Shearing box simulations in the Rayleigh unstable regime

TL;DR

This study investigates the stability and turbulence mechanisms of Rayleigh unstable flows in hydrodynamic and MHD regimes for different shear parameters, revealing distinct behaviors and turbulence pathways for regimes with shear parameter q greater or less than 2.

Contribution

It provides a comparative analysis of Rayleigh unstable flows in hydrodynamic and MHD regimes across different shear values, highlighting different turbulence pathways and the role of linear and nonlinear terms.

Findings

q>2 regime is unstable in hydrodynamic and MHD flows.

Velocity fluctuations dominate magnetic fluctuations in q>2 regime.

Magnetic field correlation becomes more localized with increased shear.

Abstract

We study the stability properties of Rayleigh unstable flows both in the purely hydrodynamic and magnetohydrodynamic (MHD) regimes for two different values of the shear $q=2.1, 4.2$ ($q = - d\ln\Omega / d\ln r$) and compare it with the Keplerian case $q=1.5$. We find that the $q>2$ regime is unstable both in the hydrodynamic and in the MHD limit (with an initially weak magnetic field). In this regime, the velocity fluctuations dominate the magnetic fluctuations. In contrast, in the $q<2$ (magnetorotational instability (MRI)) regime the magnetic fluctuations dominate. This highlights two different paths to MHD turbulence implied by the two regimes, suggesting that in the $q>2$ regime the instability produces primarily velocity fluctuations that cause magnetic fluctuations, with the causality reversed for the $q<2$ MRI unstable regime. We also find that the magnetic field correlation is increasingly localized as the shear is increased in the Rayleigh unstable regime. In calculating the time evolution of spatial averages of different terms in the MHD equations, we find that the $q>2$ regime is dominated by terms which are nonlinear in the fluctuations, whereas for $q<2$, the linear terms play a more significant role.