Planetary core dynamics and convective heat transfer scaling†

Abstract

In this article, analysis of a compilation of recent core dynamics models focuses on the properties of non-magnetic rotating convection. Numerical simulations and laboratory experiments are shown to agree qualitatively in cases with similar control parameter values. Small-scale convection columns interact with the spherical shell to generate larger-scale zonal flows. Comparing quantitative results, heat transfer data is compiled from eight recent studies of core convection. The data are plotted in terms of Nusselt and Rayleigh numbers, Nu and Ra, and also in terms of diffusivity-free, modified Nusselt and flux Rayleigh numbers, Nu* and . Based on the compiled results, it appears that an asymptotic scaling law for heat transfer in planetary core convection models has yet to be determined. Numerical modeling results support a scaling law (equivalently, Nu∼Ra ^1.2), which is likely to be affected by the Nu*– onset scaling. In contrast, laboratory experiments, which reach more extreme parameter values, support a scaling law (Nu∼Ra ^0.4). Given this significant disagreement, further laboratory and numerical modeling is needed in the fully turbulent, rapidly-rotating regime. Investigation of this regime, especially using realistic low Prandtl number fluids, will require considerable effort. Numerical models will require efficient parallelization and massive computational resources in order to resolve the range of structures that exist in strongly turbulent, rotating flows. Laboratory models will have to minimize the effects of finite thermal conductivity boundaries, which can alter the scaling behavior at high heat transfer rates.