An analytic solution of the one-dimensional diffusion equation in a non-stationary boundary layer with an application to inversion rise fumigation

Nieuwstadt, F. T. M.; Haan, B. J. de

doi:10.1016/0004-6981(81)90289-4

Cited by 32 publications

(13 citation statements)

References 13 publications

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“…Approaches to the advection-diffusion problem are not new in the literature; they are either based on numerical schemes, stochastic simulations or (semi-)analytical methods, as shown in a selection of articles (see [ScFi75], [De78], [NiDe81], [Ti89], [ShSiYa96], [LiHi97]). Note that in these works all solutions are valid for scenarios with strong restrictions with respect to their specific wind and vertical eddy diffusivity profiles.…”

Section: The Advection-diffusion Approachmentioning

confidence: 99%

Integral Methods in Science and Engineering

2013

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Section: The Advection-diffusion Approachmentioning

confidence: 99%

Integral Methods in Science and Engineering

2013

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“…A further extended solution accounting for a growing ABL height was given in terms of Jacobi polynomials [15].…”

Section: A Short Review Of Solutions Of the Advection-diffusion Equationmentioning

confidence: 99%

An Analytical Simple Formula for the Ground Level Concentration from a Point Source

et al. 2011

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Abstract:The Advection-Diffusion Equation is solved for a constant pollutant emission from a point-like source placed inside an unstable Atmospheric Boundary Layer. The solution is obtained adopting the novel analytical approach: Generalized Integral Laplace Transform Technique. The concentration solution of the equation is expressed through an infinite series expansion. After setting a realistic scenario through the wind and diffusivity parameterizations, the Ground Level Concentration (GLC) is determined, and an explicit approximate expression is provided for it, allowing an analytically simple expression for the position and value of the maximum. Remarks arise regarding the ability to express value and position of the GLC as explicit functions of the parameters defining the Atmospheric Boundary Layer scenario and the source height.

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“…Subsequently, NIEUWSTADT and DE HAAN (1981) extended that solution to the case of a growing boundary layer height. CATALANO (1982), in turn, extended the latter solution to the case of non-zero mean vertical wind profiles.…”

Section: Analytical Solutions Of the Advection-diffusion Equationmentioning

confidence: 99%

Operational Advanced Air Pollution Modeling

Tirabassi¹

2003

Pure and Applied Geophysics

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Operational models that use solutions of the advection-diffusion equation based on more realistic assumptions than that of homogeneous wind and eddy diffusivity coefficients are presented. In particular a new parameterization for a model using a solution that accepts wind and eddy diffusivity profiles described by power functions of height is introduced. The performance of the model with the new parameterization was assessed using experimental data sets.

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An analytic solution of the one-dimensional diffusion equation in a non-stationary boundary layer with an application to inversion rise fumigation

Cited by 32 publications

References 13 publications

Integral Methods in Science and Engineering

Integral Methods in Science and Engineering

An Analytical Simple Formula for the Ground Level Concentration from a Point Source

Operational Advanced Air Pollution Modeling

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