Absolute versus convective helical magnetorotational instability in a Taylor-Couette flow

Abstract

We analyze numerically the magnetorotational instability of a Taylor-Couette flow in a helical magnetic field (HMRI) using the inductionless approximation defined by a zero magnetic Prandtl number (Pm=0). The Chebyshev collocation method is used to calculate the eigenvalue spectrum for small amplitude perturbations. First, we carry out a detailed conventional linear stability analysis with respect to perturbations in the form of Fourier modes that corresponds to the convective instability which is not in general self-sustained. The helical magnetic field is found to extend the instability to a relatively narrow range beyond its purely hydrodynamic limit defined by the Rayleigh line. There is not only a lower critical threshold at which HMRI appears but also an upper one at which it disappears again. The latter distinguishes the HMRI from a magnetically-modified Taylor vortex flow. Second, we find an absolute instability threshold as well. In the hydrodynamically unstable regime before the Rayleigh line, the threshold of absolute instability is just slightly above the convective one although the critical wave length of the former is noticeably shorter than that of the latter. Beyond the Rayleigh line the lower threshold of absolute instability rises significantly above the corresponding convective one while the upper one descends significantly below its convective counterpart. As a result, the extension of the absolute HMRI beyond the Rayleigh line is considerably shorter than that of the convective instability. The absolute HMRI is supposed to be self-sustained and, thus, experimentally observable without any external excitation in a system of sufficiently large axial extension.

16 pages, 15 figures; minor revision, Phys. Rev. E (in press)

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• A unifying picture of helical and azimuthal MRI, and the universal significance of the Liu limit
• Inviscid helical magnetorotational instability in cylindrical Taylor-Couette flow
• Standard and helical magnetorotational instability: How singularities create paradoxal phenomena in MHD
• Noise-Sustained Convective Instability in a Magnetized Taylor-Couette Flow
• Nonaxisymmetric linear instability of cylindrical magnetohydrodynamic Taylor-Couette flow
• Convective, absolute and global azimuthal magnetorotational instabilities
• Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow
• Pseudo--magnetorotational instability in a Taylor-Dean flow between electrically connected cylinders
• Metamorphosis of helical magnetorotational instability in the presence axial electric current
• Absolute versus convective helical magnetorotational instabilities in Taylor-Couette flows
• Magnetic field dynamos and magnetically triggered flow instabilities
• Liquid metal experiments on the helical magnetorotational instability
• Laboratory experiments and numerical simulations on magnetic instabilities