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Dissipation-Induced Instabilities in Magnetized Flows

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Abstract

We study local instabilities of a differentially rotating viscous flow of electrically conducting incompressible fluid subject to an external azimuthal magnetic field. A hydrodynamically stable flow can be destabilized by the magnetic field both in an ideal and a viscous and resistive system giving rise to the azimuthal magnetorotational instability. A special solution to the equations of ideal magnetohydrodynamics characterized by the constant total pressure, the fluid velocity parallel to the direction of the magnetic field, and by the magnetic and kinetic energies that are finite and equal—the Chandrasekhar equipartition solution—is marginally stable in the absence of viscosity and resistivity. Performing a local stability analysis, we find the conditions under which the azimuthal magnetorotational instability can be interpreted as a dissipation-induced instability of the Chandrasekhar equipartition solution.

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  1. Helmholtz-Zentrum Dresden Rossendorf, Dresden, Germany

    O. N. Kirillov

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 60, Proceedings of the Seventh International Conference on Differential and Functional Differential Equations and InternationalWorkshop “Spatio-Temporal Dynamical Systems” (Moscow, Russia, 22–29 August, 2014). Part 3, 2016.

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Kirillov, O.N. Dissipation-Induced Instabilities in Magnetized Flows. J Math Sci 235, 455–472 (2018). https://doi.org/10.1007/s10958-018-4081-9

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