Magnetic dipole induction by the spin-over mode of the elliptic instability in a rotating liquid metal sphere
Résumé
The elliptical instability of rotating fluid flows is generated by the resonant interactionof inertial waves. In a slightly elliptically deformed sphere that rotates at arate Ω, the most unstable linear mode is the spin-over mode, which is a solid bodyrotation of angular velocity ΩSO, around an axis aligned with the maximum straindirection1. In geophysics, the elliptical instability may appear in the molten liquidcores of rotating planets, which are slightly deformed by tidal gravitational effects ofclose bodies. It may then participate to the general outer core dynamics and possiblyto the geodynamo process. In this context, Kerswell and Malkus2 showed that thepuzzling magnetic field of the Jovian satellite Io may be induced by the ellipticallyunstable motions of its liquid core that deflect Jupiter magnetic field. Our magnetohydrodynamicsexperiment is a toy-experiment of this geophysical situation anddemonstrates the possibility of the induction of a magnetic field by the flow motionscreated by the elliptical instability. The full analytical calculation of the magneticdipole induced by the spin-over has been performed and is shown in figure 1. Finally,the exponential growth of the induced magnetic field in a rotating sphere filled withGalinstan liquid metal is measured for different rotating rates. Growth rates comparewell with theoretical predictions in the limit of a vanishing Lorentz force.