Contributions of small scales to statistics of Hall MHD turbulence

A direct numerical simulation of decaying, homogeneous and isotropic turbulence of the incompressible Hall magnetohydrodynamic equations is carried out to clarify its statistical natures. Contributions of small scales to the statistics are examined. It is shown that the probability density function (PDF) of the enstrophy density is well characterized by the Gaussian distribution when the short wave number coefficients are removed, even though the vortex field shows intermittent structures. It is also shown that the local vortex structures are aligned to the magnetic field lines especially when the turbulent field is under developing and small scales are going to be excited. The alignment is lost in the relaxation process, suggesting the small scale current density field is less affected by the dissipations than the vorticity field.