Singular diffusionless limits of double-diffusive instabilities in magnetohydrodynamics

Kirillov, Oleg (2017) Singular diffusionless limits of double-diffusive instabilities in magnetohydrodynamics. Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences, 473 (2205). ISSN 1364-5021

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Official URL: https://doi.org/10.1098/rspa.2017.0344

Abstract

We study local instabilities of a differentially rotating viscous flow of electrically conducting incompressible fluid subject to an external azimuthal magnetic field. In the presence of the magnetic field the hydrodynamically stable flow can demonstrate non - axisymmetric azimuthal magnetorotational 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 < 1 or Pm >1 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 (PT) symmetric.

Item Type: Article
Uncontrolled Keywords: Hamiltonian system, energy equipartition, double diffusion, magnetorotational instability, dissipation-induced instabilities, exceptional point
Subjects: F300 Physics
F500 Astronomy
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Related URLs:
Depositing User: Oleg Kirillov
Date Deposited: 15 Aug 2017 10:16
Last Modified: 06 May 2018 05:37
URI: http://nrl.northumbria.ac.uk/id/eprint/31129

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