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Local instabilities in magnetized rotational flows: a short-wavelength approach

Published online by Cambridge University Press:  12 November 2014

O. N. Kirillov ,
F. Stefani  and
Y. Fukumoto
O. N. Kirillov*
Affiliation:
Helmholtz-Zentrum Dresden-Rossendorf, PO Box 510119, D-01314 Dresden, Germany
F. Stefani
Affiliation:
Helmholtz-Zentrum Dresden-Rossendorf, PO Box 510119, D-01314 Dresden, Germany
Y. Fukumoto
Affiliation:
Institute of Mathematics for Industry, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
*
†Email address for correspondence: [email protected]
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Abstract

We perform a local stability analysis of rotational flows in the presence of a constant vertical magnetic field and an azimuthal magnetic field with a general radial dependence. Employing the short-wavelength approximation we develop a unified framework for the investigation of the standard, helical and azimuthal version of the magnetorotational instability (MRI), as well as of current-driven kink-type instabilities. Considering the viscous and resistive setup, our main focus is on the case of small magnetic Prandtl numbers which applies e.g. to liquid-metal experiments but also to the colder parts of accretion disks. We show that the inductionless versions of MRI that were previously thought to be restricted to comparatively steep rotation profiles extend well to the Keplerian case if only the azimuthal field slightly deviates from its current-free (in the fluid) profile. We find an explicit criterion separating the pure azimuthal inductionless MRI from the regime where this instability is mixed with the Tayler instability. We further demonstrate that for particular parameter configurations the azimuthal MRI originates as a result of a dissipation-induced instability of Chandrasekhar’s equipartition solution of ideal magnetohydrodynamics.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Instability: Instability MHD and Electrohydrodynamics: MHD and Electrohydrodynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 760 , 10 December 2014 , pp. 591 - 633
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© 2014 Cambridge University Press 

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