This letter investigates the transport properties of MHD turbulence inducedby the magnetorotational instability at large Reynolds numbers Re when themagnetic Prandtl number Pm is larger than unity. Three MHD simulations of themagnetorotational instability (MRI) in the unstratified shearing box with zeronet flux are presented. These simulations are performed with the code Zeus andconsider the evolution of the rate of angular momentum transport as Re isgradually increased from 3125 to 12500 while simultaneously keeping Pm=4. Toensure that the small scale features of the flow are well resolved, theresolution varies from 128 cells per disk scaleheight to 512 cells perscaleheight. The latter constitutes the highest resolution of an MRI turbulencesimulation to date. The rate of angular momentum transport, measured using thealpha parameter, depends only very weakly on the Reynolds number: alpha isfound 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 bestresolved model, the kinetic energy power spectrum tentatively displays apower-law range with an exponent -3/2, while the magnetic energy is found toshift to smaller and smaller scales as the magnetic Reynolds number increases.A couple of different diagnostics both suggest a well-defined injection lengthof a fraction of a scaleheight. The results presented in this letter areconsistent with the MRI being able to transport angular momentum efficiently atlarge Reynolds numbers when Pm=4 in unstratified zero net flux shearing boxes.
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