Energy transfers during the interaction between two co-rotating quasi-geostrophic vortices

We investigate the strong interactions between two co-rotating quasi-geostrophic vortices. We first determine equilibrium states based on an ellipsoidal model. We then address the linear stability of the vortices to ellipsoidal perturbations. An instability will trigger a strong interaction during the nonlinear evolution of the vortex pair. Then we investigate the nonlinear evolution of a large subset of the unstable equilibrium states. The dominant type of interaction is partial merger where only a part of a vortex merges with the other one. For vortices of significantly different initial volumes, the most commonly observed interaction is the a partial straining out, where the small vortex shed some of its volume as filaments. Analysing the energies of the vortices, we show that the net energy transfer is toward large spatial scales, whereas a large number of small spatial scales are produced. Intermediate scales tend to disappear from the flow. Résumé: Nous étudions les interactions fortes entre deux tourbillons co-rotatifs quasi-géostrophiques. Nous déterminons d’abord des états d’équilibre basés sur un modèle ellipsoïdal. Puis nous analysons la stabilité linéaire des tour-billons soumis à des perturbations ellipsoïdales. Une instabilité engendrera une interaction forte durant l’évolution non-linéaire da la paire de tourbillons. Nous étudions ensuite l’évolution non-linéaire d’un large sous-ensembl