Rayleigh-Benard Convection in Spherical Shell with Infinite Prandtl Number at High Rayleigh Number

Abstract

Simulations of the Rayleigh-Benard convection with infinite Prandtl number ( Pr) and high Rayleigh numbers (Ra) in the spherical shell geometry are carried out to understand the thermal structure of the mantle and the evolution of the Earth. We focus on the features of the convection with the most basic set- ting, so the viscosity is assumed to be constant and other complexities of the mantle are not introduced. We have succeeded in calculating the thermal convection in the spherical shell with Ra up to 10 8 , and attained the numerical results for Ra ranging five orders above the critical value. For all Ra, the convection pattern is illustrated as follows; the sheet-shaped downwelling and upwelling flows originate from the boundary layers and concentrate gradually into cylindrical flows. We have examined the relationship between Ra and the Nusselt number (Nu), and obtained that Nu is proportional to Ra 0.30 . The exponent is larger than those of the existing studies. In addition, we quantify the convection pattern by the power spectrum of the temperature field for each depth in terms of spherical harmonic degrees. The analysis reveals that the structural scale of convection differs between the boundary region and the isothermal core region. The structure near the bound- ary region is characterized by the cell type structure constructed by the sheet-shaped downwelling and upwelling flows, and that of the core region by the plume type structure which consists of the cylindrical flows.