|
 |
"Topological Ideas and Fluid Mechanics," by Renzo L. Ricca and Mitchell A. Berger. Physics Today, December 1996, pages 28-34.
This article describes the application of branches of mathematics known as knot theory and braid theory to problems in fluid mechanics. These ideas first arose in efforts by the 19th century physicist, Lord Kelvin, to interpret atoms as knotted vortices in the ether. While Kelvin's ideas have since been superseded, his work catalyzed the development of knot theory and led to the development of a topological approach to fluid dynamics. Knotted and linked structures are found in all types of fluid flow, from tiny vortices to larger eddies to huge plasma loops. The article discusses the use of topological notions in areas such as astrophysics, where lines of magnetic flux that crisscross the surface of the Sun can be investigated through braid theory. In addition to treating idealized models of fluid flow, the article also discusses the behavior of real fluids, in which dissipative effects can produce topological changes.
