The non‐local character of turbulence asymmetry in the convective atmospheric boundary layer

Abstract

The inadequacy of conventional gradient diffusion in closure modelling of turbulent heat fluxes within the convective atmospheric boundary layer is often alleviated by accounting for non‐local transport effects, such as Deardorff's counter‐gradient models, Wyngaard's transport asymmetry closures or mass‐flux parametrization. This concept of large‐eddy flux transport is examined here with the principal aim of unifying these seemingly different models. Using large‐eddy simulation (LES) runs for the atmospheric boundary layer, spanning weakly to strongly convective conditions, a generic diagnostic framework that encodes the role of third‐order moments in non‐local transport is developed and tested. The premise is that these non‐local effects are responsible for the inherent asymmetry in vertical transport and hence the necessary non‐Gaussian nature of the joint probability density function (JPDF) of vertical velocity and potential temperature must account for these effects. Conditional sampling (quadrant analysis) of this JPDF and the imbalance between the flow mechanisms of ejections and sweeps are used to characterize this asymmetry, which is then linked to the third‐order moments using a cumulant‐discard method for the Gram–Charlier expansion of the JPDF. While the concept of ejection‐sweep events used here is not a simple extension of that commonly used in the surface layer, their connection to third‐order moments shows that the concepts of bottom‐up/top‐down diffusion or updraught/downdraught models are accounted for by various quadrants of the JPDF. An analogy between mass‐flux models and the relaxed eddy accumulation method reveals that there is a seemingly implicit assumption of a Gaussian JPDF in the former.