Mean scalar concentration profile in a sheared and thermally stratified atmospheric surface layer

Using only dimensional considerations, Monin and Obukhov proposed a "universal" stability correction function _c(ζ) that accounts for distortions caused by thermal stratification to the mean scalar concentration profile in the atmospheric surface layer when the flow is stationary, planar homogeneous, fully turbulent, and lacking any subsidence. For nearly 6 decades, their analysis provided the basic framework for almost all operational models and data interpretation in the lower atmosphere. However, the canonical shape of _c(ζ) and the departure from the Reynold's analogy continue to defy theoretical explanation. Here, the basic processes governing the scalar-velocity cospectrum, including buoyancy and the scaling laws describing the velocity and temperature spectra, are considered via a simplified cospectral budget. The solution to this cospectral budget is then used to derive _c(ζ), thereby establishing a link between the energetics of turbulent velocity and scalar concentration fluctuations and the bulk flow describing the mean scalar concentration profile. The resulting theory explains all the canonical features of _c(ζ), including the onset of power laws for various stability regimes and their concomitant exponents, as well as the causes of departure from Reynold's analogy.