In this study we investigate the interactions between two co-rotating vortices. These vortices are subject to rapid rotation and stable stratification such as are found in planetary atmospheres and oceans. By conducting a large number of simulations of vortex interactions, we intend to provide an overview of the interactions that could occur in geophysical turbulence. We consider a wide parameter space covering the vortices height-to-width aspect-ratios, their volume ratios and the vertical offset between them. The vortices are initially separated in the horizontal so that they reside at an estimated margin of stability. The vortices are then allowed to evolve for a period of approximately 20 vortex revolutions. We find that the most commonly observed interaction under the quasi-geostrophic (QG) regime is partial-merger, where only part of the smaller vortex is incorporated into the larger, stronger vortex. On the other hand, a large number of filamentary and small scale structures are generated during the interaction. We find that, despite the proliferation of small-scale structures, the self-induced vortex energy exhibits a mean `inverse-cascade' to larger scale structures. Interestingly we observe a range of intermediate-scale structures that are preferentially sheared out during the interactions, leaving two vortex populations, one of large-scale vortices and one of small-scale vortices. We take a subset of the parameter space used for the QG study and perform simulations using a non-hydrostatic model. This system, free of the layer-wise two-dimensional constraints and geostrophic balance of the QG model, allows for the generation of inertia-gravity waves and ageostrophic advection. The study of the interactions between two co-rotating, non-hydrostatic vortices is performed over four different Rossby numbers, two positive and two negative, allowing for the comparison of cyclonic and anti-cyclonic interactions. It is found that a greater amount of wave-like activity is generated during the interactions in anticyclonic situations. We also see distinct qualitative differences between the interactions for cyclonic and anti-cyclonic regimes.

Les tourbillons océaniques de subsurface sont des structures dynamiques qui peuplent l'océan global. Ils sont souvent générés à partir de courants d'échanges entre les bassins d'évaporation semi-fermés (comme la Mer Méditerranée, la Mer Rouge et le Golfe Persique) et l'océan ouvert ou pendant des processus de convection profonde. Ces tourbillons peuvent maintenir une géométrie cohérente sur des échelles de temps pluriannuelles et sont capables, du fait de leur migration, de transporter des quantités significatives de chaleur, sel et nutriments. Les tourbillons de subsurface contribuent donc à la redistribution tridimensionnelle des traceurs océaniques à échelle globale, d'où l'intérêt de connaître leurs positions et déplacements.En général, les tourbillons sont capables de modifier localement la surface de la mer, en générant des anomalies qui permettent leur suivi à travers des observations satellitaires. Notre étude se base sur l'utilisation de modèles analytiques et numériques pour caractériser les signatures induites à la surface par les tourbillons de subsurface; en particulier les anomalies de l'élévation (SSH), de température (SST) et de salinité (SSS) de la surface océanique.D'abord, nous avons étudié les signatures de surface (en SSH) dans un cadre idéalisé. Leurs propriétés ont été mises en relation avec la structure tridimensionnelle des tourbillons, nous permettant de déterminer que seulement les tourbillons de subsurface de meso-échelle océanique sont détectables via les observations altimétriques actuelles. En outre, en utilisant un modèle réaliste, nous avons étudié les signatures de surface des tourbillons d'eau méditerranéenne (MEDDIES) en termes de SSH, SST et SSS. L'étude a mis en évidence des différences entre les signatures en SSH et les signatures thermohalines: les premières montrent des intensités et des structures horizontales toujours liées aux changements structurels des Meddies, alors que les deuxièmes sont plutôt pilotées par la dynamique locale de surface.Enfin, nos résultats montrent que le suivi automatique des tourbillons de subsurface est plutôt envisageable à partir des techniques altimétriques, en valorisant aussi l'apport des futures missions satellitaires à haute résolution, comme SWOT. / Subsurface-intensified vortices are ubiquitous in the world ocean. They are often generated by water mass exchanges between semi-closed evaporation basins (e.g.: Mediterranean Sea, Red Sea, Persian Gulf) and the open ocean or during deep convection processes. These vortices can maintain a coherent geometry during inter-annual timescales and, due to their migration, they are able to carry large amounts of heat, salt and nutrients. Hence, the class of subsurface-intensified vortices participates to the redistribution of oceanic tracers along the three dimensions and at global scale, justifying the interest in determining their positions and mean pathways in the ocean. In general, vortices are able to locally modify the ocean surface generating anomalies that allow one to track them via satellite sensors. Our study, based on the use of analytical and numerical models, deals with the characterization of the sea-surface anomalies generated by subsurface-intensified vortices in terms of Sea-Surface Height (the elevation of the oceanic free-surface, SSH), Sea-Surface Temperature (SST) and Sea-Surface Salinity (SSS).In a first analysis, we have studied the SSH anomalies generated by subsurface vortices in an idealized context. Their properties have been related to the three-dimensional structure of the vortex, allowing us to state that only subsurface mesoscale vortices can be detected by the presentday altimetric observations. Furthermore, using a realistic model, we have studied the sea-surface expression of Mediterranean Water Eddies (MEDDIES) in SSH, SST and SSS. The study has evidenced the main differences between the Meddies-induced SSH anomalies and their thermohaline surface anomalies (i.e., SST and SSS): the first exhibit horizontal structures and intensities that can always be related to the Meddy structural changes at depth, while the second are mostly driven by the local surface dynamics.These studies show that the automatic tracking of subsurface-intensified vortices is mostly possible in an altimetric perspective, further confirming the importance of future high-resolution altimetric satellite missions, like SWOT.