Hall effects and sub-grid-scale modeling in magnetohydrodynamic turbulence simulations

Abstract

Effects of the Hall term on short-wave components of magnetohydrodynamic turbulence and sub-grid-scale modeling of the effects are studied. Direct numerical simulations of homogeneous magnetohydrodynamic turbulence with and without the Hall term are carried out. The Hall term excites short-wave components in the magnetic field, demanding a high numerical resolution to resolve the scales smaller than the ion skin depth. A k 7 / 3 -like scaling-law in the magnetic energy spectrum associated with the excitation of the short-wave components is clearly shown by the use of both an isotropic spectrum and a one-dimensional spectrum. It is also shown that the introduction of the Hall term can cause a structural transition in the vorticity field from tubes to sheets. In order to overcome a strong demand on high-resolution in space and time and to enable quicker computations, large eddy simulations with a Smagorinsky-type sub-grid-scale model are carried out. It is shown that our large eddy simulations successfully reproduce not only the energy spectrum but also tubular vortex structures, reducing the computational cost considerably.