Non-Oberbeck-Boussinesq Effects in the Ultimate State of Rapidly Rotating Rayleigh-Benard Convection

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Many of the turbulent flows occurring in nature, for example within planetary and stellar interiors, as well as atmospheres, are driven by convection and are strongly constrained by rapid rotation. An excellent and mathematically easily describable model system is rotating Rayleigh-Bénard convection. The model consists of a liquid or gas confined between a warm bottom boundary and a cold top boundary rotated around the vertical axis. But the level of turbulence and the relative rotation rates (expressed in terms of the control parameters Rayleigh and Ekman number) reached in earthbound numerical simulations and laboratory experiments of Rayleigh-Bénard convection, are not as extreme (yet) as the parameters in natural settings. Moreover, most numerical simulations and mathematical theories assume constant material properties (e.g. viscosity and thermal diffusivity), contrary to realistic fluids where they vary with temperature and pressure. Thus, interpreting results from simulations and experiments in the light of geophysical and astrophysical flows is somewhat problematic.However, there is a long-held tenet in turbulence research that if the flow only becomes turbulent enough, that is, reaches the "ultimate regime," any global transport and macroscopic features become independent of the molecular diffusivities, in particular, the viscosity and the thermal diffusivity. Hence, crucially, if the ultimate state exists, an upscaling from numerical simulations and laboratory experiments to geo- and astrophysical systems is possible despite many orders of magnitude difference in the control parameters. The objective of the proposed research is to test the hypothesis of a diffusion-free scaling of the heat and momentum transport in the ultimate state of rapidly rotating Rayleigh-Bénard convection.Even though theoretical arguments predict that the ultimate state is more easily accessible in rotating than in non-rotating systems, the numerical resolution requirements are prohibitive for a brute force approach with present-day computational resources.To alleviate the resolution constraints, I will consider a novel point of view by employing a varying thermal diffusivity and kinematic viscosity within the very same convection vessel. The variation of the material properties leads to a breaking of the top-bottom symmetry in the classical (non-ultimate) Rayleigh-Bénard problem. However, in the ultimate regime, one may expect that this symmetry gets restored, assuming that the molecular diffusivities do no longer affect the global flow state. The restoration of this symmetry can be used as an indicator and quantitative measure for reaching the ultimate regime and allows for reliable extrapolation. Further, as boundary layers are known to be key players in the transport of heat and momentum in turbulent thermal convection, I will compare simulations of boundary layer free triply periodic Rayleigh-Bénard convection with laboratory-like cylindrical set-ups that include boundary layers.