Long-duration meteor trains have fascinated observers for many years. The great Leonid meteor storms of 1866--1888 were the first to spark organized scientific study on the subject, but despite years of study, more than a century later, persistent trains remain for the most part a mystery. Over the last few years, however, the heightened Leonid activity has fueled considerable research efforts, much of it dealing with persistent trains. Some of the results of a comprehensive study of persistent trains conducted at the Starfire Optical Range (SOR) on Kirtland Air Force Base, New Mexico, during the 1998 and 1999 Leonid showers are reported here. For the first time the time evolution of persistent trains is used to determine the eddy diffusion coefficient at mesospheric heights. In three of the four trains studied, portions of the train exhibited molecular diffusion while the remainder of the train, as well as the entire fourth train, exhibited eddy diffusion. The eddy diffusion coefficients were several hundred m2 s-1, two orders of magnitude higher than the molecular rates. The sodium density in the train was sufficient to use it as a passive scalar tracer of turbulent fluctuations. The spectra are well modeled by the Heisenberg turbulence model, and the values found for the energy dissipation rate are in agreement with the eddy diffusion coefficient estimates. The gradient Richardson number and Brunt-V¿is¿ll¿ frequency were determined from lidar measurements and indicated regions of convective and dynamic instability.