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

• Published in: Science China. Physics, mechanics & astronomy Vol. 64; no. 3; p. 34711
• Main Authors: Ji, Yong, She, Zhen-Su
• Format: Journal Article
• Language: English
• Published: Beijing Science China Press 01.03.2021; Springer; Springer Nature B.V
• Subjects: Analysis; Astronomy; Boundary layers; Classical and Continuum Physics; Energy balance; Heat flux; Observations and Techniques; Physics; Physics and Astronomy; Similarity; Similarity measures; Surface layers; Symmetry; Thermal boundary layer; Thermal stratification; Turbulence; Turbulent boundary layer; open atmospheric surface layer; boundary layer turbulence; Monin-Obukhov similarity theory; symmetry-based analysis
• ISSN: 1674-7348; 1869-1927
• DOI: 10.1007/s11433-020-1652-x

The Monin-Obukhov (MO) similarity function φ m 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 φ m , similar to the Businger-Dyer (BD) formula; with a simplified model energy balance equation, φ m 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 T p . Assuming that T p 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 φ m 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.