Horizontal turbulent diffusion in a convective mixed layer

A large eddy simulation (LES) is used to estimate a reliable horizontal turbulent diffusion coefficient, K_h, in a convective mixed layer (CML). The introduction of a passive scalar field with a fixed horizontal gradient at a given time enables K_h estimation as a function of height, based on the simulated turbulent horizontal scalar flux. Here K_h is found to be of the order of 100 m² s^-1 for a typical terrestrial atmospheric CML. It is shown to scale by the product of the CML convective velocity, w_∗, and its depth, h. Here K_h is characterized by a vertical profile in the CML: it is large near both the bottom and top of the CML, where horizontal flows associated with convection are large. The equation pertaining to the temporal rate of change of a horizontal scalar flux suggests that K_h is determined by a balance between production and pressure correlation at a fully developed stage. Pressure correlation near the bottom of the CML is localized in convergence zones near the boundaries of convective cells and becomes large within an eddy turnover time, h/w_∗, after the introduction of the passive scalar field.