Instabilities in Rotating Two-layer Convection

Rotating Rayleigh–Bénard convection (RRBC) is the study of thermal convection in a horizontal fluid layer heated from below while the entire system rotates about the vertical axis, thereby combining buoyancy-driven and rotational effects. RRBC has been extensively studied to understand key aspects of fluid dynamics in many geophysical and astrophysical contexts.

Rotating convective systems, particularly in geophysical and astrophysical applications, exhibit strong depth-dependent variations in fluid properties. Simplified models that approximate the dominant dynamical processes, typically by treating depth-dependent properties as constant, are employed, rendering the problem computationally feasible while still capturing the essential physics. Consequently, the exploration and understanding of rotational effects in convective systems with depth-dependent properties remain limited, thereby motivating the systematic investigation presented in this study.

Two-layer convection is an extension of the classical RRBC framework, comprising two superposed, horizontally extended fluid layers that are heated from below. Each layer is characterised by distinct physical parameters, thereby enabling an explicit representation of depth-dependent variations in the fluid’s properties. In this thesis, we aim to advance the theoretical understanding of rotating convection with depth-dependent variations in fluid properties by analysing the instabilities that arise in a simplified rotating two-layer configuration. We first examine the role of thermal boundary conditions in steady RRBC under rapid rotation and derive an asymptotic solution for fixed-flux boundaries. Our analysis demonstrates that, in the rapidly rotating limit, the influence of thermal boundary conditions becomes negligible. We then investigate instabilities in two related configurations. First, we consider a single-fluid-layer system overlain by a solid boundary slab of finite thickness and thermal conductivity, which serves as a reduced model for a two-fluid-layer system with a strong viscosity contrast. Subsequently, we extend the analysis to the fully coupled rotating two-layer configuration. In both configurations, we determine the onset conditions and conduct a comprehensive linear stability analysis to elucidate how the system’s behaviour depends on the underlying fluid properties.