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arXiv · 1610.01603

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

S. E. Clark·Jeffrey S. Oishi
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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.

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S. E. Clark, Jeffrey S. Oishi. 2016-10-05. The weakly nonlinear magnetorotational instability in a global, cylindrical Taylor-Couette flow. https://doi.org/10.3847/1538-4357%2Faa6ff6

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