Acta Applicandae Mathematicae

, Volume 120, Issue 1, pp 177–198 | Cite as

Standard and Helical Magnetorotational Instability

How Singularities Create Paradoxical Phenomena in MHD
Article

Abstract

The magnetorotational instability (MRI) triggers turbulence and enables outward transport of angular momentum in hydrodynamically stable rotating shear flows, e.g., in accretion disks. What laws of differential rotation are susceptible to the destabilization by axial, azimuthal, or helical magnetic field? The answer to this question, which is vital for astrophysical and experimental applications, inevitably leads to the study of spectral and geometrical singularities on the instability threshold. The singularities provide a connection between seemingly discontinuous stability criteria and thus explain several paradoxes in the theory of MRI that were poorly understood since the 1950s.

Keywords

Rotating shear flow Couette-Taylor flow Accretion disk Magnetorotational instability WKB Plücker conoid Exceptional point 

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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Helmholtz-Zentrum Dresden-RossendorfDresdenGermany

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