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 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.