Simulations of Electron Magnetohydrodynamic Turbulence

We present numerical simulations of electron magnetohydrodynamic (EMHD) and electron reduced MHD (ERMHD) turbulence. Comparing scaling relations, we find that both EMHD and ERMHD turbulence show similar spectra and anisotropy. We develop new techniques to study anisotropy of EMHD turbulence. Our detailed study of anisotropy of EMHD turbulence supports our earlier result of k‖ ∝ k ⊥ scaling, where k‖ and k⊥ are wavenumbers parallel and perpendicular to (local) mean magnetic field, respectively. We find that the high-order statistics show a scaling that is similar to the SheLeveque scaling for incompressible hydrodynamic turbulence and different from that of incompressible MHD turbulence. We observe that the bispectra, which characterize the interaction of different scales within the turbulence cascade, are very different for EMHD and MHD turbulence. We show that both decaying and driven EMHD turbulence have the same statistical properties. We calculate the probability distribution functions (PDFs) of MHD and EMHD turbulence and compare them with those of interplanetary turbulence. We find that, as in the case of the solar wind, the PDFs of the increments of magnetic field strength in MHD and EMHD turbulence are well described by the Tsallis distribution. We discuss implications of our results for astrophysical situations, including the advection dominated accretion flows and magnetic reconnection. Subject headings: MHD — turbulence — solar wind