Azimuthal Magnetorotational Instability at low and high magnetic Prandtl numbers

TL;DR

This study investigates the azimuthal magnetorotational instability in Keplerian flows at low and high magnetic Prandtl numbers, revealing how instability modes and angular momentum transport vary with magnetic Prandtl number through linear and nonlinear analysis.

Contribution

It models MRI in Keplerian flows with azimuthal magnetic fields using both linear and nonlinear methods, highlighting differences in instability behavior at different magnetic Prandtl numbers.

Findings

Instability modes differ for Pm=1.4e-6 and Pm=1.

Enhanced angular momentum transport observed at Pm=1.

Distinct spatio-temporal oscillations emerge near instability onset.

Abstract

The magnetorotational instability (MRI) is considered to be one of the most powerful sources of turbulence in hydrodynamically stable quasi-Keplerian flows, such as those governing accretion disk flows. Although the linear stability of these flows with applied external magnetic field has been studied for decades, the influence of the instability on the outward angular momentum transport, necessary for the accretion of the disk, is still not well known. In this work we model Keplerian rotation with Taylor-Couette flow and imposed azimuthal magnetic field using both linear and nonlinear approaches. We present scalings of instability with Hartmann and Reynolds numbers via linear analysis and direct numerical simulations (DNS) for the two magnetic Prandtl numbers of $1.4 \cdot 10^{-6}$ and $1$. Inside of the instability domains modes with different axial wavenumbers dominate, resulting in sub-domains of instabilities, which appear different for each $Pm$. The DNS show the emergence of 1- and 2-frequency spatio-temporally oscillating structures for $Pm=1$ close the onset of instability, as well as significant enhancement of angular momentum transport for $Pm=1$ as compared to $Pm=1.4 \cdot 10^{-6}$.