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Analytical solution of advection diffusion equation in two dimensions using different shapes of wind speed and eddy diffusivity

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DOI: 10.23977/envcp.2023.020101 | Downloads: 57 | Views: 1047

Author(s)

Khaled S. M. ESSA 1, Sawsan I. M. ELSAIED 1

Affiliation(s)

1 Department of Mathematics and Theoretical Physics, Nuclear Research Center, Egyptian Atomic Energy Authority, Cairo, Egypt

Corresponding Author

Sawsan I. M. ELSAIED

ABSTRACT

The diffusion equation has been derived in two dimensions using two methods: variable separation and substituting. We compared the results from these solutions to the results from the Copenhagen experiment, taking into consideration the differences in wind speed and eddy diffusivity.

KEYWORDS

Advection-diffusion equation, Substituting method, Eddy diffusivity, Wind speed, Copenhagen experiment, Separation of variables

CITE THIS PAPER

Khaled S. M. ESSA, Sawsan I. M. ELSAIED, Analytical solution of advection diffusion equation in two dimensions using different shapes of wind speed and eddy diffusivity. Environment and Climate Protection (2023) Vol. 2: 1-7. DOI: http://dx.doi.org/10.23977/envcp.2023.020101.

REFERENCES

[1] Andrei D. Polyanin and Valentin Zaitsev, (2003) Handbook of Nonlinear Partial Differential Equations, Edition: 1stPublisher: Chapman & Hall/CRC, ISBN: 9780429205590.
[2] Bracewell R., (2000) The Fourier Transform and Its Applications. New York: McGraw-Hill, pp. 74-104. 
[3] Businger J. A., J. C. and  Wyngaard Y. Izumi, E. F. Bradley, (1971)  Flux-Profile Relationships in the Atmosphere Surface Layer. Journal of the Atmospheric Sciences, 28: 181-189, DOI: https://doi.org/10.1175/1520-0469 (1971) 028<0181: FPRITA>2.0. CO; 2
[4] Davidson Martins Moreira, and Taciana Toledo de Almeida Albuquerque, (2016) Solution of the Atmospheric Diffusion Equation with Longitudinal Wind Speed Depending on Source Distance. Revista Brasileira de Meteorologia. vol.31 no.2. DOI: 10.1590/0102-778631220150028.
[5] Gryning S.E., Holtslag and A.A.M., Irwin J.S., Sivertsen B., (1987) Applied Dispersion Modeling Based On Meteorological Scaling Parameters. Atmospheric Environment. 21 (1), 79-89, DOI: 10.1016/0004-6981(87)902733.
[6] Gryning S.E and Lyck E., (1984) Atmospheric Dispersion from Elevated Sources in an Urban Area: Comparison between Tracer Experiments and Model Calculations. Journal of Applied Meteorology and Climatology. 23, 651– 660, Https://DOI.Org/10.1175/1520-0450(1984)023<0651:Adfesi>2.0.Co;2
[7] Hanna S R, Briggs G A, and Hosker Jr, R P., (1982) Handbook on atmospheric diffusion, United States: N. p., DOI: 10.2172/5591108.
[8] Khaled S. M. Essa, (2015) Studying the Effect of the Vertical Eddy Diffusivity on the Solution of the Diffusion Equation. Journal of ecology of Health & Environment An International Journal. Vol. 3, No. 2, 43-48.
[9] Khaled S. M. Essa, Ahmed S. Shalaby, and Mahmoud A. E. Ibrahim, Ahmed M. Mosallem., (2020) Analytical Solutions of The Advection–Diffusion Equation With Variable Vertical Eddy Diffusivity And Wind Speed Using Hankel Transform, Pure and Applied Geophysics. 177, 4545–4557, https://DOI.Org/10.1007/S00024-020-02496-Y
[10] Khaled S. M. Essa, A. N. Mina and Mamdouh Higazy., (2011) Analytical Solution of Diffusion Equation In Two Dimensions Using Two Forms Of Eddy Diffusivities.  Romanian Journal of Physics, Vol. 56, Nos. 9–10, P. 1228–1240. 
[11] Moreira D.M., Vilhena M.T. and Tirabassi T., Buske D., Costa C.P. (2010) Comparison between Analytical Models to Simulate Pollutant Dispersion in the Atmosphere. International Journal of Environment and Waste Management, Vol. 6, No. 3-4, p. 327-344,  DOI: 10.1504/IJEWM.2010.035066
[12] Monin A. S., and A. M. (1953) Obukhov Dimensionless Characteristics of Turbulence in the Layer of Atmosphere near the Ground, Dokl. Akad. Nauk SSSR, 93, 257-267.
[13] Manju Agarwal, Abhinav Tandon. (2010)  Modeling of the urban heat island in the form of Mesoscale wind and of its effect on air pollution dispersal, Applied Mathematical Modelling, Volume 34,  Pages 2520-2530, Https://DOI. Org/10.1016/J.Apm. 2009.11.016.
[14] Roberts, 0. F. T., The Theoretical Scattering of Smoke in a Turbulent Atmosphere, Proc. R. SOC. (London), Ser. A, 104: (1923), 640-654.
[15] Sharan M., and Kumar P. (2009) An analytical model for crosswind integrated concentration released from a continuous source in a finite atmospheric boundary layer, Atmospheric Environment.43. 2268–2277.
[16] X. Liu and M. Nayamatullah. (2014) Semi analytical solutions for one-dimensional unsteady none equilibrium suspended sediment transport in channels with arbitrary eddy viscosity distributions and realistic boundary conditions, Journal of Hydraulic Engineering 140(5) 0401-4011, DOI: 10.1061/ (ASCE) HY.1943-7900.0000874

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