Accessing the rapidly rotation regime of convection and magnetic field generation

受自转影响的对流驱动流动普遍存在于行星内部，包括地体的液核、气态巨星的外部区域和冷恒星的对流区域。这些流动产生了可以远程观测的全球范围的磁场，因此提供了对行星和恒星原本无法到达的区域的独特洞察。然而，从流体动力学的角度来看，对这些物体深部流体内部的旋转流体动力学进行建模是一项突出的挑战，因为它们的旋转速度很快(相当于Ekman数E&lt；10-10)和湍流(雷诺数Re&gt；108)。这样的极端条件不能通过直接的3D计算机模拟来模拟，因此需要补充的方法。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2D的准地转(QG)核心动力学模型；2)适用于快速旋转极限的对流和磁场产生的渐近简化模型。对这些新模型与加州大学洛杉矶分校现有的3D模拟和对流实验进行系统的分析和比较，将使我们能够分析迄今无法进入的动力学区域中的湍流动力学和磁场的作用，并将其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.