Magnetohydrodynamic simulations of the elliptical instability in triaxial ellipsoids

The elliptical instability can take place in planetary cores and stars elliptically deformed by gravitational effects, where it generates large-scale three-dimensional flows assumed to be dynamo capable. In this work, we present the first magneto-hydrodynamic numerical simulations of such flows, using a finite-element method. We first validate our numerical approach by comparing with kinematic and dynamic dynamos benchmarks of the literature. We then systematically study the magnetic field induced by various modes of the elliptical instability from an imposed external field in a triaxial ellipsoidal geometry, relevant in a geo-and astrophysical context. Finally, in tidal induction cases, the external magnetic field is suddenly shut down and the decay rates of the magnetic field are systematically reported.