Chaotic Motion of Fluid Particles Due to the Alternate Rotations of Two Eccentric Cylinders.

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  • Atobe Takashi
    Department of Earth System Science & Technology, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816
  • Funakoshi Mitsuaki
    Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka 816

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  • Chaotic Motion of Fluid Particles Due t

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Abstract

Chaotic or regular motions of the fluid particles by the Stokes flow between two eccentric cylinders counter rotating alternately and of radius ratio 0.3 are investigated numerically and analytically. We examine the dependence of the motions on eccentricity ε, focusing on an equilibrium point of the Poincaré map of the particle position after every rotations. If both of the winding numbers of the cylinders are small, the area of the chaotic region is small and increases monotonically with ε, whereas when at least one of them is not small, this area is relatively large and takes a maximum at a certain ε. In the latter case, within a certain region of the winding numbers, the bifurcation of the equilibrium point from elliptic to hyperbolic type occurs at another value of ε=εb, resulting in the increase in the area for ε around εb. A perturbation analysis can roughly predict this region and the value of εb.

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