Intermittency and De Bruijn's oscillations

Abstract

Intermittency in fluid turbulence has been associated with log-periodic oscillations in moments of the velocity. These oscillations may have their origin in a self-similar, fractal description of the flow. The author has recently rigorously proved that such oscillations appear in the measurement of fractal dimension in boolean delay equations using a theorem of De Bruijn and a new tauberian theorem. This note applies this theory to a simple fractal to demonstrate the generality of this new technique.