The Subgrid Problem of the Thermal Convection in the Earth's Liquid Core

Abstract

The problem of the turbulent thermal convection in the Earth's liquid core is considered. Following assumptions on decreasing of the spatial scales due to the rapid rotation, we propose the subgrid model of the eddy diffusivity, which is used in the large-scale model. This approach makes it possible to model realistic regimes with small Ekman and Rossby numbers ($E\sim 10^{-14}$, $R_o \sim 10^{-8}$) and a sufficiently large Rayleigh number $R_a \sim 10^{12}$. The obtained estimate of the averaged kinetic energy is comparable with observations. The model includes rotation of the solid core due to the viscous torque.