A scale-similarity model for the subgrid-scale flux with application to MHD turbulence in the Earth’s core

Turbulent motions in the Earth’s core have a strong influence on diffusive processes for large-scale fields through the eddy diffusion. They are highly anisotropic due to the influence of the Earth’s rotation and the magnetic field. It is therefore of significance to estimate the eddy diffusivity and to model subgrid-scale processes properly. A scale-similarity model, being one of the subgrid-scale models used in large-eddy simulation, is found to reproduce anisotropy. The purpose of this study is to reexamine scale similarity of magnetohydrodynamic (MHD) turbulence in the core and to demonstrate the validity of the subgrid-scale model developed by Matsushima [Matsushima, M., 2004. Scale similarity in the Earth’s core. Earth Planets Space 56, 599–605.] in two ways. First, spatial correlation and root-mean-square amplitude of the turbulent flux estimated through use of the model are compared with those obtained through direct numerical simulations at the same time step. The model appears valid from the result. Second, numerical simulations of MHD turbulence including the model of subgrid scales are carried out, and their results of time evolution are compared with those obtained through numerical simulations excluding the model. The result also indicates the subgrid-scale model holds valid.