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Incompressible magnetohydrodynamic (MHD) turbulence under influences of the Hall and the gyro-viscous terms was studied by means of direct numerical simulations of freely decaying, homogeneous and approximately isotropic turbulence. Numerical results were compared among MHD, Hall MHD, and extended MHD models focusing on differences of Hall and extended MHD turbulence from MHD turbulence at a fully relaxed state. Magnetic and kinetic energies, energy spectra, energy transfer, vorticity and current structures were studied. The Hall and gyro-viscous terms change the energy transfer in the equations of motions to be forward-transfer-dominant while the magnetic energy transfer remains backward-transfer-dominant. The gyro-viscosity works as a kind of hyper-diffusivity, attenuating the kinetic energy spectrum sharply at a high wave-number region. However, this term also induces high-vorticity events more frequently than MHD turbulence, making the turbulent field more intermittent. Vortices and currents were found to be transformed from sheet to tubular structures under the influences of the Hall and/or the gyro-viscous terms. These observations highlight features of fluid-dynamic aspect of turbulence in sub-ion-scales where turbulence is governed by the ion skin depth and ion Larmor radius.

Extended Magnetohydrodynamic Simulations of Decaying, Homogeneous, Approximately-Isotropic and Incompressible Turbulence