Horizontal turbulent diffusion in a convective mixed layer

A large eddy simulation (LES) is used to estimate a reliable horizontal turbulent diffusion coefficient, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}K_{{h}}$, 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 $100\ {\mathrm{m}}^2\ {\mathrm{s}}^{-1}$ 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.