Analysis of azimuthal magnetorotational instability of rotating MHD flows and Tayler instability via an extended Hain-Lust equation

Abstract

We consider a differentially rotating flow of an incompressible electrically conducting and viscous fluid subject to an external axial magnetic field and to an azimuthal magnetic field that is allowed to be generated by a combination of an axial electric current external to the fluid and electrical currents in the fluid itself. In this setting we derive an extended version of the celebrated Hain-Lust differential equation for the radial Lagrangian displacement that incorporates the effects of the axial and azimuthal magnetic fields, differential rotation, viscosity, and electrical resistivity. We apply the Wentzel-Kramers-Brillouin method to the extended Hain-Lust equation and derive a new comprehensive dispersion relation for the local stability analysis of the flow to three-dimensional disturbances. We confirm that in the limit of low magnetic Prandtl numbers, in which the ratio of the viscosity to the magnetic diffusivity is vanishing, the rotating flows with radial distributions of the angular velocity beyond the Liu limit, become unstable subject to a wide variety of the azimuthal magnetic fields, and so is the Keplerian flow. In the analysis of the dispersion relation we find an evidence of a new long-wavelength instability which is caught also by the numerical solution of the boundary value problem for a magnetized Taylor-Couette flow.

24 pages, 16 figures, refs added, typos corrected

References in corpus (9)

• Experimental evidence for magnetorotational instability in a helical magnetic field
• On the Magnetic Prandtl Number Behavior of Accretion Disks
• Helical Magnetorotational Instability in Magnetized Taylor-Couette Flow
• Magnetohydrodynamic experiments on cosmic magnetic fields
• Destabilisation of hydrodynamically stable rotation laws by azimuthal magnetic fields
• Nonmodal growth of the magnetorotational instability
• Linear stability analysis of magnetized jets: the rotating case
• A unifying picture of helical and azimuthal MRI, and the universal significance of the Liu limit
• Metamorphosis of helical magnetorotational instability in the presence axial electric current

Cited by in corpus (2)

• On the appearance of non-local MRI in Keplerian accretion discs
• Non-ideal stability analysis of differentially rotating plasmas with global curvature effects