Solution of the Atmospheric Diffusion Equation for an Instantaneous Source

5 SOLUTION OF THE ATMOSPHERIC DIFFUSION EQUATION FOR AN INSTANTANEOUS SOURCE 

We begin in this section to obtain solutions for atmospheric diffusion problems. Let us consider, as we did in the previous section, an instantaneous point source of strength S at 

Note the similarity of (18.32) and (18.28). In fact, if we define a = 2Kxxt, = 2Kyyt, and cj = 2Kzzt, we note that the two expressions are identical. There is, we conclude, evidently a connection between the Eulerian and Lagrangian approaches embodied in a relation between the variances of spread that arise in a Gaussian distribution and the eddy diffusivities in the atmospheric diffusion equation. We will explore this relationship further as we proceed. 

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