# Resolution Dependence of Magnetorotational Turbulence in the Isothermal Stratified Shearing Box

## TL;DR

This study investigates how the resolution affects the properties of magnetorotational turbulence in stratified shearing boxes, revealing that shear stress and magnetic correlation length depend on resolution and do not converge.

## Contribution

It provides a detailed resolution study of MRI-driven turbulence in stratified shearing boxes, highlighting the resolution dependence of key turbulence metrics.

## Key findings

- Shear stress scales as N^{-1/3} with resolution.
- Magnetic correlation length decreases as N^{-1/2}.
- Results are consistent with previous studies but show lack of convergence.

## Abstract

Magnetohydrodynamic (MHD) turbulence driven by the magnetorotational instability can provide diffusive transport of angular momentum in astrophysical disks, and a widely studied computational model for this process is the ideal, stratified, isothermal shearing box. Here we report results of a convergence study of such boxes up to a resolution of $N = 256$ zones per scale height, performed on blue waters at NCSA with ramses-gpu. We find that the time and vertically integrated dimensionless shear stress $\overline{\alpha} \sim N^{-1/3}$, i.e. the shear stress is resolution dependent. We also find that the magnetic field correlation length decreases with resolution, $\lambda \sim N^{-1/2}$. This variation is strongest at the disk midplane. We show that our measurements of $\alpha$ are consistent with earlier studies. We discuss possible reasons for the lack of convergence.