Two-dimensional non-linear simulations of the magnetostrophic magnetorotational instability

Abstract

We have shown that a simple, modified version of the Magnetorotational Instability (MRI) can, in principle, develop in the Earth's outer liquid core in the presence of a background shear (see Petitdemange, Dormy and Balbus, MagnetoStrophic MRI in the Earth's outer core. Geophys. Res. Lett. 2008, 35 15305). We refer to this instability as the Magnetostrophic MRI (MS-MRI). In this article, we extend our investigations to the nonlinear regime and present results from global axisymmetric simulations in spherical geometry. We show that as the angular momentum is transported outward, the MS-MRI saturates by rapidly changing the initial shear profile. Therefore, the saturation process differs substantially from traditional MRI applications (e.g. accretion disks) in which the background shear is essentially fixed. We show that the MS-MRI appears as a new constraint which limits the maximum differential rotation. To illustrate this mechanism, we apply this work to a Jupiter-like planet, and argue that the magnetic field eventually destabilises the conducting zone of this planet. According to these results, purely hydrodynamic models for the deep origin of the banded structure of Jupiter may need to be modified.