Convection, dissipation, and rotation in simulations of stellar and planetary interiors and atmospheres

所有的主序星，以及许多行星，在它们的内部或大气中的某个地方都有对流运动。这种对流可以控制热量和角动量的传输，调节物体随时间的演变，并且通常会建立强大的磁场。这些磁场可能反过来在确定靠近其主星轨道的行星的可居住性方面发挥关键作用。到目前为止，大多数关于系外行星动力学的研究都集中在物体的深层内部-捕捉其对流和动力作用，但没有其大气特性-或者只捕捉行星的近表面“天气”层，而忽略或粗略地参数化这些之间的耦合。之所以需要这种方法，部分是因为这些层的物理性质不同：深层区域密度大，运动相对较慢，而靠近表面的低密度流可以达到接近声速的速度。但在现实中，这些区域之间的反馈可能是复杂而重要的：例如，在某些受辐射的系外行星中，大气层中驱动的流动可能最终“钻入”内部深处，影响它们的最终演化。目前的任何模型都无法准确地捕捉到这种反馈。这个项目将首次在同一个计算框架内对这些不同的区域进行建模。我们将使用新的开源代码Dedalus，它能够解决与深层和天气层相关的方程组，并且在大规模并行超级计算机上扩展良好。我们首先将一组与系外行星近地表层相关的简化动力学方程应用到Dedalus，并将我们的计算结果与最先进的“系外行星气候”模型的计算结果进行比较（在埃克塞特开发，并基于气象局的一般流通模型）。我们还将实施所谓的"与Dedalus内部深处相关的“非弹性”方程，再次与专门为这些地区设计的世界领先代码（称为ASH和Rayleigh）运行的单独计算进行比较。稍后，我们将把这两个计算结合起来，让气流从内部深处进入大气层，反之亦然。最后，我们将探讨允许模拟本身从一个解决方案到另一个在同一计算域中的无障碍“适应”。总的来说，我们的目标是确定深层如何影响大气中发生的环流，以及如何受到大气中发生的环流的影响。最终，我们的研究结果将帮助我们理解为什么这些行星具有所观察到的大小，大气特性和强大的环流。

All main-sequence stars, and many planets, possess convective motions somewhere in their interior or atmosphere. This convection can dominate the transport of heat and angular momentum, regulating the object's evolution over time, and also often builds powerful magnetic fields. These fields may in turn play a crucial role in, for example, determining the habitability of planets orbiting close to their host stars. So far, most studies of the dynamics in exoplanets have focused either on the deep interior of the object -- capturing its convection and dynamoaction but none of its atmospheric properties -- or else have captured only the near-surface ``weather'' layer of the planet, while ignoring or crudely parameterising the coupling between these. This approach has been required partly because the physical properties of these layers are different: thedeep regions are dense, and motions there are comparatively slow, whereas nearer the surface the low-density flows can attain velocities close to thespeed of sound. But in reality, the feedback between these regions is likely to be complex and important: for example, in certain irradiated exoplanets, flows driven in the atmospheric layers might ultimately ``burrow'' into the deep interior, impacting their ultimate evolution. Thisfeedback cannot accurately be captured by any current model.This project will seek to model these disparate regions together within the same computational framework for the first time. We will employ the new open-source code Dedalus, which is uniquely capable of solving the equation sets relevant to both the deep and weather layers, and which scales well on massively parallel supercomputers. We will start by implementing a simplified set of dynamical equations relevant to the near-surface layers of an exoplanet into Dedalus, and comparing the results of our calculations to ones done using a state-of-the-art ``exoplanet climate'' model (developed here at Exeter and based on the Met Office's general circulation model).We will also implement the so-called ``anelastic'' equations relevant to the deep interior into Dedalus, again comparing to separate calculations run with world-leading codes (called ASH and Rayleigh) designed specifically for those regions. Later, we will couple the two calculations together, allowing flows to pass from the deep interior into the atmosphere and vice versa. Finally, we will explore allowing the simulation itself to seemlessly ``adapt'' from one solution scheme to another within the same computational domain. Overall, we will be aiming to determine how the deep layers influence, and are in influenced by, the circulations occurring in the atmosphere. Ultimately, our results will help us understand why theseplanets have the sizes, atmospheric properties, and strong circulations that are observed.