This thesis presents an investigation into the dynamics of vortex rings impacting a sharply-stratified density interface. This problem has a long history and is important for understanding how individual eddies in stratified turbulence mix the density field. We tackle this problem using a combination of experimental, numerical and modelling techniques to understand the flow instability and subsequent mixing induced by the impinging vortex ring. Our findings demonstrate that there exists a critical Richardson number, corresponding to a mixing transition, beyond which the mixing efficiency is constant. Using a novel Stereo Particle Image Velocimetry (Stereo-PIV) technique, we analyze a series of vortex ring experiments. By amalgamating an ensemble of these experiments, we measure the full, time-resolved, three-dimensional velocity field of the vortex-ring interaction. These measurements capture the instability that is produced on the baroclinically generated vorticity field. This instability is identified as a Crow-like instability. At low Richardson numbers, the timescale of the interface rebound is faster than that of the instability. As a result, there exists a critical Richardson number below which the Crow-like instability will not have sufficient time to grow to large amplitude. By generating a large number of vortex-ring interactions, we measure the incremental change to the stratification. After an initialization period, there is strong evidence to suggest that the mixing due to each vortex ring becomes constant over a moderate range of Richardson numbers. We suggest that the mixing efficiency of the vortex rings does drop at low Richardson numbers (below unity) in agreement with the analysis of the Stereo-PIV measurements. A model of the system accurately predicts the dependence of the mixing rate on the Richardson number. Based upon our study of the vortex-ring system, we construct a one-dimensional turbulence model that includes the energy advection from the vortex rings. This model is validated with both physical experiments and numerical simulations of repeated vortex-ring generations. The constant mixing efficiency regime is recovered in all three methodologies. Through examining the detailed dynamics of the flow, this work suggests that there exists a critical Richardson number corresponding to a transition between mixing regimes, and that this critical Richardson number is a result of the growth of a Crow-like instability. We have highlighted how to improve current mixing-models to capture this physics. New avenues of future research are currently underway to study the mixing produced by a stratified mixing-box experiment in light of these new developments.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21366号 / 工博第4525号 / 新制||工||1705(附属図書館) / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 花崎 秀史, 教授 黒瀬 良一, 教授 稲室 隆二 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

abstract: A continuously and stably stratified fluid contained in a square cavity subjected to harmonic body forcing is studied numerically by solving the Navier-Stokes equations under the Boussinesq approximation. Complex dynamics are observed near the onset of instability of the basic state, which is a flow configuration that is always an exact analytical solution of the governing equations. The instability of the basic state to perturbations is first studied with linear stability analysis (Floquet analysis), revealing a multitude of intersecting synchronous and subharmonic resonance tongues in parameter space. A modal reduction method for determining the locus of basic state instability is also shown, greatly simplifying the computational overhead normally required by a Floquet study. Then, a study of the nonlinear governing equations determines the criticality of the basic state's instability, and ultimately characterizes the dynamics of the lowest order spatial mode by the three discovered codimension-two bifurcation points within the resonance tongue. The rich dynamics include a homoclinic doubling cascade that resembles the logistic map and a multitude of gluing bifurcations. The numerical techniques and methodologies are first demonstrated on a homogeneous fluid contained within a three-dimensional lid-driven cavity. The edge state technique and linear stability analysis through Arnoldi iteration are used to resolve the complex dynamics of the canonical shear-driven benchmark problem. The techniques here lead to a dynamical description of an instability mechanism, and the work serves as a basis for the remainder of the dissertation. / Dissertation/Thesis / Supplemental Materials Description File / zip file containing 10 mp4 formatted video animations, as well as a text readme and the previously submitted Supplemental Materials Description File / Doctoral Dissertation Mathematics 2019

Os conceitos de competência do escoamento e de capacidade de transporte foram desenvolvidos para escoamentos fluviais e acabam sendo transferidos para a modelagem de correntes de turbidez. No entanto, não é claro até que ponto o estabelecimento de analogias entre o ambiente fluvial e as correntes de turbidez pode ser realizado. Nesse contexto, o principal objetivo deste trabalho foi avaliar os conceitos de competência e de capacidade nas correntes de turbidez. O estudo foi desenvolvido experimentalmente, em um canal de inclinação variável de 4 m de comprimento, 40 cm de altura e 12 cm de largura. Um leito móvel foi construído em um trecho intermediário do canal utilizando sedimento - carvão mineral (ρ = 1405 kgm³) - com tamanho areia média. No total, 30 simulações de correntes de turbidez contínuas foram realizadas, utilizando o mesmo sedimento, porém com tamanho areia muito fina. Foram simuladas três declividades diferentes (6%, 0,3% e 0,015%), vazões de injeção entre 15 e 25 lmin, concentrações iniciais variando entre 0,03% e 5,5% e a duração dos ensaios ficou compreendida entre 3 e 30 min. O levantamento do perfil longitudinal do leito móvel, antes e após o ensaio, foi realizado e todo o sedimento foi coletado. Três quantidades distintas de sedimento foram quantificadas: a quantidade depositada antes do leito móvel, a quantidade depositada no leito móvel e a quantidade depositada depois do leito móvel. O cálculo da eficiência de transporte das correntes de turbidez no trecho do leito móvel, bem como das suas descargas sólidas, foi realizado. Também foram realizadas análises granulométricas do sedimento depositado antes e após do leito móvel. Por fim, parâmetros do fluxo foram obtidos (altura e velocidade) através de análises visuais e números adimensionais clássicos do transporte sólido em canais abertos foram avaliados. A partir da interpretação dos dados, conclui-se que os conceitos de competência do escoamento e de capacidade de transporte não foram capazes de refletir o diâmetro característico do sedimento transportado pelas correntes simuladas e a capacidade máxima de transporte desses fluxos, como normalmente ocorre em escoamentos fluviais. A relação entre a eficiência de transporte desses fluxos e a descarga sólida dos mesmos indicou que a partir de uma região a eficiência tornou-se invariante. Essa relação possui curvas com tendência logarítmica e as suas assíntotas ocorreram em valores de eficiência da ordem de 50% (inclinação de 6%) e de 40% (inclinações de 0,3% e 0,015%). A relação entre o diâmetro característico do sedimento depositado depois do leito e antes do leito indicou uma diminuição de cerca de 18% no tamanho dos grãos depositados a jusante. / The modeling of turbidity currents uses the concepts of competence and flow capacity that have been developed based on river hydraulics. However, the analogies between the fluvial environment and turbidity currents are not very clear. The main purpose of this study was to evaluate the competence and flow capacity of turbidity currents. The study was performed using an experimental channel 4 m long, 40 cm high, and 12 cm wide with variable slope. A mobile bed of medium sand-size - mineral coal (ρ=1405 kgm³) - was constructed in an intermediate area of the channel. In total, 30 simulations of continuous turbidity currents were performed and the sediment used in the turbidity currents was very fine sand-size mineral coal. The simulations were accomplished considering three different channel slopes (6%, 0.3% e 0.015%); injection discharge varied between 15 and 25 l/min, and initial volumetric concentrations varied between 0.03% and 5.5%. The simulations lasted between 3 and 30 minutes. The longitudinal profile of the mobile bed was analyzed before and after each simulation, and all the sediment was collected at the end. Three different amounts of sediment were quantified: the amount of sediment deposited before, on, and after the mobile bed. Based on this data, both the transport efficiency and solid discharge of the turbidity current on the mobile bed were determined. Particle-size distribution of the deposited sediment before and after the mobile bed was also carried out. Finally, flow parameters were obtained (high and velocity) considering visual evaluation and the classical dimensional numbers in sediment transport in open channel flows were analyzed. The data interpretation revealed that the competence and flow capacity parameters were not able to reflect the grain diameter transported by the simulated currents and a maximum flow capacity of these flows, as usually is observed in fluvial flows. The relation between the transport efficiency and solid discharge of these flows demonstrated that after a certain point, the efficiency became constant. This relation resulted in log trend curves with asymptotes located at efficiency values of approximately 50% (6% slope) and 40% (0.3% and 0.015% slopes). The characteristic diameter of the sediment deposited after the mobile bed presented a reduction of 18% when compared to the sediment deposited before the mobile bed.

The speed and efficiency of stratified turbulent mixing in homogenising temperatures, chemical composition and flow speeds makes it one of farthest reaching fluid mechanical phenomenon for life on earth. It is an aesthetically beautiful phenomenon, rich in complex physical behaviours and extremely challenging to model mathematically. Laboratory experiments have a valuable role to play to guide theoretical and numerical work towards a better understanding of this phenomenon by providing insight into real flows under controlled conditions. This dissertation addresses some aspects of the laboratory buoyancy-driven exchange flows through an inclined duct connecting two reservoirs containing fluids of different densities. We employ a novel experimental technique to perform near-instantaneous, volumetric measurements of the three-component velocity field and density field simultaneously, providing an unprecedented quantitative picture of these sustained stratified shear flows. We start by characterising the variety of observed behaviours, or flow regimes, as we vary the density difference between the two reservoirs, the angle of inclination of the duct with respect to the horizontal, the way the density difference is achieved (solutions of salt/fresh water or cold/warm water) and the geometry of the duct. These empirical observations allow us to formulate a number of specific research questions, guiding the work of the next chapters. We then focus on the regime in which Holmboe waves are observed, and demonstrate that these well-known interfacial travelling disturbances have a distinct structure when confined by solid boundaries. We characterise this structure and identify the physical mechanisms at its origin by means of linear stability theory. Since Holmboe waves are found in the intermediate, transitional regime between laminar and turbulent flows, we conjecture that their structure may be relevant to more turbulent flows, where resembling structures are indeed observed. Next, we tackle the quantitative analysis of universal transition curves separating the observed flow regimes (laminar, waves, intermittently turbulent or fully turbulent) as well and the net mass flow rate exchanged by the reservoirs. We show that these long-lasting questions in the study of exchange flows can be addressed in the framework of frictional hydraulic theory, and we derive detailed scaling laws involving only a few nondimensional parameters. Finally, we overcome some of the limitations of hydraulic theory by performing a more detailed, time-resolved, three-dimensional analysis of the energetics of the wave, intermittent and turbulent regimes. We identify and quantify the sources and sinks of energy in each regime, and identify some of the structures responsible for viscous energy dissipation and mixing. We also suggest possible future directions for the present work given recent progress in the literature.

Os conceitos de competência do escoamento e de capacidade de transporte foram desenvolvidos para escoamentos fluviais e acabam sendo transferidos para a modelagem de correntes de turbidez. No entanto, não é claro até que ponto o estabelecimento de analogias entre o ambiente fluvial e as correntes de turbidez pode ser realizado. Nesse contexto, o principal objetivo deste trabalho foi avaliar os conceitos de competência e de capacidade nas correntes de turbidez. O estudo foi desenvolvido experimentalmente, em um canal de inclinação variável de 4 m de comprimento, 40 cm de altura e 12 cm de largura. Um leito móvel foi construído em um trecho intermediário do canal utilizando sedimento - carvão mineral (ρ = 1405 kgm³) - com tamanho areia média. No total, 30 simulações de correntes de turbidez contínuas foram realizadas, utilizando o mesmo sedimento, porém com tamanho areia muito fina. Foram simuladas três declividades diferentes (6%, 0,3% e 0,015%), vazões de injeção entre 15 e 25 lmin, concentrações iniciais variando entre 0,03% e 5,5% e a duração dos ensaios ficou compreendida entre 3 e 30 min. O levantamento do perfil longitudinal do leito móvel, antes e após o ensaio, foi realizado e todo o sedimento foi coletado. Três quantidades distintas de sedimento foram quantificadas: a quantidade depositada antes do leito móvel, a quantidade depositada no leito móvel e a quantidade depositada depois do leito móvel. O cálculo da eficiência de transporte das correntes de turbidez no trecho do leito móvel, bem como das suas descargas sólidas, foi realizado. Também foram realizadas análises granulométricas do sedimento depositado antes e após do leito móvel. Por fim, parâmetros do fluxo foram obtidos (altura e velocidade) através de análises visuais e números adimensionais clássicos do transporte sólido em canais abertos foram avaliados. A partir da interpretação dos dados, conclui-se que os conceitos de competência do escoamento e de capacidade de transporte não foram capazes de refletir o diâmetro característico do sedimento transportado pelas correntes simuladas e a capacidade máxima de transporte desses fluxos, como normalmente ocorre em escoamentos fluviais. A relação entre a eficiência de transporte desses fluxos e a descarga sólida dos mesmos indicou que a partir de uma região a eficiência tornou-se invariante. Essa relação possui curvas com tendência logarítmica e as suas assíntotas ocorreram em valores de eficiência da ordem de 50% (inclinação de 6%) e de 40% (inclinações de 0,3% e 0,015%). A relação entre o diâmetro característico do sedimento depositado depois do leito e antes do leito indicou uma diminuição de cerca de 18% no tamanho dos grãos depositados a jusante. / The modeling of turbidity currents uses the concepts of competence and flow capacity that have been developed based on river hydraulics. However, the analogies between the fluvial environment and turbidity currents are not very clear. The main purpose of this study was to evaluate the competence and flow capacity of turbidity currents. The study was performed using an experimental channel 4 m long, 40 cm high, and 12 cm wide with variable slope. A mobile bed of medium sand-size - mineral coal (ρ=1405 kgm³) - was constructed in an intermediate area of the channel. In total, 30 simulations of continuous turbidity currents were performed and the sediment used in the turbidity currents was very fine sand-size mineral coal. The simulations were accomplished considering three different channel slopes (6%, 0.3% e 0.015%); injection discharge varied between 15 and 25 l/min, and initial volumetric concentrations varied between 0.03% and 5.5%. The simulations lasted between 3 and 30 minutes. The longitudinal profile of the mobile bed was analyzed before and after each simulation, and all the sediment was collected at the end. Three different amounts of sediment were quantified: the amount of sediment deposited before, on, and after the mobile bed. Based on this data, both the transport efficiency and solid discharge of the turbidity current on the mobile bed were determined. Particle-size distribution of the deposited sediment before and after the mobile bed was also carried out. Finally, flow parameters were obtained (high and velocity) considering visual evaluation and the classical dimensional numbers in sediment transport in open channel flows were analyzed. The data interpretation revealed that the competence and flow capacity parameters were not able to reflect the grain diameter transported by the simulated currents and a maximum flow capacity of these flows, as usually is observed in fluvial flows. The relation between the transport efficiency and solid discharge of these flows demonstrated that after a certain point, the efficiency became constant. This relation resulted in log trend curves with asymptotes located at efficiency values of approximately 50% (6% slope) and 40% (0.3% and 0.015% slopes). The characteristic diameter of the sediment deposited after the mobile bed presented a reduction of 18% when compared to the sediment deposited before the mobile bed.

Os conceitos de competência do escoamento e de capacidade de transporte foram desenvolvidos para escoamentos fluviais e acabam sendo transferidos para a modelagem de correntes de turbidez. No entanto, não é claro até que ponto o estabelecimento de analogias entre o ambiente fluvial e as correntes de turbidez pode ser realizado. Nesse contexto, o principal objetivo deste trabalho foi avaliar os conceitos de competência e de capacidade nas correntes de turbidez. O estudo foi desenvolvido experimentalmente, em um canal de inclinação variável de 4 m de comprimento, 40 cm de altura e 12 cm de largura. Um leito móvel foi construído em um trecho intermediário do canal utilizando sedimento - carvão mineral (ρ = 1405 kgm³) - com tamanho areia média. No total, 30 simulações de correntes de turbidez contínuas foram realizadas, utilizando o mesmo sedimento, porém com tamanho areia muito fina. Foram simuladas três declividades diferentes (6%, 0,3% e 0,015%), vazões de injeção entre 15 e 25 lmin, concentrações iniciais variando entre 0,03% e 5,5% e a duração dos ensaios ficou compreendida entre 3 e 30 min. O levantamento do perfil longitudinal do leito móvel, antes e após o ensaio, foi realizado e todo o sedimento foi coletado. Três quantidades distintas de sedimento foram quantificadas: a quantidade depositada antes do leito móvel, a quantidade depositada no leito móvel e a quantidade depositada depois do leito móvel. O cálculo da eficiência de transporte das correntes de turbidez no trecho do leito móvel, bem como das suas descargas sólidas, foi realizado. Também foram realizadas análises granulométricas do sedimento depositado antes e após do leito móvel. Por fim, parâmetros do fluxo foram obtidos (altura e velocidade) através de análises visuais e números adimensionais clássicos do transporte sólido em canais abertos foram avaliados. A partir da interpretação dos dados, conclui-se que os conceitos de competência do escoamento e de capacidade de transporte não foram capazes de refletir o diâmetro característico do sedimento transportado pelas correntes simuladas e a capacidade máxima de transporte desses fluxos, como normalmente ocorre em escoamentos fluviais. A relação entre a eficiência de transporte desses fluxos e a descarga sólida dos mesmos indicou que a partir de uma região a eficiência tornou-se invariante. Essa relação possui curvas com tendência logarítmica e as suas assíntotas ocorreram em valores de eficiência da ordem de 50% (inclinação de 6%) e de 40% (inclinações de 0,3% e 0,015%). A relação entre o diâmetro característico do sedimento depositado depois do leito e antes do leito indicou uma diminuição de cerca de 18% no tamanho dos grãos depositados a jusante. / The modeling of turbidity currents uses the concepts of competence and flow capacity that have been developed based on river hydraulics. However, the analogies between the fluvial environment and turbidity currents are not very clear. The main purpose of this study was to evaluate the competence and flow capacity of turbidity currents. The study was performed using an experimental channel 4 m long, 40 cm high, and 12 cm wide with variable slope. A mobile bed of medium sand-size - mineral coal (ρ=1405 kgm³) - was constructed in an intermediate area of the channel. In total, 30 simulations of continuous turbidity currents were performed and the sediment used in the turbidity currents was very fine sand-size mineral coal. The simulations were accomplished considering three different channel slopes (6%, 0.3% e 0.015%); injection discharge varied between 15 and 25 l/min, and initial volumetric concentrations varied between 0.03% and 5.5%. The simulations lasted between 3 and 30 minutes. The longitudinal profile of the mobile bed was analyzed before and after each simulation, and all the sediment was collected at the end. Three different amounts of sediment were quantified: the amount of sediment deposited before, on, and after the mobile bed. Based on this data, both the transport efficiency and solid discharge of the turbidity current on the mobile bed were determined. Particle-size distribution of the deposited sediment before and after the mobile bed was also carried out. Finally, flow parameters were obtained (high and velocity) considering visual evaluation and the classical dimensional numbers in sediment transport in open channel flows were analyzed. The data interpretation revealed that the competence and flow capacity parameters were not able to reflect the grain diameter transported by the simulated currents and a maximum flow capacity of these flows, as usually is observed in fluvial flows. The relation between the transport efficiency and solid discharge of these flows demonstrated that after a certain point, the efficiency became constant. This relation resulted in log trend curves with asymptotes located at efficiency values of approximately 50% (6% slope) and 40% (0.3% and 0.015% slopes). The characteristic diameter of the sediment deposited after the mobile bed presented a reduction of 18% when compared to the sediment deposited before the mobile bed.

This thesis studies the implementation of an Explicit Algebraic Reynolds-Stress Model(EARSM) for Atmospheric Boundary Layer (ABL) in an open source ComputationalFluid Dynamics (CFD) software, OpenFOAM, following the guidance provided by thewind company ENERCON that aims to make use of this novel model to improvesites’ wind-field predictions. After carefully implementing the model in OpenFOAM,the EARSM implementation is verified and validated by testing it with a stratifiedCouette flow case. The former was done by feeding mean flow properties, takenfrom OpenFOAM, in a python tool containing the full EARSM system of equationsand constants, and comparing the resulting flux profiles with the ones extracted bythe OpenFOAM simulations. Subsequently, the latter was done by comparing theprofiles of the two universal functions used by Monin-Obukhov Similarity Theory(MOST) for mean velocity and temperature to the results obtained by Želi et al. intheir study of the EARSM applied to a single column ABL, in “Modelling of stably-stratified, convective and transitional atmospheric boundary layers using the explicitalgebraic Reynolds-stress model” (2021). The verification of the model showed minordifferences between the flux profiles from the python tool and OpenFOAM thus, themodel’s implementation was deemed verified, while the validation step showed nodifference in the unstable and neutral stratification cases, but a significant discrepancyfor stably stratified flow. Nonetheless, the reason behind the inconsistency is believedto be related to the choice of boundary conditions thus, the model’s implementationitself is considered validated. Finally, the comparison between the EARSM and the k − ε model showed thatthe former is able to capture the physics of the flow properties where the latter failsto. In particular, the diagonal momentum fluxes resulting from the EARSM reflectthe observed behaviour of being different from each other, becoming isotropic withaltitude in the case of unstable stratification, and having magnitude u′u′ > v′v′ > w′w′ for stably stratified flows. On the other hand, the eddy viscosity assumption used bythe k − ε model computes the diagonal momentum fluxes as being equal to each other.Moreover, the EARSM captures more than one non-zero heat flux component in theCouette flow case, which has been observed to be the case in literature, while the eddydiffusivity assumption used by the k − ε model only accounts for one non-zero heat fluxcomponent.

Les océans de la Terre sont stratifiés en densité par les gradients de température et de salinité.L'interaction des courants de marée avec la topographie du fond océanique entraîne donc le rayonnement des ondes de gravité interne dans l'intérieur de l'océan. Ces ondes sont appelées marées internes et leur dissipation due à le déferlement des ondes nonlinéaires joue un rôle important dans le mélange de l'océan abyssal, et donc dans la circulation océanique à la grande échelle.Dans ce contexte, nous étudions la génération des ondes internes par l’oscillation d’objet de différentes géométries simplifiées afin de modéliser le marée barotropique sur la topographie océanique et considérons les effets linéaires et nonlinéaires sur ces ondes résultant d’interactions avec l'objet et entre ces ondes.La contribution relativement nouvelle de cette thèse est l'étude des aspects de flux tridimensionnels qui étaient accessibles avec notre approche expérimentale, et sont généralement difficiles à étudier par modélisation numérique et analytique.Nous étudions d'abord la structure des ondes fundamentale et des harmoniques supérieur pour un sphéroïde oscillant, émettant des ondes divergentes. Les harmoniques supérieures sont générées par l'instabilité non linéaire à la surface de l'objet avec des effets nonlinéaires dans la zone d'intersection des faisceaux fundamentales. Ils peuvent se croiser et se concentrer, donc augmenter d'énergie, et devenir dominant sur les ondes fundamentales. On détermine les structures horizontales des ondes fundamentale et des harmoniques supérieures.Subséquemment, nous considérons les ondes générées par un tore oscillant, qui convergent vers un point focal. En dehors de cette région focale, les résultats expérimentaux et les prédictions théoriques sont en bon accord, mais dans la région focale, l'amplitude de l'onde est deux fois plus grande que près du tore, conduisant à une amplification locale nonlinéaire et à un déferlement des onde pour les grandes amplitudes d'oscillations. En conséquence, la propagation des ondes fundamentales se trouve entravée dans la région focale. L'onde stationnaire se forme alors que de nouvelles ondes sont générées et émises de cette région focale.Un tore plus grand a été testé sur la plate-forme Coriolis pour comparer la focalisation des ondes de gravité internes, inertie-gravité et des ondes inertielles dans un régime faiblement visqueux. En raison de la complexité de la zone focale, une seconde harmonique est observée même quand l'amplitude d'oscillation est faible. Le champ de vorticité verticale des ondes de gravité interne présente une structure dipolaire dans la zone focale, qui se transforme dans le cas tournant en une structure de vortex "Yin-Yang". La structure globale des faisceaux des ondes inertiels est proche de celle pour des ondes de gravité internes, bien q'elle est relativement plus intense. / The Earth's oceans are stratified in density by temperature and salinity gradients.The interaction of tidal currents with ocean bottom topography results therefore in the radiation of internal gravity waves into the ocean interior. These waves are called internal tides and their dissipation owing to nonlinear wave breaking plays an important role in the mixing of the abyssal ocean, and hence in the large-scale ocean circulation.In this context we investigate the generation of internal waves by oscillating objects of different idealized geometries as a model of barotropic flow over ocean topography, and consider linear as well as nonlinear effects on these waves resulting from interactions with the object and from wave--wave interactions.The relatively novel contribution of this thesis is the investigation of three-dimensional flow aspects that were accessible with our experimental approach, and are generally difficult to investigate by numerical and analytical modelling.First we investigate the wave structure of the first and higher harmonics for an oscillating spheroid, emitting diverging waves. Higher harmonics are generated by nonlinear instability at the surface of the object together with nonlinear effects in the zone of intersection of the primary beams. They may intersect and focus, therefore increase in energy, and become dominant over the first harmonic. The horizontal structures of both, first and higher harmonics are determined.We then consider waves generated by an oscillating torus, that are converging to a focal point. Outside this focal region experimental results and theoretical predictions are in good agreement, but in the focal region the wave amplitude is twice as large as it is close to the torus, leading to local nonlinear wave amplification and incipient wave breaking for large oscillation amplitudes. As a result, the propagation of the first harmonic waves is found to be hindered in the focal region. A standing pattern forms, while new waves are generated and emitted away from this focal region.A larger torus has been tested at the Coriolis platform to compare the focusing of internal gravity, inertia--gravity and inertial waves in a low viscous regime. Owing to the complexity of the focal region, a second harmonic is observed even at low oscillation amplitude. The vertical vorticity field of internal gravity waves exhibits a dipolar structure in the focal zone, which transforms in the rotating case into a ``Yin--Yang-shaped'' monopolar vortex structure. The overall structure of the inertial wave beams is close to that for internal gravity waves, though relatively more intense.

Ce travail de thèse cherche à caractériser, à l'aide d’expériences de laboratoire, le mouvement d'un fluide stratifié à la fois tournant et cisaillé. Dans ce contexte on a considéré trois problèmes qui sont issus des observations géophysiques et astrophysiques où ces écoulements sont très communs. En premier nous avons observé expérimentalement et modélisé l'évolution en temps d'un anticyclone en milieu stratifié tournant, dans le but de comprendre la longévité des meddies, des vortex qui se forment à la sortie de la Méditerranée et peuvent perdurer pendant des années. Nos anticyclones modèles montrent une relaxation visqueuse anormale en raison de l’interaction entre stratification et cisaillement. Nos résultats expérimentaux ont été confirmés à l'aide d'un modèle géostrophique et de simulations numériques qui montrent aussi le rôle majeur joué par les circulations secondaires. Dans un deuxième temps nous avons considéré la stabilité linéaire de l'écoulement de Couette Plan, un des plus simple des écoulement plans cisaillés. On montre que cet écoulement devient instable lorsque l'on ajoute de la stratification verticale. Nous remarquons aussi que la structure spatiale de l'instabilité ressemble à celle de certains jets océaniques que l'on observe près de l'équateur. Enfin nous avons caractérisé une instabilité non linéaire dite des zombie vortex qui a été récemment découverte et pourrait jouer un rôle fondamental dans la déstabilisation des disques d'accrétion, une étape fondamentale de la formation des planétaire. Nous avons construit le diagramme de stabilité de la ZVI dans l'espace de trois fréquences caractéristiques et quantifié la dissipation visqueuse. / The present PhD work comes with the scope of characterizing, analysing and modelling some laboratory flows in the simultaneous presence of rotation, stratification and shear. To this aim we address three specific questions inspired by geophysics and astrophysics where these three ambient features are commonly relevant. First we characterize and model the time evolution of a compact anticyclone in a rotating and stratified laboratory flow. We aim to understand the longevity of analogous vortices known as meddies which populate the Atlantic ocean at the exit of the Mediterranean sea. We observe that viscous relaxation happens in an unusual way because of the balance between rotation and stratification. The results are confirmed by a quasi-geostrophic model and numerical simulations which show the crucial role played by secondary circulations. Secondly we consider the linear stability of one of the simplest parallel shear flow, namely the plane Couette Flow, and show that it becomes unstable when adding a vertical stratification. Interestingly the unstable pattern reminds of deep oceanic jets observed close to the equator. The signature of this instability is observed in an ad-hoc experimental flow and interpreted with the support of direct numerical simulations. Finally we characterize the behaviour of a recently disclosed finite amplitude instability, namely the zombie vortex instability or ZVI. This instability appears when rotation, stratification and shear are of the same order and may may destabilize proto-planetary disks. We construct a stability diagram for ZVI in the space of the three ambient frequencies and analyse the effect of viscous dissipation.