Science China Physics, Mechanics & Astronomy | 2021
Analytic derivation of Monin-Obukhov similarity function for open atmospheric surface layer
Abstract
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.