Modeling a mechanism of MHD turbulent diffusion in Earth and Planetary fluid cores

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Aiming at modeling an eddy diffusivity tensor, we have performed direct numerical simulations of MHD turbulence in a rapidly rotating system. To carry out computation using molecular diffusivity in a realistic planetary core, required is high resolution even for a very small region in the core. In the present research, the computational region is divided into several segments, which are allocated to respective CPUs on a parallel computer with large size of memory. Using results of direct numerical simulations thus obtained, we have examined scale similarity in MHD turbulence to model subgrid-scale physical processes, and we have found that scale similarity holds. On the basis of scale similarity law as well as spatial-filter width dependence, we have estimated the effect of subgrid-scales on grid-scales. We have then carried out large eddy simulations of MHD turbulence with the model of subgrid-scales. We have compared their results with those of direct numerical simulations, and confirmed that the present subgrid-scale model holds valid. That is, heat flux, kinetic energy, and magnetic energy averaged over computational time and computational region for large eddy simulation with the subgrid-scale model are closer to those for direct numerical simulations than those for numerical simulations without the model. It should be noted, however, that there is no significant difference among power spectra for velocity field, magnetic field, and temperature.