Nonmodal analysis of helical and azimuthal magnetorotational instabilities

TL;DR

This paper explores the nonmodal dynamics of helical and azimuthal magnetorotational instabilities in rotating magnetized flows, revealing significant transient amplification within stability limits predicted by modal analysis.

Contribution

It generalizes modal analysis results by investigating nonmodal growth, showing transient amplification occurs within Liu limits and linking it to hydrodynamic behavior.

Findings

Transient growth occurs within Liu limits where modal analysis predicts stability.

Nonmodal amplification is significant for both types of magnetorotational instabilities.

Nonmodal behavior is connected to the hydrodynamic problem underlying the MHD instabilities.

Abstract

Helical and azimuthal magnetorotational instabilities operate in rotating magnetized flows with relatively steep negative or extremely steep positive shear. The corresponding lower and upper Liu limits of the shear, which determine the threshold of modal growth of these instabilities, are continuously connected when some axial electrical current is allowed to pass through the rotating fluid. We investigate the nonmodal dynamics of these instabilities arising from the non-normality of shear flow in the local approximation, generalizing the results of the modal approach. It is demonstrated that moderate transient/nonmodal amplification of both types of magnetorotational instability occurs within the Liu limits, where the system is stable according to modal analysis. We show that for the helical magnetorotational instability this magnetohydrodynamic behavior is closely connected with the nonmodal growth of the underlying purely hydrodynamic problem.