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D. Bushnell: Turbulence Sensitivity and Control in Wall Flows. Proceedings of ICASE/NASA Conference on Theoretical Approaches to Turbulence, Oct. 1984. 39. H. Poincare: Sur les courbes definies par les equations differentielles, I-VI, Oeuvres, Vol.
4) Structures have various scales. The premises allow the following interpretation of observations: are interdependent. Flow structures Changes in structures occur in discrete ways at definite and repeatable values of parameters. Chaos in fluid systems can occur after a finite number of bifurcations (discrete changes). Chaos is deterministic and can be repre- sented by a strange attractor of finite dimensionality. Finally, the various scales of turbulence interact (a restatement of the observation that the structures are interdependent).
His description is reproduced in figure 11. The solution flow shown in part (a) is primarily in the direction of the arrows around the torus with relatively small transverse motion. periodic. Plotted against time, a solution would appear as noisily Parts (b), (c), and (d) show successive intersections of a set of solu- tion curves that undergo squeezing and stretching (b), rotation (c), and folding (d) in one circuit of the torus. Four iterations of this "return mapping" produce the complex layered structure shown in (e).