Lagrangian coherent structures and their heat-transport mechanism in the turbulent Rayleigh-Bénard convection

In this paper, we investigate the Lagrangian coherent structures (LCSs) and their heat-transport mechanism in turbulent Rayleigh-Bénard (RB) convection. Direct numerical simulations (DNS) are performed in a closed square cell with Rayleigh numbers (Ra) ranging from 106 to 109 and Prandtl (Pr) number fixed at Pr = 0.7. First, our results show the power-law relationship between Nusselt number (Nu) and Ra, Nu = 0.99Ra0.30±0.02, confirming the results from previous studies. To gain insights into the material transport, LCSs are extracted using the finite-time Lyapunov exponent (FTLE) method. Interestingly, lobe structures are widely present, and we elucidate their role in transporting heat from the corner rolls to large-scale circulation. Next, the relationships between LCSs and thermal plumes are examined, and we identify two behaviors of thermal plumes: first, most plumes transport along the LCSs; second, few plumes are exposed to the bulk and subsequently mix with the turbulent background. Furthermore, we quantify the heat flux along the LCSs, which contributes to about 85% of the total flux regardless of Ra. This suggests that LCSs play a significant role in heat transport. Finally, the viscous (thermal) dissipation rate along the LCSs is quantified, which is larger than 80% (60%) of the total value, suggesting that LCSs are responsible for the large viscous and thermal dissipations.