Expression of turbulent heat flux in the Earth’s core in terms of a second moment closure model

Abstract

Direct numerical simulations of local turbulence in the Earth’s core are performed. A small region in the core is represented by a rectangular box with periodic boundary conditions. A uniform magnetic field is imposed, and small-scale motions are driven by a large-scale temperature gradient parallel to the gravitational field; the system is rapidly rotating. The turbulent heat flux is computed and represented by an anisotropic eddy diffusivity tensor. This tensor is compared with an alternative expression derived directly from the basic equations by applying a second moment closure model of the type used in turbulence theory. It is found that the two methods give consistent results, although some modifications are necessary to improve the agreement. It is believed that the results of the present study will be useful in quantifying the effects of anisotropic turbulence on global geodynamo models.