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Lagrangian-based spatial-temporal topological study on the evolution and migration of coherent structures in wall turbulence

基于拉格朗日的壁湍流相干结构演化和迁移的时空拓扑研究

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Abstract

In this work, we study the development, evolution, and migration of turbulent coherent structures in the turbulent boundary layer at Reτ = 630 using time-resolved particle image velocimetry (TR-PIV). Multiple techniques, including multi-scale analysis, conditional averaging, cross-correlation, and spatial-temporal topological analysis are applied to extract the evolution principle, migration trajectory, and convection velocity vector of the targeted coherent structures from a Lagrangian perspective. The spanwise vortex structures with larger scale and intensity at a certain wall-normal height y were the main focus of the present study. In the statistical sense, spanwise vortex structures move away from the wall with the shape changing from a bulge to an ellipse, and finally to a circle. Two straight lines emerge from the mean transfer trajectory curve of the spanwise vortex, in which the horizontal one is located at the viscous sublayer (y+ < 10), the other is a logarithmic straight line existing in the range of 50 < y+ < 120, and the inclination angle of the tangential migration path is fixed at around 12°. The streamwise convection velocity Uc of scaled spanwise vortex structures satisfies Uc/U∞ = 0.5–0.6 below y = 0.03δ (i.e., Uc+ = 11–13 under y+ = 20). In particular, in the region of 50 < y+ < 120, the velocity growth curves of Uc and wall-normal convection velocity Vc follow the log-law distribution very well, and the slopes are consistent with that of the log-law region of the turbulent boundary layer. Our observations provide microscopic evidences of the logarithmic-linear distribution of the migration trajectory of spanwise vortex structures.

摘要

使用时间分辨粒子图像测速仪(TR-PIV)研究了湍流边界层中湍流相干结构在Reτ = 630条件下的发展、演化和迁移. 综合应 用多尺度分析、条件平均、互相关和时空拓扑分析等技术, 从拉格朗日视角提取目标相干结构的演化机理、迁移轨迹和对流速度 矢量分布等规律. 本研究重点关注位于壁面法向高度y上具有较大尺度和强度的展向涡结构. 统计结果显示:展向涡结构从壁面向 外移动过程中, 其形状从凸起变为椭圆, 最后变为圆形. 展向涡的迁移轨迹上呈现出两条直线, 其中水平的一条位于黏性子层(y+ < 10), 另一条则是位于50 < y+ < 120范围内的对数直线, 其与壁面的倾角固定在12°附近. 在y = 0.03δ以下位置, 具有尺度特征的展向 涡结构的流向对流速度Uc满足Uc/U∞ = 0.5~0.6(即低于y+ = 20时, Uc+ = 11~13). 在50 < y+ < 120区域, 流向对流速度Uc和壁面法向对 流速度Vc均很好地遵从了对数律分布, 且斜率与湍流边界层对数律区的一致. 本文的实验观测为展向涡结构迁移轨迹的对数线性 分布提供了微观证据.

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References

  1. T. K. Sengupta P. K. Sharma, A. Sengupta, and V. K. Suman, Tracking disturbances in transitional and turbulent flows: coherent structures, Phys. Fluids 31, 124106 (2019).

    Article  Google Scholar 

  2. X. Cui, N. Jiang, X. Zheng, and Z. Tang, Active control of multiscale features in wall-bounded turbulence, Acta Mech. Sin. 36, 12 (2020).

    Article  MathSciNet  Google Scholar 

  3. W. Li, and H. Liu, Two-point statistics of coherent structures in turbulent flow over riblet-mounted surfaces, Acta Mech. Sin. 35, 457 (2019).

    Article  MathSciNet  Google Scholar 

  4. X. Wang, Y. Wang, H. Tian, and N. Jiang, Effects of the slip wall on the drag and coherent structures of turbulent boundary layer, Acta Mech. Sin. 37, 1278 (2021).

    Article  MathSciNet  Google Scholar 

  5. S. K. Robinson, Coherent motions in the turbulent boundary layer, Annu. Rev. Fluid Mech. 23, 601 (1991).

    Article  Google Scholar 

  6. H. Tian, N. Jiang, Y. Huang, and S. Yang, Study on local topology model of low/high streak structures in wall-bounded turbulence by tomographic time-resolved particle image velocimetry, Appl. Math. Mech.-Engl. Ed. 36, 1121 (2015).

    Article  MathSciNet  Google Scholar 

  7. F. Xu, S. Zhong, and S. Zhang, Experimental study on secondary flow in turbulent boundary layer over spanwise heterogeneous micro-grooves, Phys. Fluids 32, 035109 (2020).

    Article  Google Scholar 

  8. K. T. Christensen, and R. J. Adrian, Statistical evidence of hairpin vortex packets in wall turbulence, J. Fluid Mech. 431, 433 (2001).

    Article  Google Scholar 

  9. R. J. Adrian, Hairpin vortex organization in wall turbulence, Phys. Fluids 19, 041301 (2007).

    Article  Google Scholar 

  10. H. Tian, J. Zhang, N. Jiang, and Z. Yao, Effect of hierarchical structured superhydrophobic surfaces on coherent structures in turbulent channel flow, Exp. Thermal Fluid Sci. 69, 27 (2015).

    Article  Google Scholar 

  11. R. J. Adrian, C. D. Meinhart, and C. D. Tomkins, Vortex organization in the outer region of the turbulent boundary layer, J. Fluid Mech. 422, 1 (2000).

    Article  MathSciNet  Google Scholar 

  12. Y. Yang, Identification, characterization and evolution of non-local quasi-Lagrangian structures in turbulence, Acta Mech. Sin. 32, 351 (2016).

    Article  MathSciNet  Google Scholar 

  13. M. Zhang, Q. Wu, B. Huang, and G. Wang, Lagrangian-based numerical investigation of aerodynamic performance of an oscillating foil, Acta Mech. Sin. 34, 839 (2018).

    Article  Google Scholar 

  14. C. Pan, J. J. Wang, and C. Zhang, Identification of Lagrangian coherent structures in the turbulent boundary layer, Sci. China Ser. G-Phys. Mech. Astron. 52, 248 (2009).

    Article  Google Scholar 

  15. G. S. He, C. Pan, L. H. Feng, Q. Gao, and J. J. Wang, Evolution of Lagrangian coherent structures in a cylinder-wake disturbed flat plate boundary layer, J. Fluid Mech. 792, 274 (2016).

    Article  MathSciNet  Google Scholar 

  16. S. Li, N. Jiang, S. Yang, Y. Huang, and Y. Wu, Coherent structures over riblets in turbulent boundary layer studied by combining time-resolved particle image velocimetry (TRPIV), proper orthogonal decomposition (POD), and finite-time Lyapunov exponent (FTLE), Chin. Phys. B 27, 104701 (2018).

    Article  Google Scholar 

  17. Q. Gao, C. Ortiz-Dueñas, and E. K. Longmire, Evolution of coherent structures in turbulent boundary layers based on moving tomographic PIV, Exp. Fluids 54, 1625 (2013).

    Article  Google Scholar 

  18. F. Xu, S. Zhong, and S. Zhang, Statistical analysis of vortical structures in turbulent boundary layer over directional grooved surface pattern with spanwise heterogeneity, Phys. Fluids 31, 085110 (2019).

    Article  Google Scholar 

  19. Y. Cao, J. Chen, and Z. She, The nature of near-wall convection velocity in turbulent channel flow, Acta Mech. Sin. 24, 587 (2008).

    Article  Google Scholar 

  20. G. I. Taylor, The spectrum of turbulence, Proc. R. Soc. Lond. A 164, 476 (1938).

    Article  Google Scholar 

  21. G. W. He, and J. B. Zhang, Elliptic model for space-time correlations in turbulent shear flows, Phys. Rev. E 73, 055303 (2006).

    Article  Google Scholar 

  22. G. He, G. Jin, and Y. Yang, Space-time correlations and dynamic coupling in turbulent flows, Annu. Rev. Fluid Mech. 49, 51 (2017).

    Article  Google Scholar 

  23. J. Kim, and F. Hussain, Propagation velocity of perturbations in turbulent channel flow, Phys. Fluids A-Fluid Dyn. 5, 695 (1993).

    Article  Google Scholar 

  24. J. Pei, J. Chen, Z. S. She, and F. Hussain, Model for propagation speed in turbulent channel flows, Phys. Rev. E 86, 046307 (2012).

    Article  Google Scholar 

  25. G. E. Elsinga, C. Poelma, A. Schröder, R. Geisler, F. Scarano, and J. Westerweel, Tracking of vortices in a turbulent boundary layer, J. Fluid Mech. 697, 273 (2012).

    Article  Google Scholar 

  26. A. Lozano-Durán, and J. Jiménez, Time-resolved evolution of coherent structures in turbulent channels: characterization of eddies and cascades, J. Fluid Mech. 759, 432 (2014).

    Article  MathSciNet  Google Scholar 

  27. P. Å. Krogstad, J. H. Kaspersen, and S. Rimestad, Convection velocities in a turbulent boundary layer, Phys. Fluids 10, 949 (1998).

    Article  Google Scholar 

  28. J. A. LeHew, M. Guala, and B. J. McKeon, Time-resolved measurements of coherent structures in the turbulent boundary layer, Exp. Fluids 54, 1508 (2013).

    Article  Google Scholar 

  29. C. Liu, and D. F. Gayme, An input-output based analysis of convective velocity in turbulent channels, J. Fluid Mech. 888, A32 (2020).

    Article  MathSciNet  Google Scholar 

  30. J. C. Del Álamo, and J. Jiménez, Estimation of turbulent convection velocities and corrections to Taylor’s approximation, J. Fluid Mech. 640, 5 (2009).

    Article  MathSciNet  Google Scholar 

  31. J. Zhang, H. Tian, Z. Yao, P. Hao, and N. Jiang, Mechanisms of drag reduction of superhydrophobic surfaces in a turbulent boundary layer flow, Exp. Fluids 56, 179 (2015).

    Article  Google Scholar 

  32. Z. Q. Tang, and N. Jiang, TR PIV experimental investigation on bypass transition induced by a cylinder wake, Chin. Phys. Lett. 28, 054702 (2011).

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. National Demonstration Center for Experimental Mechanics Education, Taiyuan University of Technology, Taiyuan, 030024, China

    Haiping Tian  (田海平), Xingrui Yi  (伊兴睿) & Fen Li  (李芬)

  2. Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, 518055, China

    Fang Xu  (许放)

  3. Department of Mechanics, Tianjin University, Tianjin, 300350, China

    Nan Jiang  (姜楠)

Authors
  1. Haiping Tian  (田海平)
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  2. Xingrui Yi  (伊兴睿)
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  3. Fang Xu  (许放)
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  4. Fen Li  (李芬)
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  5. Nan Jiang  (姜楠)
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Corresponding authors

Correspondence to Haiping Tian  (田海平) or Fang Xu  (许放).

Additional information

This work was supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11802195), the National Natural Science Foundation of China (Grant Nos. 12172242, and 11972251), the Key Program of the National Natural Science Foundation of China (Grant No. 11732010), Sino-German International Cooperation Project supported by Sino-German Science Center (GZ1575) and the Natural Science Foundation for Young Scientists of Shanxi Province, China (Grant No. 201801D221027).

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Tian, H., Yi, X., Xu, F. et al. Lagrangian-based spatial-temporal topological study on the evolution and migration of coherent structures in wall turbulence. Acta Mech. Sin. 38, 321465 (2022). https://doi.org/10.1007/s10409-021-09006-1

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