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

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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.