Callaham Jared L, Rigas Georgios, Loiseau Jean-Christophe, Brunton Steven L
Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA.
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK.
Sci Adv. 2022 May 13;8(19):eabm4786. doi: 10.1126/sciadv.abm4786. Epub 2022 May 11.
Improved turbulence modeling remains a major open problem in mathematical physics. Turbulence is notoriously challenging, in part due to its multiscale nature and the fact that large-scale coherent structures cannot be disentangled from small-scale fluctuations. This closure problem is emblematic of a greater challenge in complex systems, where coarse-graining and statistical mechanics descriptions break down. This work demonstrates an alternative data-driven modeling approach to learn nonlinear models of the coherent structures, approximating turbulent fluctuations as state-dependent stochastic forcing. We demonstrate this approach on a high-Reynolds number turbulent wake experiment, showing that our model reproduces empirical power spectra and probability distributions. The model is interpretable, providing insights into the physical mechanisms underlying the symmetry-breaking behavior in the wake. This work suggests a path toward low-dimensional models of globally unstable turbulent flows from experimental measurements, with broad implications for other multiscale systems.
改进湍流建模仍然是数学物理中的一个主要开放性问题。湍流极具挑战性，部分原因在于其多尺度性质以及大尺度相干结构无法从小尺度波动中分离出来这一事实。这种封闭问题是复杂系统中一个更大挑战的典型代表，在复杂系统中，粗粒化和统计力学描述会失效。这项工作展示了一种替代的数据驱动建模方法，用于学习相干结构的非线性模型，将湍流波动近似为状态依赖的随机强迫。我们在高雷诺数湍流尾流实验中演示了这种方法，表明我们的模型能够重现经验功率谱和概率分布。该模型具有可解释性，为尾流中对称性破缺行为背后的物理机制提供了见解。这项工作为从实验测量中构建全局不稳定湍流流动的低维模型指明了一条道路，对其他多尺度系统具有广泛的意义。
