Transport properties of the Azimuthal Magnetorotational Instability

Anna Guseva, Ashley P. Willis, Rainer Hollerbach, Marc Avila

Published 2017-05-10Version 1

The magnetorotational instability (MRI) is a powerful source of turbulence in Keplerian accretion disks. We here study the MRI driven by an external azimuthal magnetic field by performing direct numerical simulations spanning wide ranges of Reynolds and magnetic Prandtl numbers ($Re$ up to $4\cdot10^4$ and $Pm \in [0, 1]$). At low magnetic Reynolds number $Rm$ the transport of angular momentum is dominated by Reynolds stresses, whereas Maxwell stresses dominate for $Rm > 100$. In the limit of low $Pm$ the angular momentum transport is found to scale as $Re^2$, whereas for $Pm \geq 10^{-2}$ the scaling is enhanced with an extra factor $\sqrt{Pm} Re^2$. As a consequence, the $\alpha$-parameter of the effective viscosity depends solely on $Pm$ and ranges between $10^{-5}$ in the inductionless limit and $10^{-3}$ at $Pm=1$. Our results give a unifying picture of angular momentum transport of the MRI with an imposed azimuthal field.