Rapidly rotating Rayleigh-Bénard convection in liquid metals

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Rotating Rayleigh-Bénard convection in liquid metals is considered to be an ideal model system of the magnetohydrodynamic processes occurring in many geophysical and astrophysical settings, such as planetary cores and stellar convection zones. From a fluid dynamical point of view these flows distinguish themselves by their low Prandtl number, leading to inherently different instability mechanisms and a much earlier transition to turbulence, when compared to moderate and high Prandtl number flows. However, due to the much more demanding resolution requirements for direct numerical simulations (DNS) and the limited visual access in experiments because of the metal's opaqueness, studies are sparse. Consequently, the underlying physics, notably oscillatory convection, is not well understood. The objective of the proposed research is thus to enrich our knowledge about convective flows in liquid metals. For this purpose, high-resolution DNS of small Prandtl number convection shall be conducted in cylindrical containers with various aspect ratios, both under the influence of rapid rotation and of magnetic fields. In particular, the regime of geostrophic turbulence will be covered, which is little explored and yet the most relevant in geophysical settings. The control parameters will be chosen to match exactly the unique rotating magnetoconvection device at the Simulated Planetary Interiors Laboratory (SPINlab) at UCLA which uses liquid gallium as working fluid. This allows for a one-to-one comparison and provides the foundation for sophisticated analysis techniques. To interpret and analyse the obtained data, approaches from turbulent convection theory, system identification, and laboratory geophysical fluid dynamics shall be brought together. This means, besides using the traditional methods of studying spectra, the mean, root mean square, and higher-order statistical moments, the dynamical mode decomposition (DMD) shall be exploited. The DMD will directly link the frequencies found in the experiments and the DNS with actual flow structures and will further allow the study of their temporal evolution. Moreover, a novel view on this problem shall be gained by borrowing techniques from system identification theory. It is aimed to design a dynamic observer, which based on single thermistor measurements and in conjunction with the DNS, will be able to reconstruct the entire flow in the otherwise visually inaccessible experiment.