周期性旋涡阵列中游泳者从弹道到扩散的转变

IF 2.4 3区 物理与天体物理 Q1 Mathematics Physical review. E Pub Date : 2024-09-09 DOI:10.1103/physreve.110.034203
Taylor J. Whitney, Kevin A. Mitchell
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引用次数: 0

摘要

我们通过数值模拟和动力系统分析,研究了刚性椭球形游泳体在周期性涡流阵列中的传输问题。通过集合模拟,我们展示了一个与直觉相反的结果:较慢的游动速度可以产生快速的弹道传输,而较快的游动速度则会产生混沌和扩散传输,从长远来看,这种传输本质上是较慢的。为了解释这一现象,我们利用水流的对称性,在相空间的二维截面表面上构建了一个时间可逆的波恩卡莱回归图。在游泳速度足够小的情况下,我们在截面表面上发现了稳定的周期轨道,其周围环绕着与科尔莫戈罗夫-阿诺德-莫泽曲线类似的不变环。这些环内的轨迹是弹道轨迹。随着游泳速度的增加,周期轨道会发生一系列周期加倍的分岔,从而破坏弹道环。这些分岔与集合模拟中从弹道到扩散的转变完全吻合。我们还使用了额外的集合模拟来测试这些结果对噪声的稳健性。随着旋转扩散强度的增加,弹道行为被破坏。不过,我们估计在实验中仍可能看到弹道环。
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Ballistic to diffusive transition for swimmers in a periodic vortex array
We study the transport of rigid ellipsoidal swimmers in a periodic vortex array via numerical simulation and dynamical systems analysis. Via ensemble simulations, we show the counterintuitive result that slower swimming speeds can generate fast ballistic transport, while faster swimming speeds generate chaotic and diffusive transport, which is inherently slower in the long run. To explain this, we use the symmetry of the flow to construct a time-reversible Poincaré return map on a two-dimensional surface of section in phase space. For sufficiently small swimming speeds, we find stable periodic orbits on the surface of section surrounded by invariant tori, similar to Kolmogorov-Arnold-Moser curves. Trajectories within these tori are ballistic. As the swimming speed is increased, the periodic orbits undergo a sequence of period-doubling bifurcations that destroys the ballistic tori. These bifurcations exactly match the ballistic to diffusive transition from the ensemble simulations. Additional ensemble simulations are used to test the robustness of these results to noise. The ballistic behavior is destroyed as the strength of rotational diffusion increases. However, we estimate that the ballistic tori might still be seen in experiments.
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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