Dissipation-induced instabilities in magnetized flows

O. N. Kirillov

Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 3, Tome 60 (2016), pp. 82-101

Résumé

We study local instabilities of a differentially rotating viscous flow of electrically conducting incompressible fluid subject to an external azimuthal magnetic field. The hydrodynamically stable flow can be destabilized by the magnetic field both in the ideal and in the viscous and resistive system giving rise to the azimuthal magnetorotational instability. A special solution to the equations of the 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 when the azimuthal magnetorotational instability can be interpreted as a dissipation-induced instability of the Chandrasekhar equipartition solution.