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

Abstract

<i>Aims. <i/>This letter investigates the transport properties of MHD turbulence induced by the magnetorotational instability at large Reynolds numbers <i>Re<i/> when the magnetic Prandtl number <i>Pm<i/> is larger than unity.<i>Methods. <i/>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 <i>Re<i/> is gradually increased from 3125 to 12 500 while simultaneously keeping <i>Pm<i/> = 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.<i>Results. <i/>The rate of angular momentum transport, measured using the <i>α<i/> parameter, depends only very weakly on the Reynolds number: <i>α<i/> is found to be about 7 × 10<sup>-3<sup/> with variations around this mean value bounded by 15% in all simulations. There is no systematic evolution with <i>Re<i/>. 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.<i>Conclusions. <i/>The results presented in this letter are consistent with the MRI being able to transport angular momentum efficiently at large Reynolds numbers when <i>Pm<i/> = 4 in unstratified zero net flux shearing boxes.