A unifying picture of helical and azimuthal MRI, and the universal significance of the Liu limit

TL;DR

This paper provides a unified theoretical framework for helical and azimuthal MRI, revealing the universal significance of the Liu limit in rotating flows and predicting higher azimuthal wavenumbers under certain conditions.

Contribution

It introduces a unified description of helical and azimuthal MRI and highlights the universal Liu limit for the critical Rossby number in these instabilities.

Findings

Universal Liu limit Ro= -0.8284 identified for MRI

Unified description of helical and azimuthal MRI provided

Prediction of higher azimuthal wavenumber for small field ratios

Abstract

The magnetorotational instability (MRI) plays a key role for cosmic structure formation by triggering turbulence in the rotating flows of accretion disks that would be otherwise hydrodynamically stable. In the limit of small magnetic Prandtl number, the helical and the azimuthal version of MRI are known to be governed by a quite different scaling behaviour than the standard MRI with a vertical applied magnetic field. Using the short-wavelength approximation for an incompressible, resistive, and viscous rotating fluid we present a unified description of helical and azimuthal MRI, and we identify the universal character of the Liu limit Ro= -0.8284 for the critical Rossby number. From this universal behaviour we are also lead to the prediction of higher azimuthal wavenumber for rather small ratios of azimuthal to axial applied fields.