Singular diffusionless limits of double-diffusive instabilities in magnetohydrodynamics

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
2 Downloads (Pure)

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.
Original languageEnglish
Article number344
JournalProceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences
Volume473
Issue number2205
Early online date13 Sep 2017
DOIs
Publication statusE-pub ahead of print - 13 Sep 2017

Fingerprint

Dive into the research topics of 'Singular diffusionless limits of double-diffusive instabilities in magnetohydrodynamics'. Together they form a unique fingerprint.

Cite this