The resulting solution for solving the final equations listed above for both the Eulerian and Lagrangian models for analyzing the statistics of species in turbulent flow, both result in very similar expressions for calculating the average concentration at a location from a continuous source.  Both solutions develop a [http://www.shodor.org/master/environmental/air/plume/index.html Gaussian Plume] and are virtually identical under the assumption that the variances in the x,y,z directions are related to the eddy diffusivity:
where 
q= species emission rate, u = wind speed, σ = variance in i direction.
Under various external conditions such as directional flow speed (wind) and environmental conditions, the variances and diffusivities of turbulent diffusion are measured and used to calculate a good estimate of concentrations at a specific point from a source. This model is very useful in atmospheric sciences, especially when dealing with concentrations of contaminants in air pollution that emanate from sources such as combustion stacks, rivers, or strings of automobiles on a road.