Dissipative and nonaxisymmetric standard-MRI in Kepler disks

Abstract

Deviations from axial symmetry are necessary to maintain self-sustained MRI-turbulence. We define the parameters region where nonaxisymmetric MRI is excited and study dependence of the unstable modes structure and growth rates on the relevant parameters. We solve numerically the linear eigenvalue problem for global axisymmetric and nonaxisymmetric modes of standard-MRI in Keplerian disks with finite diffusion. For small magnetic Prandtl number the microscopic viscosity completely drops out from the analysis so that the stability maps and the growth rates expressed in terms of the magnetic Reynolds number Rm and the Lundquist number S do not depend on the magnetic Prandtl number Pm. The minimum magnetic field for onset of nonaxisymmetric MRI grows with Rm. For given S all nonaxisymmetric modes disappear for sufficiently high Rm. This behavior is a consequence of the radial fine-structure of the nonaxisymmetric modes resulting from the winding effect of differential rotation. It is this fine-structure which presents severe resolution problems for the numerical simulation of MRI at large Rm. For weak supercritical magnetic fields only axisymmetric modes are unstable. Nonaxisymmetric modes need stronger fields and not too fast rotation. If Pm is small its real value does not play any role in MRI.

4 pages, 6 figures, A&A Letter

References in corpus (6)

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• Impact of dimensionless numbers on the efficiency of MRI-induced turbulent transport
• MHD simulations of the magnetorotational instability in a shearing box with zero net flux. I. The issue of convergence
• Non-axisymmetric Magnetorotational Instabilities in Cylindrical Taylor-Couette Flow
• Viscous and Resistive Effects on the MRI with a Net Toroidal Field
• Destabilisation of hydrodynamically stable rotation laws by azimuthal magnetic fields

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• The Super-Alfvénic Rotational Instability in accretion disks about black holes
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• The angular momentum transport by standard MRI in quasi-Kepler cylindric Taylor-Couette flows
• Parametric Survey of Nonaxisymmetric Accretion Disk Instabilities: Magnetorotational Instability to Super-Alfvénic Rotational Instability
• Linear stability analysis of the Hall magnetorotational instability in a spherical domain
• Magnetic field gradient effects on the magnetorotational instability