标题： 访问快速旋转球形壳体发电机中的偶极子-多极子跃迁 显示英文标题

标题： Accessing the dipole-multipole transition in rapidly rotating spherical shell dynamos

摘要： 地磁场极性反转是地球磁场的一个关键特征，但控制这些反转过程仍不甚明了。双极性反转在许多数值发电机模拟中被发现，并且通常发生在双极性和多极性状态之间的转变附近。由于捕捉极性转换所需的长时间运行，模拟条件与地球液态铁核中的条件相去甚远。我们开发了一种一维路径理论，试图简化在日益接近现实物理条件的情况下寻找双极性到多极性转换的过程。我们构建了3条路径，所有路径都基于一个恒定的磁雷诺数$Rm$；一条旨在达到磁力、科里奥利力和阿基米德力（MAC），另外两条旨在达到惯性-MAC力平衡。由于惯性力在模拟反转中的作用，我们引入了惯性力。结果显示，在可访问的参数空间内，结果与预测合理吻合，但对于某些量，如磁场强度和磁能/动能比，结果偏离了预期行为。此外，随着沿着路径推进，模拟进入双极性非反转区域。通过增加浮力驱动（通过提高雷诺数）超过路径理论预测的值，我们能够将双极性到多极性的转变降至一个埃克曼数$E\sim 10^{-6}$，这与迄今为止报道的最极端条件相当。结果表明，我们的方法是在低$E$下寻找双极性到多极性转换的一种有效方法。然而，我们访问双极性到多极性转换的条件变得越来越难以通过数值方法实现，并且也越来越不切实际，因为$Rm$上升超出了从地质物理观测推断出的可能范围。未来的工作结合路径理论与核心浮力分布的变化，似乎是一种有前景的方法，可以在极端物理条件下访问这种转变。 显示英文摘要

摘要： Polarity reversals are a key feature of Earth's magnetic field, yet the processes governing them are still poorly understood. Dipole reversals have been found in many numerical dynamo simulations and often occur close to the transition between dipolar and multipolar regimes. Simulated conditions are far from those in Earth's liquid iron core because of the long runtimes needed to capture polarity transitions. We develop a unidimensional path theory in an attempt to simplify the search for the dipole-multipole transition at increasingly realistic physical conditions. We build 3 paths, all based on a constant magnetic Reynolds number $Rm$; one aiming for Magnetic, Coriolis, and Archimedean (MAC), and 2 aiming for inertia-MAC force balance. We add inertia due to its role in simulated reversals. Results show reasonable agreement with predictions within the accessible parameter space, but deviate from predicted behaviour for certain quantities, e.g. magnetic field strength and magnetic/kinetic energy ratio. Further, simulations move into the dipolar non-reversing regime as they are advanced along the path. By increasing the buoyancy driving (via higher Rayleigh number) above the values predicted by the path theory, we are able to access the dipole-multipole transition down to an Ekman number $E\sim 10^{-6}$, comparable to the most extreme conditions reported to date. Results demonstrate that our approach is an efficient method for seeking the dipole-multipole transition at low $E$. However, the conditions under which we access the dipole-multipole transition become increasingly hard to access numerically and also increasingly unrealistic because $Rm$ rises beyond plausible bounds inferred from geophysical observations. Future work combining path theory with variations in the core buoyancy distribution, appears a promising approach to accessing the transition at extreme physical conditions.