in nonlinearity conditions. A linear 1½ layer model forced by scatterometer wind stress data has been used to reproduce the sea level anomaly. Correlations between the results of the linear model and the altimetric data are up to 0.88. Results suggest that the linear long Rossby wave dynamics explain a significant part of the sea level anomaly annual variability in the tropical oceans. The pycnocline fluctuations at the eastern boundary are the main mechanism of generation of Rossby waves in the Atlantic and Indian oceans. The local atmospheric forcing is the principal source of the waves in the Pacific Ocean. A quasi-geostrophic nonlinear model has been used to analyze how the Rossby waves generated at the eastern boundary propagate and dissipate in idealized conditions. In latitudes lower than 32°S, the waves cross all the ocean basin until entering the region where the western boundary current meanders. In this region, energy is scattered throughout the spectrum. The Rossby waves that are in their critical latitude have an intermediate role in the energy cascade. In latitudes higher than 32°S, the Rossby waves fail to completely cross the ocean basin. Their energy is transfered to other periods in a distance of at least 1000 km from the western boundary.

As ondas de Rossby são o mecanismo de ajuste às perturbações de grande escala dos fluidos geofísicos. Elas podem ser geradas localmente, forçadas pelo rotacional da tensão de cisalhamento do vento, ou remotamente, devido às perturbações na altura da picnoclina na borda leste. Medidas altimétricas da anomalia da altura do mar tem fornecido evidências robustas da existência destas ondas. Estudos recentes mostram que vórtices não lineares de mesoescala são responsáveis por uma grande parte da variabilidade dos registros altimétricos, tendo sido observados propagando juntamente com as ondas de Rossby. Os objetivos deste estudo são identificar (1) as regiões onde as ondas de Rossby longas lineares explicam as observações, (2) qual mecanismo de geração é dominante e (3) se as ondas propagam-se de forma contínua em condições de não linearidade. Um modelo linear de 1½ camada de ondas de Rossby forçado por dados de tensão de cisalhamento do vento de escaterômetros é utilizado para reproduzir as anomalia da altura do mar. As correlações entre os resultados do modelo linear e os dados altimétricos são de até 0,88. Os resultados sugerem que a dinâmica linear de ondas de Rossby longas explica uma parte significativa da variabilidade anual da anomalia da altura do mar nas regiões tropicais. A oscilação da picnoclina na borda leste é o principal mecanismo gerador de ondas de Rossby nos oceanos Atlântico e Índico, enquanto no Pacífico a fonte dominante das ondas é a forçante atmosférica local. Um modelo quase-geostrófico não linear é utilizado para analisar como as ondas de Rossby geradas na borda leste propagam-se e dissipam-se em condições idealizadas. Em latitudes mais baixas que 32°S, as ondas atravessam toda a bacia oceânica até adentrar a região de meandramento da corrente de borda oeste. Nesta região, a energia é espalhada em todas as bandas de frequência. As ondas de Rossby que estão na latitude crítica tem um papel intermediário na cascata de energia. Em latitudes mais altas que 32°S, as ondas de Rossby não cruzam a totalidade da bacia oceânica, tendo sua energia transferida para outros períodos em uma distância de pelo menos 1000 km da borda oeste. / Rossby waves are the large scale mechanism of adjustment to perturbations of geophysical fluids. They can be generated locally, due to forcing by wind stress curl, or remotely, due to perturbations in the pycnocline level at the eastern boundary. Altimetric measurements of sea level anomaly have been providing sturdy evidences of the existence of these waves. Recent studies argue that mesoscale eddies are responsible for a substantial amount of the variability of the altimeter records. Eddies have been shown to propagate along with Rossby waves. The purposes of this study are (1) to identify the regions where linear long Rossby waves explain the observations, (2) to determine which generation mechanism is dominant, and (3) to verify if these waves can continuously propagate in nonlinearity conditions. A linear 1½ layer model forced by scatterometer wind stress data has been used to reproduce the sea level anomaly. Correlations between the results of the linear model and the altimetric data are up to 0.88. Results suggest that the linear long Rossby wave dynamics explain a significant part of the sea level anomaly annual variability in the tropical oceans. The pycnocline fluctuations at the eastern boundary are the main mechanism of generation of Rossby waves in the Atlantic and Indian oceans. The local atmospheric forcing is the principal source of the waves in the Pacific Ocean. A quasi-geostrophic nonlinear model has been used to analyze how the Rossby waves generated at the eastern boundary propagate and dissipate in idealized conditions. In latitudes lower than 32°S, the waves cross all the ocean basin until entering the region where the western boundary current meanders. In this region, energy is scattered throughout the spectrum. The Rossby waves that are in their critical latitude have an intermediate role in the energy cascade. In latitudes higher than 32°S, the Rossby waves fail to completely cross the ocean basin. Their energy is transfered to other periods in a distance of at least 1000 km from the western boundary.

Les variations du champ magnétique terrestre sont documentées par les observatoires au sol et les satellites en orbite basse, pour des échelles de temps de l'année au siècle.Sur ces périodes, la dynamique du noyau externe -- là où est principalement généré le champ magnétique -- est fortement influencée par la rotation terrestre, qui tend à imposer une invariance dans la direction parallèle à l'axe de rotation.Dans cette thèse, j'étudie un modèle s'appuyant sur cette hypothèse de bidimensionnalité du champ de vitesse, le modèle quasi-géostrophique.Je présente une nouvelle dérivation de ce modèle par une approche variationnelle, plus adaptée aux fortes pentes des frontières du domaine sphérique.Je présente une étude modale des ondes hydro-magnétiques, qui pour la première fois prend en compte l'impact d'un champ magnétique imposé non-zonal.Deux groupes d'ondes magnéto-hydrodynamiques apparaissent alors : les ondes magnéto-Coriolis (centennales) et les ondes d'Alfvéen de torsion (interannuelle).Je décris l'évolution des ondes à mesure que l'on intensifie l'effet de la rotation, jusqu'à atteindre des paramètres géophysiques.Je discute également dans quel mesure une version du modèle quasi-géostrophique où la force de Lorentz est représentée par des produits quadratiques du champ magnétique est adapté pour l'interprétation de calculs numériques tridimensionnels de la dynamo. J'observe que pour les paramètres aujourd'hui accessibles à ces calculs, les forces magnétiques sont faibles. À long terme, nous espérons utiliser le modèle quasi-géostrophique dans le contexte de l'assimilation de données satellitaires. / Variations of the Earth's magnetic field are documented by ground observatories and low-orbiting satellites, for time scales from year to century.On such periods, dynamics of the outer core -- where the creation of the magnetic field takes place -- is strongly influenced by the Earth rotation, which tends to impose invariance of the flow in the direction parallel to the rotation axis.In this thesis report, I study a model based on this bi-dimensional velocity field hypothesis, the quasi-geostrophic model.I present a new mathematical formulation of this model through a variational approach, better suited to steep slopes on the boundaries of the spherical domain.I present a modal study of hydromagnetic waves, taking into account for the first time the impact of a non-zonal imposed magnetic field.Two groups of hydromagnetic waves are present : centennial magneto-Coriolis waves and interannual torsional Alfvén waves.I describe evolution of those waves as the effect of rotation is intensified until Earth-like parameters are reached.I also discuss in what measure an other version of the quasi-geostrophic model, where Lorentz force is represented by quadratic products of the magnetic field, can be adapted to understand tridimensional dynamo numerical simulations.I observe that for parameters available today, magnetic forces are weak.In the future, we hope to use the Quasi-geostrophic model in the context of satellite data assimilation.

This dissertation examines the nature of jet-boundary interactions and the role of barotropic instabilities in the Brazil Current system while still attached to the western boundary. The motivation was due to the frequent observation of bipolar features associated to the Brazil Current flow south of Cape Frio (RJ) and off Santos Bight (22º-28ºS). Such observations were mainly obtained from sea surface temperature images, and also from few \"in situ\" hydrographic and direct velocity measurements data. Therefore, our main focus is on the formation of bipolar features associated with the flow, and the main hypothesis is that barotropic instability is responsible for the generation of such dipoles along the western boundary current jet, while it has to deal with topographic variations along its path poleward. We address the system dynamics from a semi-theoretical perspective, and also through the application of numerical modeling on a process study approach. So it includes semi-theoretical studies of jet-lateral boundary interactions in idealized configurations relevant to the Brazil Current system off Cape Frio, considering the quasi-geostrophic theory as an appropriate approximation of the system we want to investigate. Additionally, numerical modeling is used through the construction of idealized scenarios where we simplify the physics in order to isolate the dynamical process of interest. All the dynamical analyzes were initialized from synoptic hydrographic data set which comprised the Brazil Current system off Cape Frio region. We validated the quasi-geostrophic theory we assumed and obtained the kinematics characteristics of the jet. In the dynamical analyses, we started the investigation from the simplest framework applied here, where we evaluate a piecewise constant potential vorticity field in a quasi-geostrophic contour dynamics model. It dealt with a meridionally-oriented jet flowing southward along a straight western boundary. Next, in a second model, we added more complexity in the system, idealizing western boundary coastline scenarios considering a quasi-continuous potential vorticity field in a quasi-geostrophic numerical model. Finally, in a third model, we constructed a more complex scenario for the Brazil Current jet that incorporated real topography and stratification of the water column in a primitive equation numerical model. Among our main finds, we verified that purely barotropic instability is able to generate vortex dipoles. Moreover, variations in the western boundary can indeed trigger perturbations in the jet and dipoles form. Therefore, sites with abrupt change in bathymetry and coastline orientation are preferred to the formation of the BC vortical dipoles. Vortex streets and instability trains can also develop downstream of such locations as consequence of perturbing a potentially batropically unstable jet. Hence, the horizontal shear is key to the generation of vortex dipoles. A weak shear does not allow these features to form, instead, frontal eddies are possibly generated, with the predominance of anticyclones. Although the three different model strategies applied here differ in dynamical configurations and approximations, they still kept nearly the same regime for the Brazil Current vortex-dipole formation. Topographic variations such as those associated with the change of coastline orientation near Cape Frio (23ºS) account for those vortex dipoles and streets be dominantly observed within the Santos Bight. / A presente tese examina a natureza das interações entre jato e contorno e o papel de instabilidades barotrópicas no sistema Corrente do Brasil (CB) quando este ainda se encontra fluindo junto à margem continental oeste. A motivação se deu através da frequente observação de feições bipolares associadas ao escoamento da CB ao sul de Cabo Frio (RJ) e ao largo da Bacia de Santos (entre 22º e 28ºS). Tais observações se devem principalmente a imagens termais de temperatura da superfície do mar, a algumas raras observações \"in situ\" através de dados hidrográficos e medições diretas de velocidade. Assim, o principal foco é na formação de feições bipolares associadas ao fluxo médio, sendo a principal hipótese a de que instabilidade barotrópica é responsável pela formação destes dipolos ao longo da corrente quando esta tem que lidar com variações da topografia. Este estudo tenta abordar os problemas em uma perspectiva semi-teórica, e também através de modelagem numérica em uma abordagem de estudos de processo. Assim, inclui estudos semi-teóricos em configurações idealizadas relevantes para o sistema Corrente do Brasil ao largo de Cabo Frio, considerando a teoria quase-geostrófica como a aproximação apropriada para a dinâmica do sistema que queremos avaliar. Adicionalmente, a modelagem numérica é usada através da construção de cenários idealizados onde simplificamos a física a fim de isolar os processos que queremos investigar. Toda a análise dinâmica partiu de um conjunto de dados que compreendeu o sistema Corrente do Brasil ao largo de Cabo Frio. Validamos a teoria quase-geostrófica que estamos considerando e obtivemos as características cinemáticas do jato. Nas análises dinâmicas, começamos a investigação do problema partindo do cenário mais simples utilizado aqui, onde consideramos um campo de vorticidade potencial discretizado em camadas horizontais em um modelo quase-geostrófico de dinâmica de contornos. O modelo incorporou a presença de uma linha de costa retilínea orientada meridionalmente no contorno oeste. Posteriormente, incluímos mais complexidade no sistema, idealizando diferentes cenários de linha de costa e considerando um campo de vorticidade potencial quase-contínuo em um modelo numérico quase-geostrófico. Finalmente, construímos um cenário ainda mais complexo para a Corrente do Brasil, o qual incorporou a topografia real da região e a estratificação da coluna de água em um modelo numérico de equações primitivas. Dentre as principais conclusões, pudemos comprovar que instabilidade barotrópica pode promover a formação de dipolos. Além disso, variações no contorno podem consequentemente ser gatilhos para gerar perturbações no jato e dipolos se formam. Assim, locais de mudança abrupta de batimetria e orientação de linha de costa são preferidos para a formação de dipolos vorticais. Rua de vórtices e trens de instabilidade também podem se desenvolver à juzante de tais locais como consequência de se perturbar um jato potencialmente barotropicamente instável. Consequentemente, um cisalhamento horizontal é chave para a geração de dipolos vorticais. Um cisalhamento relativamente fraco não permite a formação de tais feições, e em vez disso, vórtices frontais são possivelmente gerados, com a predominância de anticiclones. Apesar de as três diferentes estratégias aplicadas aqui diferirem em termos de configurações dinâmicas e aproximações, estas ainda mantiveram aproximadamente o mesmo regime para a formação de dipolos. Variações na topografia tais como aquelas associadas com mudanças de orientação de costa próximo a Cabo Frio (23ºS) contam com o fato de dipolos vorticais e rua de vórtices serem frequentemente observados dentro da Bacia de Santos.

This dissertation examines the nature of jet-boundary interactions and the role of barotropic instabilities in the Brazil Current system while still attached to the western boundary. The motivation was due to the frequent observation of bipolar features associated to the Brazil Current flow south of Cape Frio (RJ) and off Santos Bight (22º-28ºS). Such observations were mainly obtained from sea surface temperature images, and also from few \"in situ\" hydrographic and direct velocity measurements data. Therefore, our main focus is on the formation of bipolar features associated with the flow, and the main hypothesis is that barotropic instability is responsible for the generation of such dipoles along the western boundary current jet, while it has to deal with topographic variations along its path poleward. We address the system dynamics from a semi-theoretical perspective, and also through the application of numerical modeling on a process study approach. So it includes semi-theoretical studies of jet-lateral boundary interactions in idealized configurations relevant to the Brazil Current system off Cape Frio, considering the quasi-geostrophic theory as an appropriate approximation of the system we want to investigate. Additionally, numerical modeling is used through the construction of idealized scenarios where we simplify the physics in order to isolate the dynamical process of interest. All the dynamical analyzes were initialized from synoptic hydrographic data set which comprised the Brazil Current system off Cape Frio region. We validated the quasi-geostrophic theory we assumed and obtained the kinematics characteristics of the jet. In the dynamical analyses, we started the investigation from the simplest framework applied here, where we evaluate a piecewise constant potential vorticity field in a quasi-geostrophic contour dynamics model. It dealt with a meridionally-oriented jet flowing southward along a straight western boundary. Next, in a second model, we added more complexity in the system, idealizing western boundary coastline scenarios considering a quasi-continuous potential vorticity field in a quasi-geostrophic numerical model. Finally, in a third model, we constructed a more complex scenario for the Brazil Current jet that incorporated real topography and stratification of the water column in a primitive equation numerical model. Among our main finds, we verified that purely barotropic instability is able to generate vortex dipoles. Moreover, variations in the western boundary can indeed trigger perturbations in the jet and dipoles form. Therefore, sites with abrupt change in bathymetry and coastline orientation are preferred to the formation of the BC vortical dipoles. Vortex streets and instability trains can also develop downstream of such locations as consequence of perturbing a potentially batropically unstable jet. Hence, the horizontal shear is key to the generation of vortex dipoles. A weak shear does not allow these features to form, instead, frontal eddies are possibly generated, with the predominance of anticyclones. Although the three different model strategies applied here differ in dynamical configurations and approximations, they still kept nearly the same regime for the Brazil Current vortex-dipole formation. Topographic variations such as those associated with the change of coastline orientation near Cape Frio (23ºS) account for those vortex dipoles and streets be dominantly observed within the Santos Bight. / A presente tese examina a natureza das interações entre jato e contorno e o papel de instabilidades barotrópicas no sistema Corrente do Brasil (CB) quando este ainda se encontra fluindo junto à margem continental oeste. A motivação se deu através da frequente observação de feições bipolares associadas ao escoamento da CB ao sul de Cabo Frio (RJ) e ao largo da Bacia de Santos (entre 22º e 28ºS). Tais observações se devem principalmente a imagens termais de temperatura da superfície do mar, a algumas raras observações \"in situ\" através de dados hidrográficos e medições diretas de velocidade. Assim, o principal foco é na formação de feições bipolares associadas ao fluxo médio, sendo a principal hipótese a de que instabilidade barotrópica é responsável pela formação destes dipolos ao longo da corrente quando esta tem que lidar com variações da topografia. Este estudo tenta abordar os problemas em uma perspectiva semi-teórica, e também através de modelagem numérica em uma abordagem de estudos de processo. Assim, inclui estudos semi-teóricos em configurações idealizadas relevantes para o sistema Corrente do Brasil ao largo de Cabo Frio, considerando a teoria quase-geostrófica como a aproximação apropriada para a dinâmica do sistema que queremos avaliar. Adicionalmente, a modelagem numérica é usada através da construção de cenários idealizados onde simplificamos a física a fim de isolar os processos que queremos investigar. Toda a análise dinâmica partiu de um conjunto de dados que compreendeu o sistema Corrente do Brasil ao largo de Cabo Frio. Validamos a teoria quase-geostrófica que estamos considerando e obtivemos as características cinemáticas do jato. Nas análises dinâmicas, começamos a investigação do problema partindo do cenário mais simples utilizado aqui, onde consideramos um campo de vorticidade potencial discretizado em camadas horizontais em um modelo quase-geostrófico de dinâmica de contornos. O modelo incorporou a presença de uma linha de costa retilínea orientada meridionalmente no contorno oeste. Posteriormente, incluímos mais complexidade no sistema, idealizando diferentes cenários de linha de costa e considerando um campo de vorticidade potencial quase-contínuo em um modelo numérico quase-geostrófico. Finalmente, construímos um cenário ainda mais complexo para a Corrente do Brasil, o qual incorporou a topografia real da região e a estratificação da coluna de água em um modelo numérico de equações primitivas. Dentre as principais conclusões, pudemos comprovar que instabilidade barotrópica pode promover a formação de dipolos. Além disso, variações no contorno podem consequentemente ser gatilhos para gerar perturbações no jato e dipolos se formam. Assim, locais de mudança abrupta de batimetria e orientação de linha de costa são preferidos para a formação de dipolos vorticais. Rua de vórtices e trens de instabilidade também podem se desenvolver à juzante de tais locais como consequência de se perturbar um jato potencialmente barotropicamente instável. Consequentemente, um cisalhamento horizontal é chave para a geração de dipolos vorticais. Um cisalhamento relativamente fraco não permite a formação de tais feições, e em vez disso, vórtices frontais são possivelmente gerados, com a predominância de anticiclones. Apesar de as três diferentes estratégias aplicadas aqui diferirem em termos de configurações dinâmicas e aproximações, estas ainda mantiveram aproximadamente o mesmo regime para a formação de dipolos. Variações na topografia tais como aquelas associadas com mudanças de orientação de costa próximo a Cabo Frio (23ºS) contam com o fato de dipolos vorticais e rua de vórtices serem frequentemente observados dentro da Bacia de Santos.

L'objectif principal de cette thèse est d'évaluer la contribution d'une méthode d'interpolation dynamique pour améliorer la représentation des processus océaniques à petite échelle dans les cartes altimétriques. La résolution actuelle de ces cartes construites par interpolation statistique optimale, est bien adaptée à l'étude de la variabilité mésoéchelle mais ne permet pas d'observer des structures de taille inférieures à 150-200 km, en grande partie à cause de l'échantillonnage spatio-temporel des données. La méthode d'interpolation dynamique est basée sur un modèle de propagation quasi-géostrophique (QG) à une couche et demie, dont le but est de recréer une partie de l'évolution temporelle des petites structures océaniques en utilisant la dynamique locale. Dans cette étude, nous appliquons cette méthode à la Méditerranée occidentale. En premier lieu nous avons évalué la capacité du propagateur QG à représenter la dynamique dans cette région. Nous avons ensuite utilisé ce propagateur pour réaliser l'interpolation dynamique dans un cas idéalisé spatialement, en comparant les champs reconstruits avec un modèle numérique à haute résolution. Les résultats ont montré une amélioration générale par rapport à une interpolation linéaire sur une période de 5-10 jours. La performance de la méthode à montré une disparité spatiale et temporelle, avec une amélioration plus importante pour les régions de forte variabilité et en période hivernale. Nous avons exploité deux pistes de complexification du propagateur afin de mieux modéliser la dynamique de la région, fortement influencée par les forçages atmosphériques locaux intenses, la géométrie du bassin et sa bathymétrie. Dans une seconde étude, nous avons évalué la contribution de cette méthode d'interpolation dynamique pour cartographier les données altimétriques réelles le long des traces. Pour cette étude, les structures de covariance dérivées de l'évolution du modèle QG ont été intégrées dans un schéma d'interpolation optimal. Les cartes dynamiques interpolées résultantes ont été comparées aux cartes altimétriques actuelles. Cette étude, qui participe à la préparation de l'exploitation des futures données haute résolution de la mission SWOT, a démontré l'efficacité d'un modèle relativement simple pour améliorer la résolution des cartes altimétriques. Néanmoins, tous ces résultats ont révèlé la difficulté de paramétrer de façon optimale cette méthode de cartographie pour caractériser la dynamique dans une région qui présente une forte variabilité spatiale et temporelle. Ce travail souligne aussi le besoin de mieux exploiter les différents jeux de mesures indépendantes pour évaluer rigoureusement l'amélioration des petites échelles, qui ont un impact non négligeable sur la dynamique de mésoéchelle, notamment sur les transferts énergétiques au sein de l'océan et sur les interactions physico-biologiques. / The main objectif of this thesis is to evaluate the contribution of a dynamic interpolation method to improve the representation of small scale ocean processes in altimetric maps. The current resolution of these maps constructed by a statistical optimal interpolation technique, is well adapted to the study of the mesoscale variability but does not allow us to observe structures of sizes smaller than 150-200km, largely due to the spatio-temporal sampling of the data. The dynamic interpolation method is based on a one-and-a-half layer quasi-geostrophic (QG) propagation model, aims to recreate part of the temporal evolution of small oceanic structures using the local dynamics. In this study, we apply this method to the western Mediterranean Sea. First we evaluate the QG propagator's capacity to represent the dynamics in this region. We then use this propagator to perform the dynamic interpolation in a spatially idealized case, comparing the reconstructed fields with a fine-resolution numerical model. The results show a general improvement compared to a linear interpolation over a period of 5-10 days. There is spatial and temporal disparity in the performance of the method, with a greater improvement for the regions of high variability and during the winter period. We explored ways of complexifying the QG propagator to better represent the dynamics of the region, influenced by the strong local atmospheric forcing, the geometry of the bassin and its bathymetry. In a second study, we evaluated the contribution of this dynamical interpolation method for mapping real alongtrack altimetric data. For this study, covariance structures derived from the QG model's evolution are integrated into an optimal interpolation scheme. The resulting dynamical interpolated maps are compared to the current altimetric maps. This study, which participates in the preparation of the exploitation of the future high resolution data of the SWOT mission, demonstrates the effectiveness of a relatively simple model to improve the resolution of the altimetric maps. Nevertheless, all of these results reveal the difficulty to optimally parameterize this mapping method to caracterize the dynamics in a region which presents a strong spatial and temporal variability. This work also highlights the need to better exploit the independant data to rigorously evaluate the improvement at small scales, which have significant impacts on the dynamics of the mesoscale, particularly on energy transfers within the ocean and on physico-biological interactions.

La convection thermique dans les objets naturels de grande taille est associée à de fortes variations de la pression, hydrostatique au premier ordre. C’est le cas pour l’atmosphère de la Terre (et d’autres planètes), les planètes gazeuses géantes, les étoiles, mais aussi l’intérieur des planètes telluriques. De part l’importance des effets de compressibilité, l’approximation de Boussinesq n’y est pas vérifiée et d’autres modèles, comportant également des approximations, sont utilisés : les modèles anélastiques. Toutefois, peu d’expériences ont été réalisées pour les vérifier. Cette thèse présente une expérience dont les paramètres ont été optimisés afin d’obtenir des effets de compressibilité importants en laboratoire. Pour ce faire, une gravité apparente forte est obtenue à l’aide d’une centrifugeuse et du xénon gazeux est utilisé, nous permettant d’atteindre un nombre de dissipation significatif. Ces expériences ont permis l’observation en laboratoire d’un gradient adiabatique de 3 K/cm et d’un exposant de 0,3 pour la loi de puissance caractérisant le transfert thermique turbulent entre le nombre de Nusselt et le nombre de Rayleigh superadiabatique.L’étude des fluctuations de pression et de température montrant que l’écoulement est quasi-geostrophique dû à la forte rotation imposée par la centrifugeuse, un modèle anélastique quasi-géostrophique est développé afin de réaliser des simulations numériques bidimensionnelles relatives à l’expérience. / In large natural objects, thermal convection is associated with large pressure differences, mainly due to hydrostatic balance. This is true in the atmosphere of the Earth (and other planets), in gas giant planets, in stars, but also in the interior of telluric planets. Boussinesq approximation is not valid owing to large compressibility effects, and other approximate models can be used to model these objects, like the anelastic approximation. However, very few experiments have been performed to assess these models. In the present PhD thesis, an experiment is shown, with parameters designed to maximize compressibility effects in a laboratory. In this perspective, an enhanced apparent gravity is obtained using a centrifuge, and Xenon gas is used, allowing us to reach a significant dissipation parameter. In our experiments, we have observed an adiabatic gradient of 3~K/cm and the power law between the superadiabatic Rayleigh number and the Nusselt number measuring the turbulent heat transfer is characterized by an exponent 0.3.Measurements of temperature and pressure fluctuations show that the flow is quasi-geostrophic as a result of the strong rotation rate of the centrifuge. An anelastic, quasi-geostrophic model has then been developed and solved numerically in the same configuration as the experiments.

In non-rotating fluids, boundary-layer separation occurs when the nearly inviscid flow just outside a viscous boundary-layer experiences an appreciable deceleration due to a region of adverse pressure gradient. The fluid ceases to flow along the boundary due to a flow recirculation region close to the boundary. The flow is then said to be "detached." In recent decades, attention has shifted to the study of boundary-layer separation in a rotating reference frame due to its significance in Geophysical Fluid Dynamics (GFD). Since the Earth is a rotating sphere, the so-called β-plane approximation f = f0 + βy is often used to account for the inherent meridional variation of the Coriolis parameter, f, while still solving the governing equations on a plane. Numerical simulations of currents on the β-plane have been useful in understanding ocean currents such as the Gulf Stream, the Brazil Current, and the Antarctic Circumpolar Current to name a few. In this thesis, we first consider the problem of prograde flow past a cylindrical obstacle on the β-plane. The problem is governed by the barotropic vorticity equation and is solved using a numerical method that is a combination of a finite difference method and a spectral method. A modified form of the β-plane approximation is proposed to avoid computational difficulties. Results are given and discussed for flow past a circular cylinder at selected Reynolds numbers (Re) and non-dimensional β-parameters (β^). Results are then given and discussed for flow past an elliptic cylinder of a fixed aspect ratio (r = 0.2) and at two angles of inclination (90°, 15°) at selected Re and β^. In general, it is found that the β-effect acts to suppress boundary-layer separation and to allow Rossby waves to form in the exterior flow field. In the asymmetrical case of an inclined elliptic cylinder, the β-effect was found to constrain the region of vortex shedding to a small region near the trailing edge of the cylinder. The shed vortices were found to propagate around the trailing edge instead of in the expected downstream direction, as observed in the non-rotating case. The second problem considered in this thesis is the separation of western boundary currents from a curved coastline. This problem is also governed by the barotropic vorticity equation, and it is solved on an idealized model domain suitable for investigating the effects that boundary curvature has on the tendency of a boundary current to separate. The numerical method employed is a two-dimensional Chebyshev spectral collocation method and yields high order accuracy that helps to better resolve the boundary-layer dynamics in comparison to low-order methods. Results are given for a selection of boundary curvatures, non-dimensional β-parameters (β^), Reynolds numbers (Re), and Munk Numbers (Mu). In general, it is found than an increase in β^ will act to suppress boundary-layer separation. However, a sufficiently sharp obstacle can overcome the β-effect and force the boundary current to separate regardless of the value of β^. It is also found that in the inertial limit (small Mu, large Re) the flow region to the east of the primary boundary current is dominated by strong wave interactions and large eddies which form as a result of shear instabilities. In an interesting case of the inertial limit, strong waves were found to interact with the separation region, causing it to expand and propagate to the east as a large eddy. This idealized the mechanism by which western boundary currents such as the Gulf Stream generate eddies in the world's oceans.

In non-rotating fluids, boundary-layer separation occurs when the nearly inviscid flow just outside a viscous boundary-layer experiences an appreciable deceleration due to a region of adverse pressure gradient. The fluid ceases to flow along the boundary due to a flow recirculation region close to the boundary. The flow is then said to be "detached." In recent decades, attention has shifted to the study of boundary-layer separation in a rotating reference frame due to its significance in Geophysical Fluid Dynamics (GFD). Since the Earth is a rotating sphere, the so-called β-plane approximation f = f0 + βy is often used to account for the inherent meridional variation of the Coriolis parameter, f, while still solving the governing equations on a plane. Numerical simulations of currents on the β-plane have been useful in understanding ocean currents such as the Gulf Stream, the Brazil Current, and the Antarctic Circumpolar Current to name a few. In this thesis, we first consider the problem of prograde flow past a cylindrical obstacle on the β-plane. The problem is governed by the barotropic vorticity equation and is solved using a numerical method that is a combination of a finite difference method and a spectral method. A modified form of the β-plane approximation is proposed to avoid computational difficulties. Results are given and discussed for flow past a circular cylinder at selected Reynolds numbers (Re) and non-dimensional β-parameters (β^). Results are then given and discussed for flow past an elliptic cylinder of a fixed aspect ratio (r = 0.2) and at two angles of inclination (90°, 15°) at selected Re and β^. In general, it is found that the β-effect acts to suppress boundary-layer separation and to allow Rossby waves to form in the exterior flow field. In the asymmetrical case of an inclined elliptic cylinder, the β-effect was found to constrain the region of vortex shedding to a small region near the trailing edge of the cylinder. The shed vortices were found to propagate around the trailing edge instead of in the expected downstream direction, as observed in the non-rotating case. The second problem considered in this thesis is the separation of western boundary currents from a curved coastline. This problem is also governed by the barotropic vorticity equation, and it is solved on an idealized model domain suitable for investigating the effects that boundary curvature has on the tendency of a boundary current to separate. The numerical method employed is a two-dimensional Chebyshev spectral collocation method and yields high order accuracy that helps to better resolve the boundary-layer dynamics in comparison to low-order methods. Results are given for a selection of boundary curvatures, non-dimensional β-parameters (β^), Reynolds numbers (Re), and Munk Numbers (Mu). In general, it is found than an increase in β^ will act to suppress boundary-layer separation. However, a sufficiently sharp obstacle can overcome the β-effect and force the boundary current to separate regardless of the value of β^. It is also found that in the inertial limit (small Mu, large Re) the flow region to the east of the primary boundary current is dominated by strong wave interactions and large eddies which form as a result of shear instabilities. In an interesting case of the inertial limit, strong waves were found to interact with the separation region, causing it to expand and propagate to the east as a large eddy. This idealized the mechanism by which western boundary currents such as the Gulf Stream generate eddies in the world's oceans.