Analytic derivation of Monin-Obukhov similarity function for open atmospheric surface layer

Abstract

The Monin-Obukhov (MO) similarity function φm of the atmospheric surface layer (ASL) describing the deviation from the log law of the canonical turbulent boundary layer because of thermal stratification has been traditionally determined empirically. This study presents a unified analytic expression derived from a symmetry-based theory of wall turbulence, called structural ensemble dynamics (SED), which postulates a generalized dilation symmetry principle expressing the effect of the wall on turbulence, leading to an analytic multi-regimes expression for the mixing length. For ASL in unstable and stable conditions (i.e., UC and SC), a unified two-regime formula of the mixing length is proposed, leading to a φm, similar to the Businger-Dyer (BD) formula; with a simplified model energy balance equation, φm is completely specified with no free parameter. Furthermore, the theory allows the study of the open ASL’s underlying additional physical processes such as bottom-up or top-down flux due to pressure variations Tp. Assuming that Tp is decomposed into shear-like and buoyancy-like components, we propose new explanations for two important features of typical ASL: a significantly smaller Karman constant of 0.36 and a varying φm for SC mean speed profiles. The theory is validated by the data obtained at Kansas and also at Qingtu Lake Observation Array in Northern China for a variety of heat flux conditions. In conclusion, due to pressure variations, we assert that ASL is intrinsically open and that the current theory offers a new basis for its quantification.

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References

  1. 1

    I. Marusic, B. J. McKeon, P. A. Monkewitz, H. M. Nagib, A. J. Smits, and K. R. Sreenivasan, Phys. Fluids 22, 065103 (2010).

    ADS  Article  Google Scholar 

  2. 2

    J. C. Wyngaard, Annu. Rev. Fluid Mech. 24, 205 (1992).

    ADS  Article  Google Scholar 

  3. 3

    A. S. Monin, and A. M. Obukhov, Dok. Akad. Nauk. Sssr. 151, 1963 (1954).

    Google Scholar 

  4. 4

    A. S. Monin, Annu. Rev. Fluid Mech. 2, 225 (1970).

    ADS  Article  Google Scholar 

  5. 5

    X. Li, N. Zimmerman, and M. Princevac, Bound.-Layer Meteorol. 129, 115 (2008).

    ADS  Article  Google Scholar 

  6. 6

    J. A. Businger, J. C. Wyngaard, Y. Izumi, and E. F. Bradley, J. Atmos. Sci. 28, 181 (1971).

    ADS  Article  Google Scholar 

  7. 7

    A. J. Dyer, Bound.-Layer Meteorol. 7, 363 (1974).

    ADS  Article  Google Scholar 

  8. 8

    D. M. Carl, T. C. Tarbell, and H. A. Panofsky, J. Atmos. Sci. 30, 788 (1973).

    ADS  Article  Google Scholar 

  9. 9

    H. A. Panofsky, Q. J. R. Meteorol. Soc. 87, 109 (1961).

    ADS  Article  Google Scholar 

  10. 10

    G. G. Katul, A. G. Konings, and A. Porporato, Phys. Rev. Lett. 107, 268502 (2011).

    ADS  Article  Google Scholar 

  11. 11

    G. Gioia, N. Guttenberg, N. Goldenfeld, and P. Chakraborty, Phys. Rev. Lett. 105, 184501 (2010).

    ADS  Article  Google Scholar 

  12. 12

    S. T. Salesky, G. G. Katul, and M. Chamecki, Phys. Fluids 25, 105101 (2013).

    ADS  Article  Google Scholar 

  13. 13

    D. Li, S. T. Salesky, and T. Banerjee, J. Fluid Mech. 797, R3 (2016).

    ADS  Article  Google Scholar 

  14. 14

    T. Banerjee, G. G. Katul, S. T. Salesky, and M. Chamecki, Q. J. R. Meteorol. Soc. 141, 1699 (2015).

    ADS  Article  Google Scholar 

  15. 15

    Z. S. She, X. Chen, Y. Wu, and F. Hussain, Acta Mech. Sin. 26, 847 (2010).

    ADS  MathSciNet  Article  Google Scholar 

  16. 16

    Z. S. She, X. Chen, and F. Hussain, J. Fluid Mech. 827, 322 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  17. 17

    X. Chen, F. Hussain, and Z. S. She, J. Fluid Mech. 850, 401 (2018).

    ADS  MathSciNet  Article  Google Scholar 

  18. 18

    X. Chen, and Z. S. She, Sci. China-Phys. Mech. Astron. 59, 114711 (2016), arXiv: 1604.08257.

    Article  Google Scholar 

  19. 19

    G. H. Wang, and X. J. Zheng, J. Fluid Mech. 802, 464 (2016).

    ADS  Article  Google Scholar 

  20. 20

    G. H. Wang, X. J. Zheng, and J. J. Tao, Phys. Fluids 29, 061701 (2017).

    ADS  Article  Google Scholar 

  21. 21

    H. Y. Liu, G. H. Wang, and X. J. Zheng, J. Fluid Mech. 861, 585 (2019).

    ADS  Article  Google Scholar 

  22. 22

    B. A. Kader, and A. M. Yaglom, J. Fluid Mech. 212, 637 (1990).

    ADS  MathSciNet  Article  Google Scholar 

  23. 23

    J. C. R. Hunt, and J. F. Morrison, Eur. J. Mech.-B/Fluids 19, 673 (2000).

    Article  Google Scholar 

  24. 24

    U. Högström, J. C. R. Hunt, and A. S. Smedman, Bound.-Layer Meteorol. 103, 101 (2002).

    ADS  Article  Google Scholar 

  25. 25

    E. Bou-Zeid, X. Gao, C. Ansorge, and G. G. Katul, J. Fluid Mech. 856, 61 (2018).

    ADS  MathSciNet  Article  Google Scholar 

  26. 26

    U. Högström, Bound.-Layer Meteorol. 78, 215 (1996).

    ADS  Article  Google Scholar 

  27. 27

    D. Li, and E. Bou-Zeid, Bound.-Layer Meteorol. 140, 243 (2011).

    ADS  Article  Google Scholar 

  28. 28

    C. Tong, and M. Ding, J. Atmos. Sci. 75, 3691 (2018).

    ADS  Article  Google Scholar 

  29. 29

    M. Chamecki, N. L. Dias, and L. S. Freire, Geophys. Res. Lett. 45, 6734 (2018).

    ADS  Article  Google Scholar 

  30. 30

    A. A. Townsend, J. Fluid Mech. 11, 97 (1961).

    ADS  MathSciNet  Article  Google Scholar 

  31. 31

    U. Högström, Bound.-Layer Meteorol. 42, 55 (1988).

    ADS  Article  Google Scholar 

  32. 32

    M. J. Xiao, and Z. S. She, Sci. China-Phys. Mech. Astron. 62, 994711 (2019).

    Article  Google Scholar 

  33. 33

    M. J. Xiao, and Z. S. She, Acta Mech. Sin. 36, 35 (2020).

    ADS  Article  Google Scholar 

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Correspondence to Zhen-Su She.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 91952201). The authors thank XiaoJing Zheng, and Guo-Hua Wang for sharing the QLOA data with us and for many helpful discussions.

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Ji, Y., She, ZS. Analytic derivation of Monin-Obukhov similarity function for open atmospheric surface layer. Sci. China Phys. Mech. Astron. 64, 34711 (2021). https://doi.org/10.1007/s11433-020-1652-x

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Keywords

  • Monin-Obukhov similarity theory
  • open atmospheric surface layer
  • boundary layer turbulence
  • symmetry-based analysis