We present results from direct numerical simulations of flows in spherical and oblate spheroidal shells, driven both by precession and thermal convection, with Ekman number $Ek=10^{-4}$ , non-diffusive Rayleigh numbers from $Ra=0.1$ to $Ra=10$ and unity Prandtl number. The applied precessional forcing spans seven orders of magnitude. Our experiments show a clear transition between a convective state and a precessing flow that can be approximated by a reduced dynamical model. The change in the flow is apparent in visualizations and a decomposition of the velocity into symmetric and antisymmetric components. For the flow dominated by precession, some parameter combinations show two stable solutions that can be realized by a hysteresis or a strong thermal forcing. An increase of the Rayleigh number at a constant precession rate exhibits established scaling properties for the heat transfer, with exponents $2/7$ and $6/5$ .

中文翻译：

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球壳内对流温度场影响下的进动特性

我们展示了由进动和热对流驱动的球壳和扁球壳中流动的直接数值模拟结果，埃克曼数 $Ek=10^{-4}$ ，非扩散瑞利数从 $Ra=0.1$ 到$Ra=10$ 和统一普朗特数。应用的岁差强迫跨越七个数量级。我们的实验显示了对流状态和进动流之间的清晰过渡，可以通过简化的动力学模型来近似。流动的变化在可视化和速度分解为对称和反对称分量中很明显。对于进动主导的流动，一些参数组合显示出两个稳定的解决方案，可以通过滞后或强热强迫实现。