Rotating convection is of fundamental importance in the dynamics of stellar and planetary interiors

旋转对流在恒星和行星内部的动力学中具有基本的重要性。大多数关于这个问题的工作都集中在单层流体具有恒定的物理性质的情况下，如粘度和热扩散率。然而，在现实中，这些属性随着深度的不同而变化很大。在非旋转对流中，这种可变性已经用两层模型进行了研究，其中每一层都具有不同的物理性质。两层模型可以看作是一种流体的理想化，其中的性质随深度变化平稳但强烈；因此，它允许进行广泛的分析。本项目将研究两层对流，并纳入旋转的重要影响。已经证明，非旋转双层问题表现出广泛的数学和物理有趣的行为，取决于不同的性质比以及层之间耦合的性质。因此，非常有兴趣了解包含旋转的画面是如何改变的。该项目的前半部分将涉及一个非平凡的线性稳定性分析，探索系统的各种性质对解的类型的影响。有了这些结果，该项目的后半部分将通过计算方法解决系统的非线性演化问题。

Rotating convection is of fundamental importance in the dynamics of stellar and planetary interiors. Most work on this problem has focused on the case of a single layer of fluid with constant physical properties, such as viscosity and thermal diffusivity. However, in reality, these properties vary strongly with depth. In non-rotating convection, this variability has been studied using a two-layer model, in which each layer assumes distinct physical properties. The two-layer model can be viewed as an idealisation of a fluid in which the properties vary smoothly but strongly with depth; as such, it allows for an extensive analysis.This project will study two-layer convection with the incorporation of the important influence of rotation. It has been demonstrated that the non-rotating two-layer problem exhibits a wide range of mathematically and physically interesting behaviour, dependent on various property ratios as well as the nature of the coupling between the layers. It is therefore of great interest to understand how the picture is changed by the inclusion of rotation. The first half of the project will involve a non-trivial linear stability analysis, exploring the influence of various properties of the system on the types of solution. Armed with these results, the second half of the project will address the nonlinear evolution of the system via a computational approach.