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The energy and flux budget (EFB) closure theory for a passive scalar(non-buoyant and non-inertial particles or gaseous admixtures) is developed forstably stratified turbulence. The physical background of the EFB turbulenceclosures is based on the budget equations for the turbulent kinetic andpotential energies and turbulent fluxes of momentum and buoyancy, as well asthe turbulent flux of particles. The EFB turbulence closure is designed forstratified geophysical flows from neutral to very stable stratification and itimplies that turbulence is maintained by the velocity shear at anystratification. In a steady-state, expressions for the turbulent flux ofpassive scalar and the anisotropic non-symmetric turbulent diffusion tensor arederived, and universal flux Richardson number dependencies of the components ofthis tensor are obtained. The diagonal component in the vertical direction ofthe turbulent diffusion tensor is suppressed by strong stratification, whilethe diagonal components in the horizontal directions are not suppressed, andthey are dominant in comparison with the other components of turbulentdiffusion tensor. This implies that any initially created stronglyinhomogeneous particle cloud is evolved into a thin pancake in horizontal planewith very slow increase of its thickness in the vertical direction. Theturbulent Schmidt number increases linearly with the gradient Richardsonnumber. Considering the applications of these results to the atmosphericboundary-layer turbulence, the theoretical relationships are derived whichallow to determine the turbulent diffusion tensor as a function of the verticalcoordinate measured in the units of the local Obukhov length scale. Theobtained relations are potentially useful in modelling applications of particledispersion in the atmospheric boundary-layer turbulence and free atmosphereturbulence.

Energy and flux budget closure theory for passive scalar in stably stratified turbulence