http://arxiv.org/abs/1610.06970
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 the azimuthal magnetorotational instability (AMRI) both in the diffusionless case and in the double–diffusive case with viscous and ohmic dissipation. Performing stability analysis of the amplitude transport equations of the 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, $\rm Pm=1$. At a fixed ${\rm Pm}\ne 1$ the threshold of the double-diffusive AMRI is displaced by an order one 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.
O. Kirillov
Tue, 25 Oct 16
67/69
Comments: N/A
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