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

TL;DR

This paper presents the first global weakly nonlinear analysis of the magnetorotational instability in cylindrical Taylor-Couette flow, revealing different amplitude equations for standard and helical MRI and implications for their saturated states.

Contribution

It provides the first weakly nonlinear analysis of MRI in a global Taylor-Couette geometry and of the helical MRI, using multiscale perturbation methods with realistic boundary conditions.

Findings

Standard MRI amplitude follows a real Ginzburg-Landau equation.

Helical MRI amplitude follows a complex Ginzburg-Landau equation.

The saturated state of helical MRI may be unstable on long scales.

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.