Numerical investigation of cell formation in a 2-dimensional differentially heated shell utilizing thermo-electrohydrodynamics

Today models of our atmosphere to study climate change become more and more important not only from a meteorological point of view but also from a global perspective to understand the large-scale motion of planetary waves that transport a large amount of energy. This study investigates numerically such large-scale flows in a simplified 2-dimensional model that is aligned to the AtmoFlow experiment. This experiment is the legacy of the GeoFlow experiment, which investigated planet mantle convection. The AtmoFlow experiment is a spherical shell that mimics a planet at a small scale, where terrestrial gravity is artificially induced by an equivalent electric central force field. This small planet can rotate synchronized or differentially by moving the inner and outer boundaries to simulated planetary rotation. Analogous to a real planet, the poles are cooled and the equator heated. The fluid used in the numerical simulation to mimic a planetary atmosphere is a dielectric fluid with an electric permittivity sensitive to temperature to induce convection similar to a terrestrial buoyancy. While the fluid is also sensitive to the temperate-dependent density, the spherical shell experiments are performed in free space and thus the experiment is planned to be operated on the International Space Station (ISS) after 2024. Flow patterns are retrieved using a Wollaston Shear Interferometry (WSI) and sent back to Earth's ground station.

To be able to investigate the flow structures recorded by the experiment, a numerical model is built. Here we only show 2-dimensional results of the shell in the equatorial plane without rotation. The boundary conditions in these simulations are set to an ideal fixed temperature where the inner shell is heated, and the outer is cooled. To induce thermo-electro-hydrodynamics convection, an electric voltage is applied at the inner shell whereas the outer is grounded. The resulting flow patterns evolve in time and are stationary, quasi-stationary, or chaotic structures. The arising convection cells can be classified using a time-averaged spatial Fast Fourier Transformation (FFT) of the temperature along the mid-gap of the domain to quantify a mode number. The heat transfer is expressed with the Nusselt number and increases with the Rayleigh number. This is reflected by the mode number increasing to a maximum before it decreases when the flow becomes unstable while maintaining a clear structure and mode shape with detaching plumes at the tangent cylinder.