  The three-dimensional (3D) Hall magnetohydrodynamics (HMHD) equations are
often used to study turbulence in the solar wind. Some earlier studies have
investigated the statistical properties of 3D HMHD turbulence by using simple
shell models or pseudospectral direct numerical simulations (DNSs) of the 3D
HMHD equations; these DNSs have been restricted to modest spatial resolutions
and have covered a limited parameter range. To explore the dependence of 3D
HMHD turbulence on the Reynolds number $Re$ and the ion-inertial scale $d_{i}$,
we have carried out detailed pseudospectral DNSs of the 3D HMHD equations and
their counterparts for 3D MHD ($d_{i} = 0$). We present several statistical
properties of 3D HMHD turbulence, which we compare with 3D MHD turbulence by
calculating (a) the temporal evolution of the energy-dissipation rates and the
energy, (b) the wave-number dependence of fluid and magnetic spectra, (c) the
probability distribution functions (PDFs) of the cosines of the angles between
various pairs of vectors, such as the velocity and the magnetic field, and (d)
various measures of the intermittency in 3D HMHD and 3D MHD turbulence.
