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

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Abstract

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.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering and School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, China

    Hang Cheng, Jie Shen, YiZhao Zhang, Quan Zhou, Kai Leong Chong, YuLu Liu & ZhiMing Lu

  2. The School of Sciences, Shanghai Institute of Technology, Shanghai, 200072, China

    YuLu Liu

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  1. Hang Cheng
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  2. Jie Shen
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  3. YiZhao Zhang
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  4. Quan Zhou
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  5. Kai Leong Chong
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  6. YuLu Liu
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  7. ZhiMing Lu
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Correspondence to ZhiMing Lu.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11732010, 92052201, 12072185, 91952102, 12032016).

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Cheng, H., Shen, J., Zhang, Y. et al. Lagrangian coherent structures and their heat-transport mechanism in the turbulent Rayleigh-Bénard convection. Sci. China Technol. Sci. 65, 966–976 (2022). https://doi.org/10.1007/s11431-021-1970-8

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