A K-Theory of Dispersion,Settling and Deposition in the Atmospheric Surface Layer |
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| Authors: | Ronald B Smith |
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| Institution: | (1) Department of Geology and Geophysics, Yale University, P.O. Box 208109, New Haven, CT 06520-8109, USA |
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| Abstract: | Dispersion estimates with a Gaussian plume model are often incorrect because of particle settling (β), deposition (γ) or the vertical gradient in diffusivity (K
v
(z) = K
0 + μz). These “non-Gaussian” effects, and the interaction between them, can be evaluated with a new Hankel/Fourier method. Due
to the deepening of the plume downwind and reduced vertical concentration gradients, these effects become more important at
greater distance from the source. They dominate when distance from the source exceeds L
β
= K
0
U/β
2, L
γ
= K
0
U/γ
2 and L
μ
= K
0
U/μ
2 respectively. In this case, the ratio β/μ plays a central role and when β/μ = 1/2 the effects of settling and K gradient exactly cancel. A general computational method and several specific closed form
solutions are given, including a new dispersion relation for the case when all three non-Gaussian effects are strong. A more
general result is that surface concentration scales as C(x) ~ γ
−2 whenever deposition is strong. Categorization of dispersion problems using β/μ, L
γ
and L
μ
is proposed. |
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| Keywords: | Air pollution Deposition Diffusion Dispersion Settling Surface layer Transport |
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