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.