Zonal Flows and Long-Lived Axisymmetric Pressure Bumps in Magnetorotational Turbulence

TL;DR

This paper investigates how increasing the size of shearing box simulations affects magnetorotational turbulence, revealing the emergence of zonal flows and pressure bumps driven by large-scale magnetic structures and inverse cascades.

Contribution

It demonstrates that larger simulation boxes lead to significant magnetic and flow structures, and introduces improved algorithms to reduce numerical diffusivity in modeling turbulence.

Findings

Maxwell and Reynolds stresses increase with box size up to two scale heights.

Large-scale magnetic structures induce zonal flows and banded density patterns.

New numerical methods improve the accuracy of shearing box simulations.

Abstract

We study the behavior of magnetorotational turbulence in shearing box simulations with a radial and azimuthal extent up to ten scale heights. Maxwell and Reynolds stresses are found to increase by more than a factor two when increasing the box size beyond two scale heights in the radial direction. Further increase of the box size has little or no effect on the statistical properties of the turbulence. An inverse cascade excites magnetic field structures at the largest scales of the box. The corresponding 10% variation in the Maxwell stress launches a zonal flow of alternating sub- and super-Keplerian velocity. This in turn generates a banded density structure in geostrophic balance between pressure and Coriolis forces. We present a simplified model for the appearance of zonal flows, in which stochastic forcing by the magnetic tension on short time-scales creates zonal flow structures with life-times of several tens of orbits. We experiment with various improved shearing box algorithms to reduce the numerical diffusivity introduced by the supersonic shear flow. While a standard finite difference advection scheme shows signs of a suppression of turbulent activity near the edges of the box, this problem is eliminated by a new method where the Keplerian shear advection is advanced in time by interpolation in Fourier space.