A unified analytical solution of the steady-state atmospheric diffusion equation
A unified analytical solution of the steady-state atmospheric diffusion equation for a finite and semi-infinite/infinite media was developed using the classic integral transform technique (CITT) which is based on a systematized method of separation of variable.The solution was obtained considering a...
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todo:paper_13522310_v55_n_p201_PerezGuerrero2023-10-03T16:10:12Z A unified analytical solution of the steady-state atmospheric diffusion equation Pérez Guerrero, J.S. Pimentel, L.C.G. Oliveira-Júnior, J.F. Heilbron Filho, P.F.L. Ulke, A.G. Analytical solution Associated eigenvalue problem Atmospheric diffusion equation Integral transform Analytical procedure Atmospheric diffusion equations Closed-form analytical solutions Convergence behaviors Copenhagen Eddy Diffusivities Eigenvalue problem Finite media Functional forms Integral transform Integral transform technique Mean wind speed Mean-winds Prairie Grass Turbulent diffusion coefficients Vertical coordinates Eigenvalues and eigenfunctions Integral equations Partial differential equations Diffusion diffusion eigenvalue numerical model prairie steady-state equilibrium wind velocity article atmospheric diffusion controlled study diffusion coefficient literature methodology prairie priority journal steady state velocity wind Copenhagen [(CTY) Hovedstaden] Denmark Hovedstaden A unified analytical solution of the steady-state atmospheric diffusion equation for a finite and semi-infinite/infinite media was developed using the classic integral transform technique (CITT) which is based on a systematized method of separation of variable.The solution was obtained considering an arbitrary mean wind velocity depending on the vertical coordinate (. z) and a generalized separable functional form for the eddy diffusivities in terms of the longitudinal (. x) and vertical coordinates (. z).The examples described in this article show that the well known closed-form analytical solutions, available in the literature, for both finite and semi-infinite/infinite media are special cases of the present unified analytical solution. As an example of the strength of the developed methodology, the Copenhagen and Prairie Grass experiments were simulated (finite media with the mean wind speed and the turbulent diffusion coefficient described by different functional forms). The results indicate that the present solutions are in good agreement with those obtained using other analytical procedures, previously published in the literature. It is important to note that the eigenvalue problem is associated directly to the atmospheric diffusion equation making possible the development of the unified analytical solution and also resulting in the improvement of the convergence behavior in the series of the eigenfunction-expansion. © 2012 Elsevier Ltd. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_13522310_v55_n_p201_PerezGuerrero |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Analytical solution Associated eigenvalue problem Atmospheric diffusion equation Integral transform Analytical procedure Atmospheric diffusion equations Closed-form analytical solutions Convergence behaviors Copenhagen Eddy Diffusivities Eigenvalue problem Finite media Functional forms Integral transform Integral transform technique Mean wind speed Mean-winds Prairie Grass Turbulent diffusion coefficients Vertical coordinates Eigenvalues and eigenfunctions Integral equations Partial differential equations Diffusion diffusion eigenvalue numerical model prairie steady-state equilibrium wind velocity article atmospheric diffusion controlled study diffusion coefficient literature methodology prairie priority journal steady state velocity wind Copenhagen [(CTY) Hovedstaden] Denmark Hovedstaden |
| spellingShingle |
Analytical solution Associated eigenvalue problem Atmospheric diffusion equation Integral transform Analytical procedure Atmospheric diffusion equations Closed-form analytical solutions Convergence behaviors Copenhagen Eddy Diffusivities Eigenvalue problem Finite media Functional forms Integral transform Integral transform technique Mean wind speed Mean-winds Prairie Grass Turbulent diffusion coefficients Vertical coordinates Eigenvalues and eigenfunctions Integral equations Partial differential equations Diffusion diffusion eigenvalue numerical model prairie steady-state equilibrium wind velocity article atmospheric diffusion controlled study diffusion coefficient literature methodology prairie priority journal steady state velocity wind Copenhagen [(CTY) Hovedstaden] Denmark Hovedstaden Pérez Guerrero, J.S. Pimentel, L.C.G. Oliveira-Júnior, J.F. Heilbron Filho, P.F.L. Ulke, A.G. A unified analytical solution of the steady-state atmospheric diffusion equation |
| topic_facet |
Analytical solution Associated eigenvalue problem Atmospheric diffusion equation Integral transform Analytical procedure Atmospheric diffusion equations Closed-form analytical solutions Convergence behaviors Copenhagen Eddy Diffusivities Eigenvalue problem Finite media Functional forms Integral transform Integral transform technique Mean wind speed Mean-winds Prairie Grass Turbulent diffusion coefficients Vertical coordinates Eigenvalues and eigenfunctions Integral equations Partial differential equations Diffusion diffusion eigenvalue numerical model prairie steady-state equilibrium wind velocity article atmospheric diffusion controlled study diffusion coefficient literature methodology prairie priority journal steady state velocity wind Copenhagen [(CTY) Hovedstaden] Denmark Hovedstaden |
| description |
A unified analytical solution of the steady-state atmospheric diffusion equation for a finite and semi-infinite/infinite media was developed using the classic integral transform technique (CITT) which is based on a systematized method of separation of variable.The solution was obtained considering an arbitrary mean wind velocity depending on the vertical coordinate (. z) and a generalized separable functional form for the eddy diffusivities in terms of the longitudinal (. x) and vertical coordinates (. z).The examples described in this article show that the well known closed-form analytical solutions, available in the literature, for both finite and semi-infinite/infinite media are special cases of the present unified analytical solution. As an example of the strength of the developed methodology, the Copenhagen and Prairie Grass experiments were simulated (finite media with the mean wind speed and the turbulent diffusion coefficient described by different functional forms). The results indicate that the present solutions are in good agreement with those obtained using other analytical procedures, previously published in the literature. It is important to note that the eigenvalue problem is associated directly to the atmospheric diffusion equation making possible the development of the unified analytical solution and also resulting in the improvement of the convergence behavior in the series of the eigenfunction-expansion. © 2012 Elsevier Ltd. |
| format |
JOUR |
| author |
Pérez Guerrero, J.S. Pimentel, L.C.G. Oliveira-Júnior, J.F. Heilbron Filho, P.F.L. Ulke, A.G. |
| author_facet |
Pérez Guerrero, J.S. Pimentel, L.C.G. Oliveira-Júnior, J.F. Heilbron Filho, P.F.L. Ulke, A.G. |
| author_sort |
Pérez Guerrero, J.S. |
| title |
A unified analytical solution of the steady-state atmospheric diffusion equation |
| title_short |
A unified analytical solution of the steady-state atmospheric diffusion equation |
| title_full |
A unified analytical solution of the steady-state atmospheric diffusion equation |
| title_fullStr |
A unified analytical solution of the steady-state atmospheric diffusion equation |
| title_full_unstemmed |
A unified analytical solution of the steady-state atmospheric diffusion equation |
| title_sort |
unified analytical solution of the steady-state atmospheric diffusion equation |
| url |
http://hdl.handle.net/20.500.12110/paper_13522310_v55_n_p201_PerezGuerrero |
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