The role of thermal boundary conditions in rotating Rayleigh-Bénard convection

Rotating Rayleigh–Bénard convection (RRBC) is ubiquitous in nature. RRBC is present in the dynamics of planetary cores and atmospheres. Numerical models of RRBC are limited in their ability to represent geophysical convective flows. In addition, while thermal boundary conditions which are physically appropriate for geophysical flows are available, many numerical models chose to simplify the boundaries to be fixed temperature and all thermal conditions to be homogeneous. We are motivated to explore the significance of these simplified conditions by exploring the effects of physically-appropriate thermal boundary conditions on RRBC. We study RRBC in a cylindrical domain, which is appropriate both for comparison to experimental models and for understanding dynamics in the polar regions of planetary flows. On the horizontal boundaries, the fixed temperature condition is compared to the astrophysically appropriate fixed flux, mixed (fixed temperature on the lower boundary and fixed flux on the upper boundary) conditions, and the Robin condition which straddles the fixed flux and fixed temperature conditions. We show that at rapid rotation, convection onset is independent of thermal boundary condition, extending the theory presented in Calkins et al. (2015). We also define a novel parameter for comparing systems with Robin boundary conditions to those fixed temperature boundaries. We show that, while the fixed temperature thermal boundary condition is sufficient for modelling the bulk flow of experimental RRBC systems, natural systems may require use of the Robin condition. Subsequently, we investigate the effect of inhomogeneous insulation on lateral walls, motivated by the irregular heat flux which the Earth’s mantle applies to the outer core. The inhomogeneity is sinusoidal along the azimuthal axis with azimuthal mode mθ which is varied relative to the dominant length-scale of convection in three scenarios: larger length-scale than convection; the same length-scale as convection; and a secondary convective length-scale. The first instance is appropriate for molten planetary cores, while the latter two are of interest for experimental studies. The main results are: large-length scale mθ causes a convection roll rotation about the domain to slow, and matching mθ to the convective length-scale- or a multiple of it- causes convection rolls to be pinned. Finally, an experimental set-up is proposed based on the simplified precipitation model in Hernadez-Duenas et al. (2012). The specifications for the set-up are determined using the results of numerically modelled RRBC with the Robin condition. The experiment would have applications in Numerical Weather Prediction.