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

我们研究了一个矩形截面的弯曲管道中的流动，该管道具有第二曲率比为8的纵横比。特别是，周期和准周期流发生以上的Hopf分叉进行了数值计算。将符号动力学应用于包含一系列流型的多周期流动。结果表明：没有一种流型具有稳定的平衡态，但由每种流型组成的流型是稳定的。间歇性不对称流动存在Dean数。相应的吸引子表明，该吸引子的分维近似为二维。发现吸引子在沿着轨道上有伸缩折叠现象，由此可见shaos是一个奇异的吸引子。研究结果发表在《日本机械工程师学会会刊》上。此外，我们还用同时位移代替连续位移的方法对相同的流动进行了数值模拟。预期后一种方法尽可能降低不对称干扰。结果表明：在实验条件下，得到了结构不稳定的对称流动。稳定到稳定到稳定流的分岔观察到下面的Hopf分岔。在Hopf分岔点以上，观察到了几次双周期行为。吸引子的几何形状被发现是简单的，这类似于Rossler带模型。对吸引子进行了初步研究，得到了直通道内流动的模型方程，并对理论过程进行了初步研究，得到了直通道内流动的模型方程，期望理论过程能适用于弯管流动。

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.