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When wind blows over a stratified lake an interface tilt is often generated, and internal waves usually appear after the wind stops. Internal waves in lakes are studied in many literatures, but most assume a hydrostatic pressure balance. In this thesis we discuss the internal Poincare waves and Kelvin waves in a rotating, continuously stratified, flat-bottom, circular lake with fully nonlinear and non-hydrostatic effects. An analytical solution is derived for the linearized system and it provides initial conditions used in the MIT General Circulation Model (MITgcm). This model is chosen due to its non-hydrostatic capability. Both Poincare waves and Kelvin waves are considered. The analytical solution of the linear system is verified numerically when the wave amplitude is small. As the wave amplitude increases the waves become more nonlinear. Poincare waves steepen and generate solitary-like waves with shorter wavelengths, but most of the energy contained in these waves is transferred back and forth between the parent wave and the solitary-like waves. Kelvin waves, on the other hand, steepen and lose their energy to solitary-like waves. The appearance of the solitary-like waves is not absolutely clear and higher resolution is required to clear up the details of this process. This conclusion agrees with de la Fuente et al (2008) who discussed the internal waves in a two-layer model. Moreover, in the Kelvin waves case, unexpected small waves are generated at the side boundaries and travel inwards. The wave amplitude and wavelength of these spurious waves become smaller as the horizontal resolution increases. One possible reason to explain these waves is the use of square grids to approximate the circular lake.

When wind blows over a stratified lake an interface tilt is often generated, and internal waves usually appear after the wind stops. Internal waves in lakes are studied in many literatures, but most assume a hydrostatic pressure balance. In this thesis we discuss the internal Poincare waves and Kelvin waves in a rotating, continuously stratified, flat-bottom, circular lake with fully nonlinear and non-hydrostatic effects. An analytical solution is derived for the linearized system and it provides initial conditions used in the MIT General Circulation Model (MITgcm). This model is chosen due to its non-hydrostatic capability. Both Poincare waves and Kelvin waves are considered. The analytical solution of the linear system is verified numerically when the wave amplitude is small. As the wave amplitude increases the waves become more nonlinear. Poincare waves steepen and generate solitary-like waves with shorter wavelengths, but most of the energy contained in these waves is transferred back and forth between the parent wave and the solitary-like waves. Kelvin waves, on the other hand, steepen and lose their energy to solitary-like waves. The appearance of the solitary-like waves is not absolutely clear and higher resolution is required to clear up the details of this process. This conclusion agrees with de la Fuente et al (2008) who discussed the internal waves in a two-layer model. Moreover, in the Kelvin waves case, unexpected small waves are generated at the side boundaries and travel inwards. The wave amplitude and wavelength of these spurious waves become smaller as the horizontal resolution increases. One possible reason to explain these waves is the use of square grids to approximate the circular lake.

The Madden-Julian Oscillation (MJO) and the Convectively Coupled Equatorial Waves (CCEW) are coherent structures of convection and various large-scale fields. These phenomena are not well understood, despite their importance to the tropical climate. A toy model of the CCEW consisting of a pair of shallow water wave modes coupled by a simple convective parameterization is considered. The linear behavior of the system is analyzed, showing a growth spectrum that is similar to the spectrum that is observed. To explore the processes involved in propagation and maintenance of the MJO disturbance, we analyze the MSE budget of the disturbance within a numerical model. In an idealized experiment, the column-integrated long-wave heating is the only significant source of column-integrated MSE acting to maintain the MJO-like anomaly balanced against the combination of column-integrated horizontal and vertical advection of MSE and Latent Heat Flux. Eastward propagation of the MJO-like disturbance is associated with MSE generated by both column-integrated horizontal and vertical advection of MSE, with the column long-wave heating generating MSE that retards the propagation. The contribution to the eastward propagation by the column-integrated horizontal advection term is dominated by meridional advection of MSE by anomalous synoptic eddies caused by the suppression of eddy activity ahead of the MJO convection. This suppression is linked to the barotropic conversion mechanism; with the gradients of the low frequency wind experienced by the synoptic eddies within the MJO envelope acting to modulate the Eddy Kinetic Energy. The meridional eddy advection’s contribution to poleward propagation is dominated by the mean state’s (meridionally varying) eddy activity acting on the anomalous MSE gradients associated with the MJO. In a follow-up experiment, the variations in the propagation speed of MJO with variations in the imposed SST distribution are seen to be driven by the variations in meridional advection of the mean MSE profile by the MJO-related winds, which are in turn dominated by the variations in the mean MSE profile due to the variations of the SST. A brief investigation of the MSE budget for a more realistic case shows an increase in the MSE sink due to meridional advection as the MJO progresses from genesis over the Indian Ocean to decay in the central Pacific. The increase in this sink appears to be the cause of MJO’s demise. / Physics

Cette thèse s'inscrit dans un contexte d'étude de la dynamique des fronts atmosphériques et océaniques et de l'origine des ondes de gravité dans l'atmosphère. Pour cela on s'intéresse à un front composé de deux couches de fluides miscibles en milieu tournant et soumis à un cisaillement vertical. Un travail à la fois expérimental et numérique met en évidence des phénomènes agéostrophiques qui vont au-delà de la configuration équilibrée usuelle d'un front barocline. D'abord, l'étude des différents régimes instables d'un front en configuration annulaire en terme de nombre de Rossby et de Burger révèle une instabilité agéostrophique couplant des mouvements équilibrés et divergents grâce à la résonance entre une onde de Rossby et une onde de Kelvin. Cette instabilité Rossby-Kelvin a été confirmée numériquement grâce aux structures des perturbations en champs de vitesse dans chaque couche. Ensuite, des structures de petite échelle présentes sur le front ont aussi été observées expérimentalement. Les caractéristiques de l'interface en terme de nombre de Richardson et épaisseurs de l'interface en vitesse et en densité suggère une instabilité de cisaillement de Hölmböe. Une simulation directe numérique axisymmétrique avec un nombre de Schmidt valant 700 confirme cette conjecture. Des ondes inertie-gravité supplémentaires sont observées numériquement sur un mode instable Rossby-Kelvin et le mécanisme de génération de ces ondes est discuté. Enfin l'étude numérique d'un front stable a mis en évidence la présence de couches d'Ekman internes avec une structure additionnelle pour des valeurs élevées de nombre de Schmidt et un faible nombre de Rossby. Dans le cas de front en in/outcropping, la dynamique est modifiée par l'interaction du front avec les couches d'Ekman au niveau du point singulier d'épaisseur nulle. Elle dépend à la fois de la circulation verticale et du mélange sur le nez du front et des nombreuses instabilités possibles associées à des résonances d'ondes horizontalement et verticalement. / This thesis has to be seen within the general study of atmospheric and oceanic fronts and the origin of gravity waves in the atmosphere. In this context we focus on a front in a rotating two-layer miscible fluid under vertical shear. Both experimental and numerical study highlights ageostrophic phenomena going beyond the usual geostrophic equilibrated configuration of a baroclinic front. First, the classification of different instability regimes of a front in an annular configuration as a fonction of Rossby number and Burger number reveals an ageostrophic instability coupling equilibrated and divergent motions due to a resonance between a Rossby wave and a Kelvin wave. This Rossby-Kelvin instability is confirmed numerically by the structure of the perturbation velocity fields in each layer. Second, small-scale structures have also been observed experimentally. Caracteristics of the interface in function of Richardson number and density and velocity interface thicknesses suggests the presence of the Hölmböe shear instability. A direct numerical simulation with an axisymmetric configuration and with a Schmidt number 700 confirms this conjecture. Other smalle-scale perturbations compatible with inertia-gravity waves have been observed numerically superimposed on an unstable Rossby-Kelvin front and the wave generation mechanism is discussed. In addition, a numerical study of a stable front highlighted the presenec of internal Ekman layers with an additional interfacial structure in the case of high Schmidt number and small Rossby number. For fronts in in/outcropping, front dynamics is modified by interaction with Ekman boundary layer at the location of the intersection zero-thickness singular point. It depends on both vertical circulation and mixing on the nose of the front and the various possible instabilities associated to horizontal or vertical wave resonances.

The Madden-Julian Oscillation (MJO), a tropical phenomenon that exists on the time scale of 30-90 days, commonly initiates over the Indian Ocean and slowly propagates into the western Pacific as a series of convective events, which have time scales on the order of hours or days. These events and the overall MJO convective envelope may interact with convectively coupled waves such as Kelvin waves that propagate more rapidly eastward with time scales of 3-5 days. Radar and sounding data collected during the DYNAMO/AMIE/CINDY2011 field campaign from October 2011 to February 2012 in the central Indian Ocean are used to study the interaction between Kelvin waves and the MJO in terms of atmospheric and cloud properties. The focus is on characterizing the precipitation characteristics, convective cloud spectrum, and atmospheric profiles of Kelvin waves during the active and suppressed phases of the MJO to gain insight on MJO initiation. Characteristics of waves identified using different satellite thresholds and filtering methods are compared. Composites of the radar and sounding observations are calculated for a total of ten Kelvin waves and three MJO events that occurred during the field campaign. Analyzed radar products include convective-stratiform classification of rain rate, rain area, and echo-top heights, as well as cloud boundaries. Sounding data includes profiles of wind speed and direction and relative humidity. Kelvin waves that occur during the suppressed MJO are convectively weaker than Kelvin waves during the active MJO, but display previously documented structure of low-level convergence and a moist atmosphere prior to the wave passage. During the active MJO, Kelvin waves have stronger convective and stratiform rain, and the entire event is longer, suggesting a slower moving wave. The Kelvin wave vertical structure is somewhat overwhelmed by the convective envelope associated with the MJO. When the MJO is developing, the Kelvin wave displays a moisture-rich environment after the passage, providing deep tropospheric moisture that is postulated to be important for the onset of the MJO. The convective cloud population prior to MJO initiation shows increased moisture and a population of low- to mid-level clouds. The moisture precedes shallow convection, which develops into the deep convection of the MJO, supporting the discharge-recharge theory of MJO initiation. Additionally, enhanced moisture after the passage of the pre-MJO Kelvin wave could also support the frictional Kelvin-Rossby wave-CISK theory of MJO initiation. With a better understanding of the interaction between the initiation of the MJO and Kelvin waves, the relationships between the environment and the onset of the convection of the MJO can be improved.

La thèse est une contribution à l’étude des tourbillons longitudinaux qui se développent sur la lunette arrière des véhicules automobiles, dans l’idée de provoquer leur éclatement afin de réduire la traînée aérodynamique. On conçoit tout d’abord un système d’acquisition dénommé A-SPIV, permettant de reconstruire le champ moyen de vitesse 3D d’un sillage turbulent à partir de plans stéréo-PIV acquis par translation du système caméras-laser, sans qu’il soit nécessaire de le recalibrer. En complément, on propose une méthode de reconstruction de la pression moyenne reposant sur les données A-SPIV et sur une mesure de la pression pariétale. L’ensemble forme un nouveau protocole expérimental, validé dans le sillage d’un corps d’Ahmed 25° et dont les résultats à haut Reynolds sont comparés à la littérature existante. L'analyse topologique des tourbillons longitudinaux suggère l’existence d’un éclatement tourbillonnaire spontané dans le sillage proche, malgré l’absence de point de stagnation. On démontre formellement l’existence de cet éclatement par deux critères théoriques qui considèrent ce phénomène, soit comme la conséquence d’une réorganisation de la vorticité, soit comme la résultante d’une accumulation, en un point critique, d’ondes inertielles se propageant le long du tourbillon. Les analyses sous-jacentes sont menées dans un repère cylindrique attaché à l’axe tourbillonnaire et prédisent une même position d’éclatement, en bon accord avec la position singulière issue des mesures A-SPIV. La thèse se conclut par une analyse de stabilité globale de l'écoulement moyen qui suggère un lien possible entre l’éclatement et une instabilité globale de l’écoulement tourbillonnaire. / This thesis is a contribution to the study of the longitudinal vortices developing in the near wake of ground vehicles, with the general purpose of reducing the aerodynamic drag by triggering the vortex breakdown phenomenon. We present a new data acquisition system called A-SPIV, allowing to reconstruct a 3D turbulent time-averaged velocity field from stereo-PIV planes measured by translation of the whole cameras-laser system, with no need to recalibrate. We also propose a method to reconstruct the mean pressure in the bulk from the A-SPIV data and from a dedicated wall static pressure measurement. This new overall experimental protocol is applied to a standard aerodynamic test-case, the 25° Ahmed body, all results being compared and validated at high turbulent Reynolds number against existing data from the literature. A thorough analysis of the longitudinal vortices suggests the occurrence of a spontaneous vortex breakdown in the near-wake, although there exist no stagnation point in the experimental data. Such vortex breakdown is therefore evidenced using two different theoretical criteria considering the phenomenon as the consequence of either a reorganization of the vorticity, or an accumulation of inertial waves propagating along the vortex core. The underlying analyses are carried out in a cylindrical system attached to the vortex axis and predict a single breakdown position, in good agreement with the singular position initially inferred from the A-SPIV data. The thesis ends with a global stability analysis of the turbulent mean flow suggesting a possible connection between the occurrence of vortex breakdown and a global instability of the longitudinal vortex.