A vortex ring (or toroidal vortex), is a donut-shaped region of circulation that moves through the fluid medium. A vortex ring tends to move in the direction perpendicular to the plane of the ring, possibly extending out a considerable distance. The movement of the fluid can be classified as poloidal (related to the short route around a torus), across the circular axis of the donut, in such a way that the inner part of the ring moves faster toward the front side.[more]
Vortex rings are produced by dolphins, humpback and beluga whales, volcanoes, atomic/hydrogen bombs, fire eaters, and obviously, by smokers. Vortex rings were first analyzed mathematically by H. von Helmholtz in 1858 .[less]
The relevant equations are enumerated in the Initialization Code.
 H. von Helmholtz, "On Integrals of the Hydrodynamic Equations that Correspond to Vortex Motions," Journal für die reine und angewandte Mathematik, 55, 1858 pp. 22–55.
 Extraordinary Toroidal Vortices. [Video] (Feb 12, 2010) www.youtube.com/watch?v=mHyTOcfF99o.
 Wikipedia. "Vortex Ring." (Nov 14, 2012) en.wikipedia.org/wiki/Vortex_ring.