Zahnow Jens C, Feudel Ulrike
Institute of Physics, University of Oldenburg, 26129 Oldenburg, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Feb;77(2 Pt 2):026215. doi: 10.1103/PhysRevE.77.026215. Epub 2008 Feb 21.
The motion of small, spherical particles of finite size in fluid flows at low Reynolds numbers is described by the strongly nonlinear Maxey-Riley equations. Due to the Stokes drag, the particle motion is dissipative, giving rise to the possibility of attractors in phase space. We investigate the case of an infinite cellular flow field with time-periodic forcing. The dynamics of this system are studied in a part of the parameter space. We focus particularly on the size of the particles, whose variations are most important in active physical processes, for example, for aggregation and fragmentation of particles. Depending on their size the particles will settle on different attractors in phase space in the long-term limit, corresponding to periodic, quasiperiodic, or chaotic motion. One of the invariant sets that can be observed in a large part of this parameter region is a quasiperiodic motion in the form of a torus. We identify some of the bifurcations that these tori undergo, as particle size and mass ratio relative to the fluid are varied. In this way we provide a physical example for sub- and supercritical pitchfork bifurcations of tori.
在低雷诺数下，流体中有限尺寸的小球形颗粒的运动由强非线性的马克西 - 莱利方程描述。由于斯托克斯阻力，颗粒运动是耗散的，这使得相空间中存在吸引子成为可能。我们研究具有时间周期强迫的无限细胞流场的情况。在参数空间的一部分中研究该系统的动力学。我们特别关注颗粒的大小，其变化在诸如颗粒聚集和破碎等活跃物理过程中最为重要。从长期来看，根据颗粒大小，它们会在相空间中落在不同的吸引子上，对应于周期性、准周期性或混沌运动。在该参数区域的很大一部分中可以观察到的不变集之一是以环面形式存在的准周期运动。随着颗粒大小和相对于流体的质量比的变化，我们确定了这些环面所经历的一些分岔。通过这种方式，我们为环面的亚临界和超临界叉形分岔提供了一个物理示例。
