Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"Topological Ideas and Fluid Mechanics," by Renzo L. Ricca and MitchellA. Berger. Physics Today, December 1996, pages 28-34.

This article describes the application of branches of mathematics known as knottheory and braid theory to problems in fluid mechanics. These ideas firstarose in efforts by the 19th century physicist, Lord Kelvin, to interpret atomsas knotted vortices in the ether. While Kelvin's ideas have since beensuperseded, his work catalyzed the development of knot theory and led to the development ofa topological approach to fluid dynamics. Knotted and linked structures arefound in all types of fluid flow, from tiny vortices to larger eddies to hugeplasma loops. The article discusses the use of topological notions in areassuch as astrophysics, where lines of magnetic flux that crisscross the surfaceof the Sun can be investigated through braid theory. In addition to treatingidealized models of fluid flow, the article also discusses the behavior of realfluids, in which dissipative effects can produce topological changes.