Towards realistic models of magnetic field generation in planetary cores

受旋转影响的对流驱动流在行星内部无处不在，包括类地天体的液体核心、气态巨星的外部区域和低温恒星的对流区域。这些流产生全球范围的磁场，可以远程观察，从而提供了独特的见解，否则无法进入行星和恒星的区域。然而，从流体动力学的角度来看，由于这些天体的快速旋转速率（相当于埃克曼数E < 10-10）和湍流（雷诺数Re > 108），对这些天体深部流体内部的旋转流体动力学建模是一个突出的挑战。这种极端条件无法通过直接的三维计算机模拟来模拟，因此需要补充方法。该项目将结合理论和计算工作来改进：1)利用快速旋转极限将（磁流体）动力学方程简化为二维的核动力学准地转（QG）模型；2)在快速旋转极限下有效的对流和磁场生成渐近简化模型。将这些新模型与加州大学洛杉矶分校进行的现有3D模拟和对流实验进行系统分析和比较，将使湍流动力学和磁场的作用能够在迄今为止无法进入的动力学体系中进行分析，并直接应用于行星内部。

Convection-driven flows influenced by rotation are ubiquitous in planetary interiors, including the liquid cores of terrestrial bodies, the outer regions of gas giants and the convective regions of cool stars. These flows generate global-scale magnetic fields that can be observed remotely and hence provide unique insight into otherwise inaccessible regions of planets and stars. However, from a fluid dynamical perspective, modelling the rotating fluid dynamics in the deep fluid interiors of these bodies represents an outstanding challenge because of the rapid rotation rates (equivalent to Ekman numbers E < 10-10) and turbulent flow (Reynolds number Re > 108). Such extreme conditions cannot be modelled by direct 3D computer simulation and so complementary approaches are required. This project will combine theoretical and computational work to improve: 1) quasi-geostrophic (QG) models of core dynamics that exploit the rapidly rotating limit to reduce the (magneto)hydrodynamic equations to 2D; 2) an asymptotically reduced model of convection and magnetic field generation that is valid in the limit of rapid rotation. Systematic analysis and comparisons of these new models with existing 3D simulations and convection experiments conducted at UCLA will allow the turbulent dynamics and the role of magnetic fields to be analysed in hitherto inaccessible dynamical regimes with direct application to planetary interiors.