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

为了模拟涡旋扩散张量，我们对快速旋转系统中的MHD湍流进行了直接的数值模拟。为了在真实的行星核心中使用分子扩散系数进行计算，即使是核心中非常小的区域，也需要高分辨率。在本研究中，将计算区域划分为几个段，在具有大内存的并行计算机上将这些段分配给各自的CPU。利用所获得的直接数值模拟结果，我们考察了MHD湍流中的尺度相似性来模拟亚格子尺度的物理过程，发现尺度相似性是成立的。基于尺度相似律和空间滤波片宽度依赖关系，我们估计了次网格尺度对网格尺度的影响。在此基础上，利用亚格子模型对MHD湍流进行了大涡模拟。我们将它们的结果与直接数值模拟的结果进行了比较，证实了该次网格尺度模式的有效性。也就是说，采用次网格尺度模式的大涡模拟的计算时间和计算区域的平均热通量、动能和磁能更接近于直接数值模拟的热通量、动能和磁能。然而，值得注意的是，速度场、磁场和温度的功率谱之间没有显著差异。

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.