http://arxiv.org/abs/1507.04711
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 $q=1.5$. The Rayleigh stability criterion states that hydrodynamic shear flows are stable for $q<2$ but with a weak magnetic field, Rayleigh stable flows are unstable to the magnetorotational instability (MRI). The shearing box approximation is not particularly suited for the $q>2$ regime as the volume averaged velocities ($k=0$ mode) are unstable in this regime but the advantage of using a pseudospectral code is that the $k=0$ mode is conserved. We find that the $q>2$ regime is unstable to turbulence both in the hydrodynamic and in the MHD limit (with an initially weak magnetic field). In the $q>2$ regime, the velocity fluctuations dominate the magnetic fluctuations whereas in the $q<2$ 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, a trend not present for the MRI unstable regime.
F. Nauman and E. Blackman
Fri, 17 Jul 15
4/54
Comments: 7 pages, 8 figures, 1 table, submitted to MNRAS
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