二维瑞利-贝纳德流中周期轨道的表征
Characterizing periodic orbits in two-dimensional Rayleigh-Bénard flows
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中文总结 AI 辅助
针对二维瑞利-贝纳德流混沌过渡区，计算表征定态与周期轨道，结合弗洛凯分析揭示轨道分岔、对称性破缺及热输运特性，明确轨道的动力学相关性。
中文摘要 AI 辅助
不稳定周期轨道与定态被认为是时空混沌和湍流的核心结构，但在热驱动流的过渡区，这类结构的计算研究仍较为匮乏。本工作在普朗特数Pr=1的二维瑞利-贝纳德流中，计算并表征了1个定态和3族周期轨道，研究处于混沌转变附近。我们发现，流在通往混沌的过程中，成为准周期后会在多组轨道间跳跃。利用弗洛凯分析研究所得轨道的稳定性并表征其分岔，表明基频与次频的出现、相位锁定机制均与轨道动力学相关。我们详细研究流如何追随所得轨道，确定各轨道在哪些动力学区域具有相关性。分析还揭示两点关键结论：(1)混沌 onset 前所有对称性均被打破；(2)该 onset 不改变热输运行为。
英文摘要
Unstable periodic orbits and steady states are believed to form the backbone of spatiotemporal chaos and turbulence, yet their computation in thermally driven flows remains scarce for transitional regimes. In this work we compute and characterize a steady state and three families of periodic orbits in two-dimensional Rayleigh-Bénard at $\mathrm{Pr}=1$, near the transition to chaos. We find that in its route to chaos, the flow hops between several sets of orbits after becoming quasiperiodic. We use Floquet analysis to study the stability of the orbits obtained and characterize their bifurcations, showing how the appearance of primary and secondary frequencies, as well as phase-locking mechanisms, are all related to the dynamics of the orbits. We study in detail how the flow shadows the orbits found and determine in which regimes each orbit is dynamically relevant or not. Our analysis also reveals two important insights: (1) all symmetries are broken before the onset of chaos, and (2) this onset does not alter the behavior of the heat transport.
发表机构
- Universidad de San Andrés（圣安德烈斯大学）
- Departamento de Física, Universidad de Buenos Aires（布宜诺斯艾利斯大学物理系）
- CONICET（阿根廷国家科学研究委员会）
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