Changes in pattern formation and behavior in rotating Rayleigh-Benard convection due to inhomogeneous thermal insulation

The investigation of planetary cores is of great interest to those seeking to better understand magnetic fields and the life-processes of planets. Like many large-scale systems, planetary cores are unable to be modelled perfectly by numerical simulations or physical experiments. However, it is of constant importance to improve numerical and experimental methods and designs to better replicate full-scale processes. Many previous studies have over-looked the effects of the inhomogeneous insulation from the Earth's mantle on convection in the core. A few numerical studies have taken this effect into consideration for rotating Rayleigh-Benard convection (RBC) in spherical geometries. Experimental models are desirable to further understand the motion of fluid in the center of planets; however, due to physical limits, spherical systems are difficult to recreate experimentally. Therefore, cylindrical geometries are useful to study varied thermal flux on sidewalls both experimentally and numerically. While some studies have numerically and experimentally considered changes in temperature along the sidewall, there has been little consideration for variations in heat flux, which is the more physically appropriate boundary condition. 

The present study seeks to explore rotating RBC in a cylindrical domain with sidewalls inhomogeneously insulated in an experimentally-achievable system. It is experimentally plausible that the material of a cylindrical cell could varying in thickness, and therefore thermal conductivity, or have patches of heating and/or cooling attached to the sidewall to vary the thermal flux on the side boundaries. To imitate this numerically, a sinusoidal pattern of increasing and decreasing heat flux is applied to the sidewall in two cases: one whereby heat flux fluctuates between positive and negative, and another whereby the heat flux is strictly positive. Additionally the mode and amplitude of the wave is considered. The mode will either match the mode of the system with insulating sidewall conditions or have a larger wavelength to better simulate planetary cores. The amplitude is increased as necessary to achieve significant results. For simplicity, the top and bottom boundary conditions are fixed temperature.

Changes in heat transport and temporal behavior are measured with a global Nusselt number, Nu, time series. Additional variables such as mean zonal flow, number and location of convection rolls, and transitions to time-dependence are considered. Results indicate that large-wavelength heat flux on the sidewalls causes two modes to inhabit the system, existing on opposite sides of the cylinder: the mode natural to the homogeneously insulated system exists where heat flux is high and a large-wavelength mode dominates where heat flux is lower. However, the implementation of heat flux along the sidewalls with the same wavelength of the insulated system results in near-time independence as the amplitude increases. These results indicate that variation in heat flux boundary conditions can cause significant changes in rotating RBC behavior. Experimental studies could be used to validate or refute these conclusions. Overall, it is clear that numerical studies of molten planetary cores heterogeneously heated by mantles must take these irregularities into consideration to improve our understanding of core convection.