Closure of the heat flux budget with the ejection-sweep cycle in the convective atmospheric boundary layer

Abstract:

The inadequacy of conventional gradient-diffusion in modeling scalar fluxes within the convective atmospheric boundary-layer is often alleviated by accounting for nonlocal transport effects, such as Deardorff’s counter-gradient hypothesis, Wyngaard’s transport asymmetry closures, or mass-flux parametrizations. Such nonlocal effects are a manifestation of the inherent asymmetry in vertical transport, which is in turn associated with third-order moments (skewness and fluxes of fluxes). In this work, we examine the role of the turbulent transport term in the sensible heat flux budget within the convective boundary layer, with the principal aim of reconciling the aforementioned models to various closure assumptions of this term. In particular, by connecting turbulent heat transport and the ejection-sweep events in the flow field, we establish a generic framework upon which such closure models can be derived. These ejections and sweeps are tied to third-order moments (asymmetry) in the Gram-Charlier cumulant expansion of the joint probability distribution of vertical velocity and potential temperature. The heat flux budget is solved under several assumptions on closure timescales, skewness profiles, and relations between the mixed third-order moments to recover the necessary conditions for adequate vertical profile of the heat flux. The surface layer scaling laws and their contribution to turbulence fluxes is also included and discussed.