The influence of the cell inclination on the heat transport and large-scale circulation in liquid metal convection

Inclined turbulent thermal convection in liquid sodium is studied at large Rayleigh numbers $Ra\gtrsim 10^{7}$ based on the results of both experimental measurements and high-resolution numerical simulations. For a direct comparison, the considered system parameters are set to be similar: $Ra=1.67\times 10^{7}$ in the direct numerical simulations (DNS), $Ra=1.5\times 10^{7}$ in the large-eddy simulations and $Ra=1.42\times 10^{7}$ in the experiments, while the Prandtl number of liquid sodium is very small ( $Pr\approx 0.009$ ). The cylindrical convection cell has an aspect ratio of one; one circular surface is heated, while the other one is cooled. Additionally, the cylinder is inclined with respect to gravity and the inclination angle varies from $\unicode[STIX]{x1D6FD}=0^{\circ }$ , which corresponds to Rayleigh–Bénard convection (RBC), to $\unicode[STIX]{x1D6FD}=90^{\circ }$ , as in a vertical convection (VC) set-up. Our study demonstrates quantitative agreement of the experimental and numerical results, in particular with respect to the global heat and momentum transport, temperature and velocity profiles, as well as the dynamics of the large-scale circulation (LSC). The DNS reveal that the twisting and sloshing of the LSC at small inclination angles periodically affects the instantaneous heat transport (up to $\pm 44\,\%$ of the mean heat transport). The twisted LSC is associated with a weak heat transport, while the sloshing mode that brings together the hot and cold streams of the LSC is associated with a strong heat transport. The experiments show that the heat transport scales as $Nu\sim Ra^{0.22}$ in both limiting cases (RBC and VC) for Rayleigh numbers around $Ra\approx 10^{7}$ , while any inclination of the cell, $0