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，包括地球物体的液体核心，气体巨星的外部区域和冷恒星的对流区域。这些流动产生的全球规模的磁场可以远程观察，从而提供了对行星和恒星的其他无法到达的区域的独特见解。然而，从流体动力学的角度来看，在这些机构的深层流体内部的旋转流体动力学建模是一个突出的挑战，因为快速旋转速率（相当于埃克曼数E < 10-10）和湍流（雷诺数Re > 108）。这种极端条件不能通过直接的3D计算机模拟来建模，因此需要补充方法。该项目将联合收割机的理论和计算工作相结合，以改善：1）准地转（QG）模型的核心动力学，利用快速旋转的限制，以减少（磁）流体动力学方程到2D; 2）一个渐进减少模型的对流和磁场的产生，是有效的快速旋转的限制。系统分析和比较这些新的模型与现有的三维模拟和对流实验在加州大学洛杉矶分校进行将允许湍流动力学和磁场的作用进行分析，在迄今为止无法访问的动力学制度，直接应用到行星内部。

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.