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Diffusion in the Stably Stratified Atmospheric Boundary Layer

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  • 1 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, England CB3 9EW
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Abstract

The assumptions, techniques and methods of improving Gaussian plume modeling are briefly reviewed. Then the statistical theory for the diffusion of a substance S into a turbulent flow in homogeneous and inhomogeneous flows, and neutral and stably stratified flows is introduced. In stably stratified flows the mixing of the temperature and the substance S between fluid elements is of critical importance in determining the growth of a plume, so that the plume's depth is not in general determined by the displacements of fluid elements through the source, nor by the conventional Lagrangian statistics. But the plume depth, far downwind of the source, can be related to the local thermal diffusivity in the atmospheric boundary layer. The conditions are deduced under which this result can be used in stable conditions. The structure of turbulence in the stable boundary layer (SBL) is discussed. It is concluded that it is probably too variable to be characterized reliably by typical profiles of the turbulence and mean velocity for general air-pollution dispersion calculations, in the same way as the convective boundary layer can be characterized. It is also shown that the observed variability of the SBL is consistent with the observed variations in the growth rates of the plumes.

The effects of a shear on vertical and lateral diffusion are briefly discussed and also the lateral spreading of initially well-mixed plumes.

Abstract

The assumptions, techniques and methods of improving Gaussian plume modeling are briefly reviewed. Then the statistical theory for the diffusion of a substance S into a turbulent flow in homogeneous and inhomogeneous flows, and neutral and stably stratified flows is introduced. In stably stratified flows the mixing of the temperature and the substance S between fluid elements is of critical importance in determining the growth of a plume, so that the plume's depth is not in general determined by the displacements of fluid elements through the source, nor by the conventional Lagrangian statistics. But the plume depth, far downwind of the source, can be related to the local thermal diffusivity in the atmospheric boundary layer. The conditions are deduced under which this result can be used in stable conditions. The structure of turbulence in the stable boundary layer (SBL) is discussed. It is concluded that it is probably too variable to be characterized reliably by typical profiles of the turbulence and mean velocity for general air-pollution dispersion calculations, in the same way as the convective boundary layer can be characterized. It is also shown that the observed variability of the SBL is consistent with the observed variations in the growth rates of the plumes.

The effects of a shear on vertical and lateral diffusion are briefly discussed and also the lateral spreading of initially well-mixed plumes.

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