Are Attractors Relevant to Turbulence?

James P. Crutchfield
Physics Department
University of California
Berkeley, CA 94720, USA

Kunihiko Kaneko
Center for Complex Systems Research
Univeristy of Illinois at Urbana-Champaign
Champaign, Illinois 61280, USA

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 goverened 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.

Citation

J. P. Crutchfield and K. Kaneko. "Are Attractors Relevant to Turbulence?" Phys. Rev. Let. 60 1988: 2715-2718.

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