A generalized analytical solution for turbulent dispersion with inhomogeneous wind and diffusion coefficient

A technique is presented to solve analytically the turbulent diffusion equation for the concentration of a passive contaminant emitted from an elevated continuous source into the atmosphere. A generalized method of solution using Sturm–Liouville and WKB theories is developed to overcome difficulties due to the height‐dependent wind velocity and diffusion coefficient appearing in the diffusion equation. The method presented in this paper is able to derive an asymptotic expression for the concentration obtained from the solution of the atmospheric diffusion equation which involves explicitly inhomogeneous wind velocity and diffusion coefficient. The diffusion equation model derived from this method can be applied in a practical prediction of contaminant concentration in a turbulent atmosphere. This revised version was published online in August 2006 with corrections to the Cover Date.