The weakly nonlinear magnetorotational instability in a global, cylindrical Taylor-Couette flow

Abstract

We conduct a global, weakly nonlinear analysis of the magnetorotational instability (MRI) in a Taylor-Couette flow. This is a multiscale perturbative treatment of the nonideal, axisymmetric MRI near threshold, subject to realistic radial boundary conditions and cylindrical geometry. We analyze both the standard MRI, initialized by a constant vertical background magnetic field, and the helical MRI, with an azimuthal background field component. This is the first weakly nonlinear analysis of the MRI in a global Taylor-Couette geometry, as well as the first weakly nonlinear analysis of the helical MRI. We find that the evolution of the amplitude of the standard MRI is described by a real Ginzburg-Landau equation (GLE), while the amplitude of the helical MRI takes the form of a complex GLE. This suggests that the saturated state of the helical MRI may itself be unstable on long spatial and temporal scales.

18 pages, 8 figures, accepted to ApJ

References in corpus (8)

• Experimental observation and characterization of the magnetorotational instability
• Experimental evidence for magnetorotational instability in a helical magnetic field
• Helical Magnetorotational Instability in Magnetized Taylor-Couette Flow
• A weakly nonlinear analysis of the magnetorotational instability in a model channel flow
• On the nonlinear saturation of the magnetorotational instability near threshold in a thin-gap Taylor-Couette setup
• Local and global aspects of the linear MRI in accretion disks
• On the Anisotropic Nature of MRI-Driven Turbulence in Astrophysical Disks
• The weakly nonlinear magnetorotational instability in a local geometry

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• The Magnetorotational Instability Prefers Three Dimensions
• Improved photometric redshifts with colour-constrained galaxy templates for future wide-area surveys
• Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow