Abstract

The elliptical instability is a generic instability which takes place in any rotating fluid whose streamlines are (even slightly) elliptically deformed. Its presence in an aeronautical context is well established, but its existence in geo- or astrophysical large scale flows raises many issues. In this talk, I present the first numerical simulations of the elliptical instability in an ellipsoidal geometry, relevant for planets. These simulations allow to quantify the influence of different natural geophysical complexities (oblateness, convective or stratified flows, etc.), and to derive the scaling laws needed to bridge the gap between numerics and planetary or stellar applications. Results on the magnetohydrodynamic flows driven by the elliptical instability are then presented and validated numerically. Finally, the obtained results are used to study the presence of the elliptical instability in known planets, moons, and stars. Telluric bodies are first considered, and a stability analysis adapted to this context shows that the instability can be expected in the Early Earth, the Early Moon, Europa and three exoplanets (55CnCe, CoRoT-7b et GJ1214b). To conclude, the possible development of the instability in extra-solar Hot-Jupiters systems is considered, showing its possible relevance for some of them, such as the system of Tau-boo.