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

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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.