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