Analytical Solutions of the Advection–Diffusion Equation with Variable Vertical Eddy Diffusivity and Wind Speed Using Hankel Transform

• Published in: Pure and applied geophysics Vol. 177; no. 9; pp. 4545 - 4557
• Main Authors: Essa, Khaled S. M., Shalaby, Ahmed S., Ibrahim, Mahmoud A. E., Mosallem, Ahmed M.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01-09-2020; Springer Nature B.V
• Subjects: Advection; Advection-diffusion equation; Diffusion; Diffusion coefficients; Diffusion rate; Diffusivity; Earth and Environmental Science; Earth Sciences; Eddy diffusion; Eddy diffusivity; Exact solutions; Geophysics/Geodesy; Mathematical models; Power law; Vortices; Water pollution; Wind; Wind speed; Hankel transform; Copenhagen experiment; Hanford experiment; stable and unstable conditions
• ISSN: 0033-4553; 1420-9136
• DOI: 10.1007/s00024-020-02496-y

Hankel transform was employed to solve the two-dimensional steady state advection–diffusion equation considering a continuous point source with vertical eddy diffusivity as a power law of vertical height and downwind distance, also, taking wind speed as power law. The analytical model was evaluated and compared with Hanford diffusion experiment in stable conditions and Copenhagen diffusion experiment in unstable and neutral conditions which was done by reducing the general analytical model to a one with linear vertical eddy diffusivity and constant downwind speed profile. Comparison with other analytical models was held. The presented model predictions show a good agreement with observations and lay inside a factor of two with observed data of both Hanford and Copenhagen diffusion experiments.