Coarse-graining study of homogeneous and isotropic Hall magnetohydrodynamics turbulence

Inter-scale magnetic energy transfer associated with the Hall effects in homogeneous and isotropic magnetohydrodynamics (MHD) turbulence and the applicability of a Smagorinsky-type diffusive sub-grid-scale (SGS) model to Hall MHD turbulence are studied numerically. Low-pass filter analysis on magnetic energy transfer functions shows that their profiles change considerably when the cut-off wave number is comparable to the Taylor-scale wave number. It is shown that the Smagorinsky-type model is applicable to Hall MHD turbulence as a basic SGS model, while the Hall effects tend to overestimate the grid-scale magnetic energy transfer.