Are Attractors Relevant to Turbulence?

Abstract

The statistical hypothesis underlying the "strange attractor" explanation of fluid turbulence is suspect. Spatially extended systems generically exhibit long transients that preclude observation of the behavior governed by the asymptotic invariant measure. Even if the local dynamics is periodic, when it is coupled into a spatial system complex "turbulent" behavior can exist for times that grow faster than exponentially with increasing system volume. The nature of the attractor is irrelevant to the observed behavior when such systems are of even moderate size.