New Global Fractal Formalism Describes Paths to Turbulence

One motivation for the intensive study of nonlinear physical systems is the hope that, despite their complex structures, they might possess universal features shared by entire classes of similar nonlinear processes. This hope was strikingly realized several years ago when Mitchell Feigenbaum (then at Los Alamos, now at Cornell) discovered that a few universal ratios—independent of any dynamical details—characterized all systems whose periods doubled repeatedly as they approached turbulence (PHYSICS TODAY, March 1981, page 17). At the point of infinite period doubling, the orbits of Feigenbaum’s system showed a complex behavior in which one could discern a scale‐invariant, or fractal, structure. Recently a team of theorists has developed a method for describing a new global structure of these fractal objects. The predictions generated by this formalism agree quite well with experimental measurements performed at the University of Chicago on a fluid as it approached turbulence by two distinct paths.

This article is only available in PDF format