Luithardt Harry H., Kadtke James B., Pedrizzetti Gianni
Institute for Nonlinear Science, MS-0402, University of California, San Diego, La Jolla, California 92093-0402Institute for Pure and Applied Physical Science, MS-0360, University of California, San Diego, La Jolla, California 92093-0360Dipartimento di Ingegneria Civile, Universita' di Firenze, via Santa Marta 3, 50139 Firenze, Italy.
Chaos. 1994 Dec;4(4):681-691. doi: 10.1063/1.166045.
Previously, we have presented a simple model for the interaction of a fluid vortex structure with a moving bluff body, and demonstrated the existence of a trapping mechanism related to chaotic scattering. This single point vortex model required explicit perturbation to generate chaos and the subsequent complex dynamics. Here, we present a model which attempts to introduce internal degrees-of-freedom in the vortex structure in the simplest manner, by replacing the single vortex with a like-signed pair. We show that this model exhibits chaotic trapping without the need of explicit perturbation, however, the region of parameter space for which trapping occurs is exceedingly small due to the spatially dependent form of the perturbation. We claim that this result explains some the behavior observed in Navier-Stokes simulations of the same vortex-body system, where we find close correspondence between the dynamics of an extended vorticity distribution and the single vortex model. Finally, we generalize the model to unequal strength vortex pairs, and find more complex behavior which includes "partial" capture of the weaker vortex by the body. (c) 1994 American Institute of Physics.
此前，我们提出了一个流体涡旋结构与运动钝体相互作用的简单模型，并证明了与混沌散射相关的捕获机制的存在。这个单点涡旋模型需要明确的扰动来产生混沌及随后的复杂动力学。在此，我们提出一个模型，该模型试图以最简单的方式在涡旋结构中引入内部自由度，即将单个涡旋替换为同向涡旋对。我们表明，该模型无需明确的扰动就能呈现混沌捕获，然而，由于扰动的空间依赖形式，发生捕获的参数空间区域极小。我们认为这一结果解释了在相同涡旋 - 物体系统的纳维 - 斯托克斯模拟中观察到的一些行为，在这些模拟中，我们发现扩展涡量分布的动力学与单个涡旋模型之间存在密切对应关系。最后，我们将该模型推广到不等强度的涡旋对，并发现了更复杂的行为，包括物体对较弱涡旋的“部分”捕获。（c）1994 美国物理研究所。
