The utility of dynamical systems approaches Comment 3

Abstract

This is a commentary on the utility of the dynamical systems approach to the understanding of transitional and turbulent flows. After a few initial remarks on the position paper by Holmes, I present a summary of three aspects: Universality in transition to chaos in wake flows, the description and dynamics of intermittent fields in fully turbulent flows, and the nature of vorticity and scalar interfaces in turbulent free shear flows. I will show that novel techniques from low-dimensional chaos and fractal geometry yield new and useful information on quantities of central interest in turbulence. The claim is that the dynamical systems appraoch has made definite contributions, not merely enlarged our vocabulary, but the way ahead visa -vis the turbulence problem has remained hazy.