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.
Keywords
Cite
@article{arxiv.1610.01603,
title = {The weakly nonlinear magnetorotational instability in a global, cylindrical Taylor-Couette flow},
author = {S. E. Clark and Jeffrey S. Oishi},
journal= {arXiv preprint arXiv:1610.01603},
year = {2017}
}
Comments
18 pages, 8 figures, accepted to ApJ