Chaos Structure of the Flows in a Curved Duct of Rectangular Cross-section

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We studied flows in a curved duct of a rectangular cross-section having an aspect ratio of 2nd curvature ratio of 8. In particular, periodic and quasi-periodic flow occurring above the Hopf bifurcation were calculated numerically. The symbolic dynamics was applied to the multi periodic flows which include a series of flow patterns. Results were as follows ; no flow patterns have stable equilibrium state, but a flow pattern consisting of each the pattern was stable. There existed the Dean number where asymmetric flow occurred intermittently. The corresponding attractor showed that fracial demension of the attractor was nearly two dimensional. A stretching and folding of the attractors was found along orbits, from which shaos seems to be strange attractor. the results were published in the Transaction of the Japan society of mechanical engineers. Furthermore, we simulated numerically the same flows by the method of the simultaneous displacement instead of the successive displacement. It was expected that the latter method decreased asymmetric distubance as possible. The results were as follws ; symmetric flows were obtained which were structurally unstable. Bifurcation of steady into steady into steady flow was observed below the Hopf bifurcation. Above the Hopf bifurcation, a few times of the double periodic behavior were observed. The geometry of the attractor was found to be simple, which resembled the Rossler band model. Consequently the attractor preliminary study, the model equation for the flow in a straight channel was obtained, and the theoretical procedure was preliminary study, the model equation for the flow in a straight channel was obtained, and the theoretical procedure was expected to be applicable to a curved duct flow.