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.
Original languageEnglish
Pages (from-to)455-472
Number of pages18
JournalJournal of Mathematical Sciences
Volume235
Issue number4
Early online date11 Oct 2018
DOIs
Publication statusPublished - 1 Dec 2018

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