Non-Oberbeck-Boussinesq effects in turbulent convection in cryogenic helium at high Rayleigh numbers

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Experiments of turbulent Rayleigh-Bénard convection (RBC) in cryogenic helium gas reach the highest possible Rayleigh numbers with a vigorous turbulence under controlled laboratory conditions that come close to those in real atmospheric flows and can thus provide us deeper insights into the turbulent transport mechanisms of heat and momentum in these natural systems. These high Rayleigh numbers require however to operate the helium working fluid close to the phase boundary or even the critical point of the pressure-temperature phase plane which causes fluctuations of all material parameters such as kinematic viscosity or thermal conductivity. These fluctuations result in deviations from the Oberbeck-Boussinesq (OB) regime of thermal convection with a well-defined up-down symmetry of the flow and its statistics. In this project, we want to investigate these deviations -- the so-called non-Oberbeck-Boussinesq (NOB) effects -- and its impact on the turbulent transport systematically. Therefore we bring the expertise in cryogenic experiments on the Czech side and in massive direct numerical simulations of turbulent convection on the German side in a joint Czech-German proposal together. The detailed parameter dependencies on temperature and pressure will be obtained from the XHEPAK software that models the equation of state of the cryogenic helium gas in its full complexity. The resulting material parameter dependencies enter the numerical simulations and can be directly compared with the idealized OB limit as well as experiments at the same Rayleigh numbers. Our work helps to better understand the inconclusive results obtained in different high-Rayleigh-number laboratory experiments with respect to the existence of a transition of the RBC flow into the ultimate regime (with a significantly enhanced turbulent heat transfer).