Eddy Diffusivity and Countergradient Transport in the Convective Atmospheric Boundary Layer

Abstract

To describe the heat and scalar fluxes in the convective boundary layer, we propose expressions for eddy diffusivities and countergradient terms. The latter expressions can be used in a modified flux-gradient approach, which takes account for nonlocal convective vertical exchange. The results for heat are based on a derivation similar to that of Deardorff by utilizing the turbulent heat-flux equation, but the closure assumptions applied to the heat-flux budgets are different. As a result, the physical interpretation for the countergradient term differs; our countergradient term results from the third-moment transport effect, while Deardorff's results from the buoyancy production term. On the basis of our analysis, we are able to calculate an eddy diffusivity for heat, using large-eddy simulation results. The results are presented in the form of a similarity profile, using the convective velocity scale w* and the inversion height zi. It is shown that the latter profile is well behaved and that it matches the results of surface-layer theory. Using the top-down and bottom-up decomposition, we have generalized our findings for any scalar, such as the moisture field or an air pollution contaminant. We show that the eddy diffusivity profile for scalar C is sensitive to the entrainment?surface flux ratio of C. Therefore, a different scalar field should have a different eddy-diffusivity profile. The proposed expressions for the eddy diffusivities and the countergradient terms are easy to apply in (large-scale) atmospheric and diffusion models.