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Journal Articles Physics of the Earth and Planetary Interiors Year : 2013

Axisymmetric and non-axisymmetric magnetostrophic MRI modes

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Abstract

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.
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Dates and versions

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

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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⟩
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