Relationship between wall shear stresses and streamwise vortices

  • Lihao Wang
  • Weixi HuangEmail author
  • Chunxiao Xu
  • Lian Shen
  • Zhaoshun Zhang


The relationship between wall shear stresses and near-wall streamwise vortices is investigated via a direct numerical simulation (DNS) of turbulent flows over a wavy boundary with traveling-wave motion. The results indicate that the wall shear stresses are still closely related to the near-wall streamwise vortices in the presence of a wave. The wave age and wave phase significantly affect the distribution of a two-point correlation coefficient between the wall shear stresses and streamwise vorticity. For the slow wave case of c/Um = 0.14, the correlation is attenuated above the leeward side while the distribution of correlation function is more elongated and also exhibits a larger vertical extent above the crest. With respect to the fast wave case of c/Um = 1.4, the distribution of the correlation function is recovered in a manner similar to that in the flat-wall case. In this case, the maximum correlation coefficient exhibits only slight differences at different wave phases while the vertical distribution of the correlation function depends on the wave phase.

Key words

direct numerical simulation (DNS) wall shear stress near-wall streamwise vortex two-point correlation 

Chinese Library Classification


2010 Mathematics Subject Classification



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The authors would like to thank Tsinghua National Laboratory for Informa- tion Science and Technology for support in parallel computation.


  1. [1]
    ROBINSON, S. K. Coherent motions in the turbulent boundary layer. Annual Review of Fluid Mechanics, 23, 601–639 (1991)CrossRefGoogle Scholar
  2. [2]
    ZHU, Y. D. Experimental and numerical study of flow structures of the second-mode instability. Applied Mathematics and Mechanics (English Edition), 40(2), 273–282 (2019) CrossRefGoogle Scholar
  3. [3]
    SUN, B. H. Thirty years of turbulence study in China. Applied Mathematics and Mechanics (English Edition), 40(2), 193–214 (2019) CrossRefGoogle Scholar
  4. [4]
    JIMENEZ, J. Cascades in wall-bounded turbulence. Annual Review of Fluid Mechanics, 44, 27–45 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    WALLACE, J. M. Quadrant analysis in turbulence research: history and evolution. Annual Review of Fluid Mechanics, 48, 131–158 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    HAMILTON, J. M., KIM, J., and WALEFFE, F. Regeneration mechanisms of near-wall turbulence structures. Journal of Fluid Mechanics, 287, 317–348 (1995)CrossRefzbMATHGoogle Scholar
  7. [7]
    HE, G., JIN, G., and YANG, Y. Space-time correlations and dynamic coupling in turbulent flows. Annual Review of Fluid Mechanics, 49, 51–70 (2017)CrossRefzbMATHGoogle Scholar
  8. [8]
    CHOI, H., MOIN, P., and KIM, J. Direct numerical simulation of turbulent flow over riblets. Journal of Fluid Mechanics, 255, 503–539 (1993)CrossRefzbMATHGoogle Scholar
  9. [9]
    WALSH, M. Turbulent boundary layer drag reduction using riblets. AIAA 20th Aerospace Sciences Meeting, AIAA, Orlando (1982)Google Scholar
  10. [10]
    LIU, K. N., CHIRISTODOULOU, C., RICCIUS, O., and JOSEPH, D. D. Drag reduction in pipes lined with riblets. AIAA Journal, 28, 1697–1698 (1990)CrossRefGoogle Scholar
  11. [11]
    NAKAO, S. Application of V shape riblets to pipe flows. Journal of Fluids Engineering, 113, 587–590 (1991)CrossRefGoogle Scholar
  12. [12]
    KRAVCHENKO, A. G., CHOI, H., and MOIN, P. On the relation of near-wall streamwise vortices to wall skin friction in turbulent boundary layers. Physics of Fluids, 5, 3307–3309 (1993)CrossRefGoogle Scholar
  13. [13]
    KIM, J., CHOI, J. I., and SUNG, H. J. Relationship between wall pressure fluctuations and streamwise vortices in a turbulent boundary layer. Physics of Fluids, 14, 898–901 (2002)CrossRefzbMATHGoogle Scholar
  14. [14]
    GE, M., XU, C., and CUI, G. Detection of near-wall streamwise vortices by measurable information at wall. Journal of Physics, 318, 022040 (2011)Google Scholar
  15. [15]
    GE, M., XU, C., and CUI, G. Active control of turbulence for drag reduction based on the detection of near-wall streamwise vortices by wall information. Acta Mechanica Sinica, 31, 512–522 (2015)CrossRefGoogle Scholar
  16. [16]
    SULLIVAN, P. P. and MCWILLIAMS, J. C. Dynamics of winds and currents coupled to surface waves. Annual Review of Fluid Mechanics, 42, 19–42 (2010)CrossRefzbMATHGoogle Scholar
  17. [17]
    BARRETT, D. S., TRIANTAFYLLOU, M. S., YUE, D. K. P., GROSENBAUGH, M. A., and WOLFGANG, M. J. Drag reduction in fish-like locomotion. Journal of Fluid Mechanics, 392, 183–212 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    SHELTON, R. M., THORNYCROFT, P., and LAUDER, G. V. Undulatory locomotion of flexible foils as biomimetic models for understanding fish propulsion. Journal of Experimental Biology, 217, 2110–2120 (2014)CrossRefGoogle Scholar
  19. [19]
    DE MARCHIS, M., NAPOLI, E., and ARMENIO, V. Turbulence structures over irregular rough surfaces. Journal of Turbulence, 11, 1–32 (2010)CrossRefGoogle Scholar
  20. [20]
    SULLIVAN, P. P., MCWILLIAMS, J. C., and MOENG, C. H. Simulation of turbulent flow over idealized water waves. Journal of Fluid Mechanics, 404, 47–85 (2000)CrossRefzbMATHGoogle Scholar
  21. [21]
    SHEN, L., ZHANG, X., YUE, D. K., and TRIANTAFYLLOU, M. S. Turbulent flow over a flexible wall undergoing a streamwise traveling wave motion. Journal of Fluid Mechanics, 484, 197–221 (2003)CrossRefzbMATHGoogle Scholar
  22. [22]
    YANG, D. and SHEN, L. Characteristics of coherent vortical structures in turbulent flows over progressive surface waves. Physics of Fluids, 21, 125106 (2009)CrossRefzbMATHGoogle Scholar
  23. [23]
    GE, M., XU, C., and CUI, G. Direct numerical simulation of flow in channel with time-dependent wall geometry. Applied Mathematics and Mechanics (English Edition), 31, 97–108 (2010) MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    LIU, Y., YANG, D., GUO, X., and SHEN, L. Numerical study of pressure forcing of wind on dynamically evolving water waves. Physics of Fluids, 22, 041704 (2010)CrossRefzbMATHGoogle Scholar
  25. [25]
    YANG, D. and SHEN, L. Simulation of viscous flows with undulatory boundaries, part II: coupling with other solvers for two-fluid computations. Journal of Computational Physics, 230, 5510–5531 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    KIHARA, N., HANAZAKI, H., MIZUYA, T., and UEDA, H. Relationship between airflow at the critical height and momentum transfer to the traveling waves. Physics of Fluids, 19, 015102 (2007)CrossRefzbMATHGoogle Scholar
  27. [27]
    YANG, D. and SHEN, L. Direct-simulation-based study of turbulent flow over various waving boundaries. Journal of Fluid Mechanics, 650, 131–180 (2010)CrossRefzbMATHGoogle Scholar
  28. [28]
    ZHOU, J., ADRIAN, R. J., BALACHANDAR, S., and KENDALL, T. M. Mechanisms for gen-erating coherent packets of hairpin vortices in channel flow. Journal of Fluid Mechanics, 387, 353–396 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    LEE, C., KIM, J., and CHOI, H. Suboptimal control of turbulent channel flow for drag reduction. Journal of Fluid Mechanics, 358, 245–258 (1998)CrossRefzbMATHGoogle Scholar
  30. [30]
    KASAGI, N., SUZUKI, Y., and FUKAGATA, K. Microelectromechanical systems-based feedback control of turbulence for skin friction reduction. Annual Review of Fluid Mechanics, 41, 231–251 (2009)CrossRefzbMATHGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Lihao Wang
    • 1
  • Weixi Huang
    • 1
    Email author
  • Chunxiao Xu
    • 1
  • Lian Shen
    • 2
  • Zhaoshun Zhang
    • 1
  1. 1.Applied Mechanics Laboratory, Department of Engineering MechanicsTsinghua UniversityBeijingChina
  2. 2.Department of Mechanical Engineering and Saint Anthony Falls LaboratoryUniversity of MinnesotaMinneapolisUSA

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