Research Spotlight: Rhiannon Nicholls

Journal of Fluid Mechanics, 1033: A21. DOI:10.1017/jfm.2026.11353
Rhiannon A.M. Nicholls, Evy Kersalé, David W. Hughes, Christopher J. Davies and Fryderyk Wilczynski

Publication: Rotating Rayleigh–Bénard convection with fixed-flux thermal boundary conditions.

Rotating Rayleigh–Bénard convection (RRBC) is the study of thermal convection in a horizontal fluid layer heated from below while the entire system is rotated 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. Mechanical and thermal boundary conditions play an important role in our ability to apply simplified models to real-world scenarios. In studies of convection, two limiting cases for thermal boundary conditions are frequently examined: (i) ‘perfectly conducting’ or fixed-temperature boundary conditions, where the temperature remains constant along the bounding surfaces; and (ii) ‘perfectly insulating’ or fixed-flux boundary conditions, where (for uniform thermal conductivity) the normal derivative of temperature is fixed at the boundaries. Thermal boundary conditions relevant to geophysical and astrophysical contexts often fall within the spectrum between these fixed-flux and fixed-temperature extremes. Comprehending the dynamics at these two extremes is therefore crucial to advancing our understanding of geophysical and astrophysical systems.

For Boussinesq, linear RRBC under rapid rotation, the case with impermeable, stress-free and fixed-temperature boundaries is notable as it can be solved analytically. The case with fixed-flux boundaries presents greater complexity as the eigenfunctions are no longer simple trigonometric functions. However, since under the constraint of rapid rotation the balance between Coriolis, buoyancy and viscous terms leads to a very small preferred horizontal length scale, the solution in the bulk of the fluid is independent of the choice of boundary conditions. Thus, different mechanical and thermal boundary conditions can be explored through perturbative methods; this enables analytical progress beyond the impermeable, stress-free and fixed-temperature case. Exploiting this property, we derive asymptotic solutions for the linear onset of steady, Boussinesq RRBC under rapid rotation with impermeable, stress-free, fixed-flux boundary conditions.

Our approach centres on deriving the governing equations and corresponding solutions for the departures from the fixed-temperature system. Specifically, this involves constructing a composite boundary layer structure comprising an Ekman layer and a thermal boundary layer to accommodate the fixed-flux boundary condition. The asymptotic corrections that capture the differences between the two systems are combined with the fixed-temperature solution to construct the corresponding solution for the fixed-flux system.