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

TL;DR

This paper develops an energy and flux budget closure theory for passive scalars in stably stratified turbulence, providing new analytical expressions for turbulent fluxes and diffusion tensors applicable to atmospheric boundary-layer modeling.

Contribution

The paper introduces a novel EFB closure model for passive scalars in stratified turbulence, deriving universal flux dependencies and anisotropic diffusion tensor expressions.

Findings

Vertical turbulent diffusion is suppressed under strong stratification.

Horizontal diffusion remains dominant and is unaffected by stratification.

Turbulent Schmidt number increases linearly with the gradient Richardson number.

Abstract

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.