Horizontal turbulent diffusivity in a convective mixed layer

Numerical models of geophysical flows, which have extremely large Reynolds numbers, inevitably need to parameterize turbulent transports. Various kinds of parameterizations of the turbulent transports are proposed in the literature. Most of the parameterizations in atmospheric models, however, address vertical turbulent transports, and there have been surprisingly little studies on the horizontal ones. However, horizontal turbulent transports are essential when a reliable prediction of dispersion of pollutant is required, and also are increasing their importance as the horizontal resolution of the models becomes sub-kilometer. In this study, a Large Eddy Simulation (LES) is used to estimate a reliable horizontal turbulent diffusivity of a passive scalar in a convective mixed layer (CML). The LES resolves turbulent eddies associated with convection cells in the CML which is produced by heating a stably stratified atmosphere from below at a constant surface heat flux Q. At a certain instant after the CML is well developed, a fixed horizontal gradient of a passive scalar is introduced. The resulting ensemble average of horizontal turbulent fluxes is used to estimate the horizontal diffusivity. A budget analysis of the horizontal turbulent flux is also made to clarify the physical mechanism to cause the horizontal diffusion. The horizontal turbulent diffusivity of the passive scalar thus obtained is found to be on the order of 100 m² s^-1 for a CML in a typical terrestrial atmosphere in a quasi-steady state. Furthermore, its vertical profile is shown to become universal when its magnitude is scaled by a product of the convective velocity w_* = (gαQ)^1/3 and the depth of CML h, and the height by h, where g is the gravity acceleration and α volume expansion coefficient: the scaled horizontal turbulent diffusivity is large near the top and bottom of the CML, and its dimensional value at the middle height is given by 0.08×w_*h. The diffusivity in the stably stratified layer above the CML is two order of magnitudes smaller. The budget analysis of the horizontal turbulent flux shows that the quasi-steady value of the horizontal diffusivity is determined by a balance between its production and pressure-diffusion terms, where the pressure-diffusion term near the bottom of the CML is localized in horizontal boundaries of convective cells. When the horizontal gradient of the passive scalar is introduced, the pressure-diffusion increases from its initial value of 0 and becomes large enough to balance with the production within an eddy turn over time of h/w_*, which is roughly several tens minutes. Universal vertical profile of non-dimensional diffusion coefficient K_H/(w_*h)