Large-eddy simulation of Rayleigh–Bénard convection at extreme Rayleigh numbers

Abstract

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. [“Classical 1/3 scaling of convection holds up to Ra=1015,” Proc. Natl. Acad. Sci. U. S. A. 117, 7594–7598 (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., “Classical 1/3 scaling of convection holds up to Ra=1015,” Proc. Natl. Acad. Sci. U. S. A. 117, 7594–7598 (2020)]. The Reynolds numbers in our simulations span 3 orders of magnitude from 1000 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 the ultimate convection regime.