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

Abstract

Aims. 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. Methods. 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 12  500 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. Results. The rate of angular momentum transport, measured using the α parameter, depends only very weakly on the Reynolds number: α is found to be about 7 × 10