Mean velocity and temperature profiles in a sheared diabatic turbulent boundary layer

Abstract

In the atmospheric surface layer, modifications to the logarithmic mean velocity and air temperature profiles induced by thermal stratification or convection are accounted for via stability correction functions ϕm and ϕh, respectively, that vary with the stability parameter ς. These two stability correction functions are presumed to be universal in shape and independent of the surface characteristics. To date, there is no phenomenological theory that explains all the scaling laws in ϕh with ς, how ϕh relates to ϕm, and why ϕh ⩽ ϕm is consistently reported. To develop such a theory, the recently proposed links between the mean velocity profile and the Kolmogorov spectrum of turbulence, which were previously modified to account for the effects of buoyancy, are generalized here to include the mean air temperature profile. The resulting theory explains the observed scaling laws in ϕm and ϕh reported in many field and numerical experiments, predicts their behaviors across a wide range of atmospheric stability conditions, and elucidates why heat is transported more efficiently than momentum in certain stability regimes. In particular, it is shown that the enhancement in heat transport under unstable conditions is linked to a “scale-resonance” between turnover eddies and excursions in the instantaneous air temperature profiles. Excluding this scale-resonance results in the conventional Reynolds analogy with ϕm = ϕh across all stability conditions.