SIMULATIONS OF MAGNETOROTATIONAL TURBULENCE WITH A HIGHER-ORDER GODUNOV SCHEME

We apply a new, second-order Godunov code, Athena, to studies of the magnetorotational instability (MRI) using unstratified shearing box simulations with a uniform net vertical field and a sinusoidally varying zero net vertical field. The Athena results agree well with similar studies that used different numerical algorithms, including the observation that the turbulent energy decreases with increasing resolution in the zero net field model. We conduct analyses to study the flow of energy from differential rotation to turbulent fluctuations to thermalization. A study of the time correlation between the rates of change of different volume-averaged energy components shows that energy injected into turbulent fluctuations dissipates on a timescale of Omega(-1), where Omega is the orbital frequency of the local domain. Magnetic dissipation dominates over kinetic dissipation, although not by as great a factor as the ratio of magnetic to kinetic energy. We Fourier-transform the magnetic and kinetic energy evolution equations and, using the assumption that the time-averaged energies are constant, determine the level of numerical dissipation as a function of length scale and resolution. By modeling numerical dissipation as if it were physical in origin, we characterize numerical resistivity and viscosity in terms of effective Reynolds and Prandtl numbers. The resulting effective magnetic Prandtl number is similar to 2, independent of resolution or initial field geometry. MRI simulations with effective Reynolds and Prandtl numbers determined by numerical dissipation are not equivalent to those where these numbers are set by physical resistivity and viscosity. These results serve, then, as a baseline for future shearing box studies where dissipation is controlled by the inclusion of explicit viscosity and resistivity.