MHD simulations of the magnetorotational instability in a shearing box with zero net flux: the case Pm=4

TL;DR

This study uses high-resolution MHD simulations to analyze the magnetorotational instability in unstratified shearing boxes with zero net flux at large Reynolds numbers and Pm=4, revealing weak dependence of angular momentum transport on Re.

Contribution

It provides the highest resolution MRI turbulence simulation to date and demonstrates consistent angular momentum transport at large Re with Pm=4 in zero net flux conditions.

Findings

Angular momentum transport rate is approximately constant across Re.

Magnetic energy shifts to smaller scales as Re increases.

Kinetic energy spectrum shows a power-law range with exponent -3/2.

Abstract

This letter investigates the transport properties of MHD turbulence induced by the magnetorotational instability at large Reynolds numbers Re when the magnetic Prandtl number Pm is larger than unity. Three MHD simulations of the magnetorotational instability (MRI) in the unstratified shearing box with zero net flux are presented. These simulations are performed with the code Zeus and consider the evolution of the rate of angular momentum transport as Re is gradually increased from 3125 to 12500 while simultaneously keeping Pm=4. To ensure that the small scale features of the flow are well resolved, the resolution varies from 128 cells per disk scaleheight to 512 cells per scaleheight. The latter constitutes the highest resolution of an MRI turbulence simulation to date. The rate of angular momentum transport, measured using the alpha parameter, depends only very weakly on the Reynolds number: alpha is found to be about 0.007 with variations around this mean value bounded by 15% in all simulations. There is no systematic evolution with Re. For the best resolved model, the kinetic energy power spectrum tentatively displays a power-law range with an exponent -3/2, while the magnetic energy is found to shift to smaller and smaller scales as the magnetic Reynolds number increases. A couple of different diagnostics both suggest a well-defined injection length of a fraction of a scaleheight. The results presented in this letter are consistent with the MRI being able to transport angular momentum efficiently at large Reynolds numbers when Pm=4 in unstratified zero net flux shearing boxes.