Symmetries, scaling laws and convergence in shearing-box simulations of MRI driven turbulence

TL;DR

This paper investigates the convergence properties of shearing-box simulations of MRI-driven turbulence, demonstrating asymptotic independence from domain size and linking weak flux cases to zero-flux scenarios, with implications for astrophysical angular momentum transport.

Contribution

It provides a detailed analysis of convergence in MRI turbulence simulations, highlighting the role of symmetries, scaling laws, and the impact of magnetic flux on turbulence behavior.

Findings

Solutions become asymptotically independent of domain size.

Weak magnetic flux cases smoothly connect to zero-flux cases.

Angular momentum transport is proportional to diffusive flux, limiting astrophysical relevance.

Abstract

We consider the problem of convergence in homogeneous shearing box simula- tions of magneto-rotationally driven turbulence. When there is no mean magnetic flux, if the equations are non dimensionalized with respect to the diffusive scale, the only free parameter in the problem is the size of the computational domain. The problem of convergence then relates to the asymptotic form of the solutions as the computational box size becomes large. By using a numerical code with a high order of accuracy we show that the solutions become asymptotically inde- pendent of domain size. We also show that cases with weak magnetic flux join smoothly to the zero flux cases as the flux vanishes. These results are consistent with the operation of a subcritical small-scale dynamo driving the turbulence. We conclude that for this type of turbulence the angular momentum transport is a proportional to the diffusive flux and therefore has limited relevance in as- trophysical situations.