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 .