Appendix—Three-dimensional interpretation of the two-dimensional advection-diffusion equation

The realism of Shir's results may at first appear paradoxical. His numerical model is two-dimensional, so that the simulated stacks are actually line sources, whereas real-atmosphere stacks are (essentially) point sources. The physical dimensions of the source strengths aren't even the same for the two cases. Moreover, even in a unidirectional wind field, atmospheric turbulence acts to diffuse the plume in the three directions, not two. This point is especially important in view of the basic differences between two- and three-dimensional turbulence, which arise from the absence of vortex stretching in the two-dimensional case.