Magnetic field induced by elliptical instability in a rotating spheroid
Résumé
The tidal or elliptical instability of rotating fluid flows is generated by the resonant interaction of inertial waves. In a slightly elliptically deformed rotating sphere, the most unstable linear mode is called the spin-over mode and is a solid body rotation versus an axis aligned with the maximum strain direction. In the non viscous case, this instability corresponds to the median moment of inertia instability of solid rotating bodies. This analogy is furthermore illustrated by an elliptical top experiment, which shows the expected inviscid heteroclinic behaviour. In geophysics, the elliptical instability may appear in the molten liquid cores of rotating planets, which are slightly deformed by tidal gravitational effects of close bodies. It may then participate to the general outer core dynamics and possibly to the geodynamo process. In this context, Kerswell and Malkus (Kerswell, R.R. and Malkus, W.V.R., Tidal instability as the source for Io's magnetic signature, Geophys. Res. Lett., 1998, 25, 603-606) showed that the puzzling magnetic field of the Jovian satellite Io may indeed be induced by the elliptically unstable motions of its liquid core that deflect Jupiter magnetic field. Our magnetohydrodynamics experiment is a toy-experiment of this geophysical situation and demonstrates for the first time the possibility of an induction of a magnetic field by the flow motions due to the elliptical instability. A full analytical calculation of the magnetic dipole induced by the spin-over is presented. Finally, exponential growths of this induced magnetic field in a slightly deformed rotating sphere filled with Galinstan liquid metal are measured for different rotating rates. Their growth rates compare well with theoretical predictions in the limit of a vanishing Lorentz force.
Loading...