  The energy and flux budget (EFB) closure theory for a passive scalar
(non-buoyant and non-inertial particles or gaseous admixtures) is developed for
stably stratified turbulence. The physical background of the EFB turbulence
closures is based on the budget equations for the turbulent kinetic and
potential energies and turbulent fluxes of momentum and buoyancy, as well as
the turbulent flux of particles. The EFB turbulence closure is designed for
stratified geophysical flows from neutral to very stable stratification and it
implies that turbulence is maintained by the velocity shear at any
stratification. In a steady-state, expressions for the turbulent flux of
passive scalar and the anisotropic non-symmetric turbulent diffusion tensor are
derived, and universal flux Richardson number dependencies of the components of
this tensor are obtained. The diagonal component in the vertical direction of
the turbulent diffusion tensor is suppressed by strong stratification, while
the diagonal components in the horizontal directions are not suppressed, and
they are dominant in comparison with the other components of turbulent
diffusion tensor. This implies that any initially created strongly
inhomogeneous particle cloud is evolved into a thin pancake in horizontal plane
with very slow increase of its thickness in the vertical direction. The
turbulent Schmidt number increases linearly with the gradient Richardson
number. Considering the applications of these results to the atmospheric
boundary-layer turbulence, the theoretical relationships are derived which
allow to determine the turbulent diffusion tensor as a function of the vertical
coordinate measured in the units of the local Obukhov length scale. The
obtained relations are potentially useful in modelling applications of particle
dispersion in the atmospheric boundary-layer turbulence and free atmosphere
turbulence.
