Large-eddy simulation of Rayleigh-Benard convection at extreme Rayleigh numbers

We adopt the stretched spiral vortex sub-grid model for large-eddy simulation (LES) of turbulent convection at extreme Rayleigh numbers. We simulate Rayleigh-Bénard convection (RBC) for Rayleigh numbers ranging from 106 to 1015 and for Prandtl numbers 0.768 and 1. We choose a box of dimensions 1:1:10 to reduce computational cost. Our LES yields Nusselt and Reynolds numbers that are in good agreement with the direct-numerical simulation (DNS) results of Iyer et al. (2020), albeit with a smaller grid size and at significantly reduced computational expense. For example, in our simulations at Ra = 1013, we use grids that are 1/120 times the grid-resolution as that of the DNS (Iyer et al. 2020). The Reynolds numbers in our simulations span 3 orders of magnitude from 1,000 to 1,700,000. Consistent with the literature, we obtain scaling relations for Nusselt and Reynolds numbers as Nu ∼ Ra0.321 and Re ∼ Ra0.495. We also perform LES of RBC with periodic side-walls, for which we obtain the corresponding scaling exponents as 0.343 and 0.477 respectively. Our LES is a promising tool to push simulations of thermal convection to extreme Rayleigh numbers, and hence enable us to test the transition to ultimate convection regime.