Laws of Effluent Dispersion in the Steady-State Atmospheric Surface Layer in Stable and Unstable Conditions

S. A. Lebedeff Institute for Space Studies, NASA Goddard Space Flight Center, New York, N. Y. 10025

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S. Hameed Institute for Space Studies, NASA Goddard Space Flight Center, New York, N. Y. 10025

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Abstract

The two-dimensional diffusion equation has been solved by an integral method to obtain the distribution of ground-level concentration of an inert effluent emitted from a semi-infinite area source in a steady-state and horizontally homogeneous atmospheric surface layer. Mean wind velocity and eddy diffusivity profiles derived from empirically determined flux-profile relations of Businger et al. (1971) for stable and unstable surface layers were used. It is found that concentration as a function of downwind distance can be described by a simple formula over distances of practical interest in surface layer dispersion. Corresponding results for a cross-wind infinite line source are obtained by simple differentiation. The concentration distribution is completely determined by the friction velocity u *, the Monin-Obukhov length L, the roughness length z0, and the effluent source strength Q. The generalization of the integral method needed to obtain accurate solutions of the diffusion equation with the given wind velocity and diffusivity profiles is discussed in an appendix.

Abstract

The two-dimensional diffusion equation has been solved by an integral method to obtain the distribution of ground-level concentration of an inert effluent emitted from a semi-infinite area source in a steady-state and horizontally homogeneous atmospheric surface layer. Mean wind velocity and eddy diffusivity profiles derived from empirically determined flux-profile relations of Businger et al. (1971) for stable and unstable surface layers were used. It is found that concentration as a function of downwind distance can be described by a simple formula over distances of practical interest in surface layer dispersion. Corresponding results for a cross-wind infinite line source are obtained by simple differentiation. The concentration distribution is completely determined by the friction velocity u *, the Monin-Obukhov length L, the roughness length z0, and the effluent source strength Q. The generalization of the integral method needed to obtain accurate solutions of the diffusion equation with the given wind velocity and diffusivity profiles is discussed in an appendix.

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