Strange attractors in weakly turbulent Couette-Taylor flow

Abstract

We have conducted an experiment on the transition from quasiperiodic to weakly turbulent flow of a fluid contained between concentric cylinders with the inner cylinder rotating and the outer cylinder at rest. Power spectra, phase-space portraits, and circle maps obtained from velocity time-series data indicate that the nonperiodic behavior which we have observed is deterministic, that is, it is described by strange attractors. We discuss various problems that arise in computing the dimension of strange attractors constructed from experimental data and show that these problems impose severe requirements on the quantity and accuracy of data necessary for determining dimensions greater than about 5. In the present experiment the attractor dimension increases from 2 at the onset of turbulence to about 4 at a Reynolds number 50% above the onset of turbulence.