What Is the Numerically Converged Amplitude of Magnetohydrodynamics Turbulence in Stratified Shearing Boxes?

Abstract

We study the properties of the turbulence driven by the magnetorotational instability (MRI) in a stratified shearing box with outflow boundary conditions and an equation of state determined by self-consistent dissipation and radiation losses. A series of simulations with increasing resolution are performed within a fixed computational box. We achieve numerical convergence with respect to radial and azimuthal resolution. As vertical resolution is improved, the ratio of stress to pressure increases slowly, but the absolute levels of both the stress and the pressure increase noticeably. These results are in contrast with those of previous work on unstratified shearing boxes, in which improved resolution caused a diminution in the magnetic field strength. We argue that the persistence of strong magnetic field at higher resolution found in the stratified case is due to buoyancy. In addition, we find that the time-averaged vertical correlation length of the magnetic field near the disk midplane is ≃ 3 times larger than found in previous unstratifed simulations, decreasing slowly with improved vertical resolution. We further show that the undulatory Parker instability drives the magnetic field upwelling at several scaleheights from the midplane that is characteristic of stratified MHD-turbulent disks.

Relativistic jets: Physics and simulations

“…This happens on 10 orbit timescale and is consistent with a simple α-Ω dynamo (Brandenburg et al 1995;Stone et al 1996;Hirose et a. 2006;Guan 2009;Shi et a. 2010;Gressel2010;Davis et al 2010;Simon et al 2010).…”

General Overview of Black Hole Accretion Theory

“…The result that stress increases with net magnetic flux has also been confirmed in localized regions of global simulations (Sorathia, Reynolds & Armitage 2010). Adding in vertical gravity in stratified simulations enables convergence of the turbulent stresses even without net magnetic flux and explicit viscosity and resistivity (Shi, Krolik & Hirose 2010;Davis, Stone & Pessah 2010). A major difference between unstratified and stratified shearing box simulations is that gravity allows for magnetic buoyancy, and this is clearly playing a role as alternating signs of azimuthal field continually develop in a dynamo within the MRI turbulence and rise outward (Brandenburg et al 1995).…”

Turbulence and Steady Flows in Three-Dimensional Global Stratified Magnetohydrodynamic Simulations of Accretion Disks

“…The reason of this butterfly structure and its role for the MRI is still under discussion. Recent studies show the connection to the MHD dynamo (Gressel 2010) and magnetic buoyancy (Shi et al 2010). …”

“…Ideal MHD simulations including stratification found at least convergence for zero-net flux local simulations (Davis et al 2010;Flaig et al 2010). Here, the vertical resolution plays the key role for the convergence (Shi et al 2010). Despite the simplicity of box simulations and their interesting results obtained over the last years, the study of radial extended structures are very restricted.…”