Instabilities of rotational flows in azimuthal magnetic fields of arbitrary radial dependence
arXiv:1307.1576 · doi:10.1088/0169-5983/46/3/031403
Abstract
Using the WKB approximation we perform a linear stability analysis for a rotational flow of a viscous and electrically conducting fluid in an external azimuthal magnetic field that has an arbitrary radial profile B_{phi}(R). In the inductionless approximation, we find the growth rate of the three-dimensional perturbation in a closed form and demonstrate in particular that it can be positive when the velocity profile is Keplerian and the magnetic field profile is slightly shallower than R^{-1}.
15 pages, 2 figures, slightly extended, the case of finite Rm treated, results were partially presented at the IUTAM Symposium on Vortex Dynamics, Fukuoka, Japan, March 10 2013
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