空间扩展Kolmogorov湍流中的相对周期轨道：从全局到局域复现
Relative periodic orbits in spatially extended Kolmogorov turbulence: from global to localized recurrence
查看机构详情
- University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
- Xingjian College, Tsinghua University（清华大学行健学院）
机构由 AI 辅助整理，请以论文原文为准。
浏览论文内容
中文总结 AI 辅助
本研究利用分布式降阶模型（分块自编码器与神经ODE）在扩展Kolmogorov湍流中搜索相对周期轨道，成功收敛14个RPOs，并发现局域化复现解，展示了学习方法在精确相干态搜索中的有效性。
中文摘要 AI 辅助
复现不变解为解释湍流提供了动力学框架，但在空间扩展流动中，其计算变得越来越困难，因为接近全域的复现事件很少见。我们研究了在[Lx,Ly] = [2π,12π]域中、Re = 10的二维Kolmogorov流动，使用了一个由基于分块的自动编码器和神经常微分方程组成的分布式降阶模型。近复现候选通过潜在多重射击进行细化，解码到物理空间，在全Navier-Stokes动力学下进行筛选，并提供给全状态Newton-Krylov求解器。十四个候选收敛到相对周期轨道（RPOs），周期为3.65 < T < 16.45。该目录包含全域填充状态和具有限制在狭窄横向区域内的复现活动的RPOs。弱调制的周围环境通常保持有限振幅，且与层流解不同。选定的局部RPOs在雷诺数延续下持续存在，并且在截断其周围环境的相当大部分后，复现状态可以重新收敛。此外，在Ly = 12π处训练的模型在Ly = 6π和8π处无需重新训练即可生成收敛的RPO种子。这些结果表明，分布式学习动力学可以为扩展域中的精确相干态搜索提供有用的初始条件，并揭示了具有强烈局部化时间动力学的复现解。
英文摘要
Recurrent invariant solutions provide a dynamical framework for interpreting turbulence, but their computation becomes increasingly difficult in spatially extended flows, where close whole-domain recurrences are rare. We study two-dimensional Kolmogorov flow in a [Lx,Ly] = [2pi,12pi] domain with Re = 10 using a distributed reduced-order model composed of a patch-based autoencoder and a neural ordinary differential equation. Near- recurrence candidates are refined by latent multiple shooting, decoded to physical space, screened under the full Navier-Stokes dynamics and supplied to a full-state Newton- Krylov solver. Fourteen candidates converge to relative periodic orbits (RPOs), with periods 3.65 < T <16.45. The catalogue contains both domain-filling states and RPOs with recurrent activity localised to a restricted cross-stream region. The weakly modulated surroundings generally remain finite-amplitude and distinct from the laminar solution. Selected localised RPOs persist under continuation in Reynolds number, and recurrent states can be reconverged after truncating substantial portions of their surroundings. In addition, the model trained at Ly = 12pi generates convergent RPO seeds at Ly = 6pi and 8pi without retraining. These results demonstrate that distributed learned dynamics can provide useful initial conditions for exact coherent states searches in extended domains and reveal recurrent solutions with strongly localised temporal dynamics.
