4.6 Article

Comparison of quasi-geostrophic, hybrid and 3-D models of planetary core convection

期刊

GEOPHYSICAL JOURNAL INTERNATIONAL
卷 231, 期 1, 页码 129-158

出版社

OXFORD UNIV PRESS
DOI: 10.1093/gji/ggac141

关键词

Earth Core; thermal vection; theories and simulations; Numerical modelling

资金

  1. IDRIS Jean Zay CPU cluster [2021-A0070410095]
  2. European Research Council (ERC) under the European Union [772561]
  3. European Research Council (ERC) [772561] Funding Source: European Research Council (ERC)

向作者/读者索取更多资源

This study investigates rapidly rotating convection in a thick spherical shell geometry relevant to planetary cores. The results are compared between quasi-geostrophic (QG), 3-D, and hybrid QG-3D models. The study finds that the 3-D model and QG model show similar results under strong driving, while the hybrid model and 3-D model are closer under weak driving. This research provides insights into convection patterns in planetary cores and the importance of different modeling approaches.
We present investigations of rapidly rotating convection in a thick spherical shell geometry relevant to planetary cores, comparing results from quasi-geostrophic (QG), 3-D and hybrid QG-3D models. The 170 reported calculations span Ekman numbers, Ek, between 10(-4) and 10(-10), Rayleigh numbers, Ra, between 2 and 150 times supercritical and Prandtl numbers, Pr, between 10 and 10(-2). The default boundary conditions are no-slip at both the ICB and the CMB for the velocity field, with fixed temperatures at the ICB and the CMB. Cases driven by both homogeneous and inhomogeneous CMB heat flux patterns are also explored, the latter including lateral variations, as measured by Q*, the peak-to-peak amplitude of the pattern divided by its mean, taking values up to 5. The QG model is based on the open-source pizza code. We extend this in a hybrid approach to include the temperature field on a 3-D grid. In general, we find convection is dominated by zonal jets at mid-depths in the shell, with thermal Rossby waves prominent close to the outer boundary when the driving is weaker. For the thick spherical shell geometry studied here the hybrid method is best suited for studying convection at modest forcing, Ra <= 10 Ra-c when Pr = 1, and departs from the 3-D model results at higher Ra, displaying systematically lower heat transport characterized by lower Nusselt and Reynolds numbers. We find that the lack of equatorially-antisymmetric motions and z-correlations between temperature and velocity in the buoyancy force contributes to the weaker flows in the hybrid formulation. On the other hand, the QG models yield broadly similar results to the 3-D models, for the specific aspect ratio and range of Rayleigh numbers explored here. We cannot point to major disagreements between these two data sets at Pr >= 0.1, with the QG model effectively more strongly driven than the hybrid case due to its cylindrically averaged thermal boundary conditions. When Pr is decreased, the range of agreement between the hybrid and 3-D models expands, for example up to Ra <= 15 Ra-c at Pr = 0.1, indicating the hybrid method may be better suited to study convection in the low Pr regime. We thus observe a transition between two regimes: (i) at Pr >= 0.1 the QG and 3-D models agree in the studied range of Ra/Ra-c while the hybrid model fails when Ra > 15 Ra-c and (ii) at Pr = 0.01 the QG and 3-D models disagree for Ra > 10 R-c, while the hybrid and 3-D models agree fairly well up to Ra similar to 20 Ra-c. Models that include laterally varying heat flux at the outer boundary reproduce regional convection patterns that compare well with those found in similarly forced 3-D models. Previously proposed scaling laws for rapidly rotating convection are tested; our simulations are overall well described by a triple balance between Coriolis, inertia and Archimedean forces with the length-scale of the convection following the diffusion-free Rhines-scaling. The magnitude of Pr affects the number and the size of the jets with larger structures obtained at lower Pr. Higher velocities and lower heat transport are seen on decreasing Pr with the scaling behaviour of the convective velocity displaying a strong dependence on Pr. This study is an intermediate step towards a hybrid model of core convection also including 3-D magnetic effects.

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