An extended similarity theory for the stably stratified atmospheric surface layer

Abstract An error propagation analysis is conducted to estimate random errors in the friction velocity u* and the Monin–Obukhov similarity theory (MOST) stability variable z/L from estimated random errors in the turbulent fluxes. Errors in the dimensionless mean wind shear φm and mean temperature gradient φh are also estimated. To the authors’ knowledge, this is the first time that errors in calculated values of z/L, φm, and φh have been systematically analyzed. Random errors in z/L are found to be large for unstable conditions, reaching values of 40% or greater. It is shown through statistical hypothesis tests that random errors cannot explain departures of calculated values of φm and φh from theory. The deviation of calculated values of φm from empirical curves is found to have a strong diurnal variation that increases with height; deviations of φh from theory are not found to have clear diurnal variation. These results support the findings of previous studies, which have suggested that additional dimensionless parameters representing additional physical processes need to be included in the set of governing parameters for surface layer similarity. Implications for atmospheric surface layer turbulence are also discussed.

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Turbulent diffusion of instantaneous clouds in the atmospheric surface layer: measurements and comparison with Lagrangian similarity theory

Physics Letters A ◽

10.1016/s0375-9601(98)00171-6 ◽

1998 ◽

Vol 242 (1-2) ◽

pp. 51-62 ◽

Cited By ~ 3

Author(s):

Eugene Yee

Keyword(s):

Surface Layer ◽

Turbulent Diffusion ◽

Atmospheric Surface Layer ◽

Similarity Theory

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Monin–Obukhov Similarity and Local-Free-Convection Scaling in the Atmospheric Boundary Layer Using Matched Asymptotic Expansions

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-18-0016.1 ◽

2018 ◽

Vol 75 (10) ◽

pp. 3691-3701 ◽

Cited By ~ 3

Author(s):

Chenning Tong ◽

Mengjie Ding

Keyword(s):

Surface Layer ◽

Free Convection ◽

Asymptotic Expansions ◽

Atmospheric Surface Layer ◽

Similarity Theory ◽

Potential Temperature ◽

Matched Asymptotic Expansions ◽

Obukhov Length ◽

Local Free Convection ◽

Valid Solution

The Monin–Obukhov similarity theory (MOST) is the foundation for understanding the atmospheric surface layer. It hypothesizes that nondimensional surface-layer statistics are functions of [Formula: see text] only, where z and L are the distance from the ground and the Obukhov length, respectively. In particular, it predicts that in the convective surface layer, local free convection (LFC) occurs at heights [Formula: see text] and [Formula: see text], where [Formula: see text] is the inversion height. However, as a hypothesis, MOST is based on phenomenology. In this work we derive MOST and the LFC scaling from the equations for the velocity and potential temperature variances using the method of matched asymptotic expansions. Our analysis shows that the dominance of the buoyancy and shear production in the outer ([Formula: see text]) and inner ([Formula: see text]) layers, respectively, results in a nonuniformly valid solution and a singular perturbation problem and that [Formula: see text] is the thickness of the inner layer. The inner solutions are found to be functions of [Formula: see text] only, providing a proof of MOST for the vertical velocity and potential temperature variances. Matching between the inner and outer solutions results in the LFC scaling. We then obtain the corrections to the LFC scaling near the edges of the LFC region ([Formula: see text] and [Formula: see text]). The nondimensional coefficients in the expansions are determined using measurements. The resulting composite expansions provide unified expressions for the variance profiles in the convective atmospheric surface layer and show very good agreement with the data. This work provides strong analytical support for MOST.

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