Axisymmetric and non-axisymmetric magnetostrophic MRI modes - INSU - Institut national des sciences de l'Univers Access content directly
Journal Articles Physics of the Earth and Planetary Interiors Year : 2013

Axisymmetric and non-axisymmetric magnetostrophic MRI modes


The magnetorotational-instability is central to the understanding of many astrophysical magnetohydrodynamic flows (in particular accretion discs). We have recently shown that a modified version of this instability, the magnetostrophic MRI (MS-MRI), is relevant to the dynamics of the Earth liquid core (Petitdemange et al., 2008). Our previous study used a purely axial imposed magnetic field and considered only axisymmetric instabilities. We investigate here the effects of a large scale toroidal magnetic field on the development and saturation of the MS-MRI both in an axisymmetric setup and in fully three-dimensional configurations. We use direct numerical modeling of the full MHD equations (both in the linear and non-linear regimes) in a spherical geometry. We interpret our results using WKB expansions and shearing coordinates. We find that three-dimensional MS-MRI modes exhibit a strong helical structure for parameters relevant to planetary interiors. Three-dimensional MS-MRI modes share some similarities with their axisymmetric counterparts. They are amplified on the same short timescale. When non-linear effects become significant, they act to decrease the shear. During saturation, the magnetic structure expands spatially, while drifting at a constant rate along the direction of the rotation axis. A striking result is that an m=1 mode can dominate in the non-linear regime when a sufficiently large toroidal field is present. Three-dimensional MS-MRI modes could play an important role in planetary interior dynamics. They can cause rapid magnetic field variations and also act to limit the shear in the conducting liquid core.
Not file

Dates and versions

insu-03581759 , version 1 (20-02-2022)



Ludovic Petitdemange, Emmanuel Dormy, Steven Balbus. Axisymmetric and non-axisymmetric magnetostrophic MRI modes. Physics of the Earth and Planetary Interiors, 2013, 223, pp.21-31. ⟨10.1016/j.pepi.2013.03.003⟩. ⟨insu-03581759⟩
5 View
0 Download



Gmail Facebook Twitter LinkedIn More