Singular diffusionless limits of double-diffusive instabilities in MHD

Kirillov, Oleg (2018) Singular diffusionless limits of double-diffusive instabilities in MHD. In: MHD Days and GdRI Dynamo Meeting, 26th - 28th November 2018, Dresden, Germany.

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Official URL: https://www.hzdr.de/db/Cms?pOid=57203

Abstract

We study local instabilities of a differentially rotating viscous flow of electrically conducting in-compressible fluid subject to an external azimuthal magnetic field. In the presence of the magnetic field, the hydrodynamically stable flow can demonstrate non-axisymmetric azimuthal magnetoro-tational instability (AMRI) both in the diffusionless case and in the double-diffusive case with viscous and ohmic dissipation. Performing stability analysis of amplitude transport equations of short-wavelength approximation, we find that the threshold of the diffusionless AMRI via the Hamilton-Hopf bifurcation is a singular limit of the thresholds of the viscous and resistive AMRI corresponding to the dissipative Hopf bifurcation and manifests itself as the Whitney umbrella singular point. A smooth transition between the two types of instabilities is possible only if the magnetic Prandtl number is equal to unity, Pm = 1. At a fixed Pm non equal to unity, the threshold of the double-diffusive AMRI is displaced by finite distance in the parameter space with respect to the diffusionless case even in the zero dissipation limit. The complete neutral stability surface contains three Whitney umbrella singular points and two mutually orthogonal intervals of self-intersection. At these singularities, the double-diffusive system reduces to a marginally stable system which is either Hamiltonian or parity-time-symmetric.

Item Type: Conference or Workshop Item (Other)
Uncontrolled Keywords: magnetohydrodynamcs (MHD), Magnetorotational instability, magnetohydrodynamic waves, Rotating shear flow, Asymptotic expansions, Stability analysis
Subjects: F300 Physics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Paul Burns
Date Deposited: 21 Mar 2019 17:38
Last Modified: 21 Mar 2019 17:38
URI: http://nrl.northumbria.ac.uk/id/eprint/38489

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