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WKB thresholds of standard, helical, and azimuthal magnetorotational instability

Published online by Cambridge University Press:  21 February 2013

Oleg Kirillov  and
Frank Stefani
Oleg Kirillov
Affiliation:
Helmholtz-Zentrum Dresden-Rossendorf POB 51 01 19, 01314 Dresden, Germany email: o.kirillov@hzdr.de, f.stefani@hzdr.de
Frank Stefani
Affiliation:
Helmholtz-Zentrum Dresden-Rossendorf POB 51 01 19, 01314 Dresden, Germany email: o.kirillov@hzdr.de, f.stefani@hzdr.de
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Abstract

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We consider rotating flows of an electrically conducting, viscous and resistive fluid in an external magnetic field with arbitrary combinations of axial and azimuthal components. Within the short-wavelength approximation, the local stability of the flow is studied with respect to perturbations of arbitrary azimuthal wavenumbers. In the limit of vanishing magnetic Prandtl number (Pm) we find that the maximum critical Rossby number (Ro) for the occurrence of the magnetorotational instability (MRI) is universally governed by the Liu limit ${\rm Ro}_{Liu}=2-2\sqrt{2}\approx -0.828$ which is below the value for Keplerian rotation RoKepler = −0.75.

Keywords

Magnetorotational instabilityWKB approximationaccretion disks

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