Boundary-Layer Meteorology

, 129:371 | Cite as

A K-Theory of Dispersion, Settling and Deposition in the Atmospheric Surface Layer

Original Paper


Dispersion estimates with a Gaussian plume model are often incorrect because of particle settling (β), deposition (γ) or the vertical gradient in diffusivity (Kv(z) = K0μz). 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 Lβ = K0U/β2, Lγ = K0U/γ2 and Lμ = K0U/μ2 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, Lγ and Lμ is proposed.


Air pollution Deposition Diffusion Dispersion Settling Surface layer Transport 

List of Symbols

U, V

Horizontal wind components (m s−1)


Vertical diffusivity at z = 0 (ground or canopy top) (m2 s−1)


Vertical diffusivity (m2 s−1)


Horizontal diffusivity (m2 s−1)

x, y

Horizontal coordinates (m)


Distance above ground or canopy top (m)


Offset vertical distance (m)


Scale factor for vertical distance (m−1/2)


Scaled offset vertical distance


η at the ground or canopy top


Logarithmic derivative of Ĉat z  =  0 (m−1)

k, l

Horizontal wavenumber components (m−1)

C(x, y, z)

Concentration (kg m−3)


Fourier Transform of C(x, y, z) (kg m−1)

S(x, y)

Source strength (kg m−2 s−1)


Horizontal dimension of source (m)


Intrinsic frequency (s−1)


in situ decay rate (s−1)


Particle settling speed (m s−1)


Deposition velocity (m s−1)


Vertical K gradient (m s−1)


Coefficient in asymptotic formulae


Various horizontal length scales (m)


Hankel function of the first kind of order p


Non-dimensional downstream distance

A, B, C

Regime symbols


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Geology and GeophysicsYale UniversityNew HavenUSA

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