Numerical Study of Compressible Magnetohydrodynamic Turbulence in Two Dimensions

We have studied forced turbulence of compressible magnetohydrodynamic (MHD) flows through two-dimensional simulations with different numerical resolutions. First, hydrodynamic turbulence with Mach number 〈M_s〉 _init ≡ 〈v〉_rms/c_s = 1 and density compression 〈δρ/ρ〉_rms ≃ 0.45 was generated by enforcing a random force. Then, initial, uniform magnetic fields of various strengths were added with Alfvénic Mach number 〈M_A〉_init ≡ 〈v〉 _rms/c_A,init ≫ 1. An isothermal equation of state was employed, and no explicit dissipation was included. In our simulations, the maximum amplification factor of magnetic energy depends on resolution and is proportional to n_x^1.32, where n_x is the number of grid cells spanned by the computational box size. After the MHD turbulence is saturated, the resulting flows are categorized as very weak field (VWF), weak field (WF), and strong field (SF) classes, which have 〈M _A〉 〈v〉_rms/〈c_A〉 _rms ≫ 1, 〈M_A〉 > 1, and 〈MA〉 ∼ 1, respectively. The flow character in the VWF cases is similar to that of hydrodynamic turbulence. In the WF cases, the magnetic energy is still smaller than the kinetic energy in the global sense, but the magnetic field can become locally important. Hence, not only in the SF regime but also in the WF regime, turbulent transport is suppressed by the magnetic field. In the SF cases, the energy power spectra in the inertial range, although no longer power-law, exhibit a range with slopes close to ∼1.5, hinting at the Iroshnikov-Kraichnan spectrum. These characteristics of the VWF, WF, and SF classes are consistent with their incompressible turbulence counterparts, indicating that a modest compressibility of 〈p/p〉_rms ≲ 0.45 or so does not play a significant role in turbulence. Our simulations were able to produce the SF-class behaviors only with a high resolution of at least 1024² grid cells. With lower resolutions, we observed the formation of a dominant flux tube, which accompanies the separation of the magnetic field from the background flow. The specific requirements for the simulation of the SF class should depend on the code (and the numerical scheme) as well as the initial setup, but our results do indicate that very high resolution would be required for converged results in simulation studies of MHD turbulence.