Nonmodal growth of the magnetorotational instability

TL;DR

This paper uses nonmodal analysis to show that the magnetorotational instability can exhibit rapid linear growth across all wavelengths, highlighting the importance of nonmodal physics in MRI turbulence.

Contribution

It introduces a nonmodal approach to analyze MRI growth, revealing that shearing waves can grow at the maximum MRI rate regardless of wavelength, contrasting with traditional modal results.

Findings

Shearing wave energy can grow at the maximum MRI rate for any wavelength.

Over short timescales, shearing waves dominate static structures.

Fast linear growth at all wavelengths suggests nonmodal physics is crucial in MRI turbulence.

Abstract

We analyze the linear growth of the magnetorotational instability (MRI) in the short time limit using nonmodal methods. Our findings are quite different to standard results, illustrating that shearing wave energy can grow at the maximum MRI rate, $-d\Omega/d \ln r,$ for any choice of azimuthal and vertical wavelengths. In addition, by comparing the growth of shearing waves with static structures, we show that over short time-scales shearing waves will always be dynamically more important than static structures in the ideal limit. By demonstrating that fast linear growth is possible at all wavelengths, these results suggest that nonmodal linear physics could play a fundamental role in MRI turbulence.