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

In this paper, we investigate the Lagrangian coherent structures (LCSs) and their heat-transport mechanism in turbulent Rayleigh-Benard (RB) convection. Direct numerical simulations (DNS) are performed in a closed square cell with Rayleigh numbers (Ra) ranging from 10(6) to 10(9) and Prandtl (Pr) number fixed at Pr = 0.7. First, our results show the power-law relationship between Nusselt number (Nu) and Ra, Nu = 0.99Ra(0.30 +/- 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.

Automated summary

This paper investigates the Lagrangian coherent structures (LCSs) and their heat-transport mechanism in turbulent Rayleigh-Benard convection. The results show a power-law relationship between Nusselt number and Rayleigh number, and the presence of lobe structures that play a significant role in heat transport. Furthermore, most thermal plumes transport along the LCSs, while only a few mix with the turbulent background.