论文标题

通过流动动态模式分解,数据驱动的数据驱动识别湍流的时空结构

Data-driven identification of the spatio-temporal structure of turbulent flows by streaming Dynamic Mode Decomposition

论文作者

Yang, Rui, Zhang, Xuan, Reiter, Philipp, Linkmann, Moritz, Lohse, Detlef, Shishkina, Olga

论文摘要

流动动态模式分解(SDMD)(Hemati等,Phys。Fluids26(2014))是动态模式分解(DMD)的低存储版本(Schmid,J。FluidMech。656(2010)),一种数据驱动的方法,用于提取时空流动流动模式。流DMD通过使用新可用数据的增量更新近似动态模式来避免将整个数据顺序存储在内存中。在本文中,我们使用SDMD来识别和提取不同湍流的主要时空结构,需要分析大型数据集。首先,将SDMD的效率和准确性与经典DMD进行了比较,该数据集由通过直接数值模拟圆柱体后面的唤醒流进行直接数值模拟而获得的公开测试数据集进行了比较。流式DMD不仅可靠地再现流的最重要的动力学特征;我们的计算还强调了其所需的计算资源的优势。随后,我们使用SDMD分析了三个不同的湍流,这些流都显示出一定程度的大规模连贯性:快速旋转的雷利 - 贝纳德对流,水平对流和渐近吸力边界层。不同频率和空间范围的结构可以清楚地分开,并且仅使用几个动态模式捕获动力学的显着特征。总而言之,我们证明SDMD是在广泛的湍流中识别时空结构的强大工具。

Streaming Dynamic Mode Decomposition (sDMD) (Hemati et al., Phys. Fluids 26(2014)) is a low-storage version of Dynamic Mode Decomposition (DMD) (Schmid, J. Fluid Mech. 656 (2010)), a data-driven method to extract spatio-temporal flow patterns. Streaming DMD avoids storing the entire data sequence in memory by approximating the dynamic modes through incremental updates with new available data. In this paper, we use sDMD to identify and extract dominant spatio-temporal structures of different turbulent flows, requiring the analysis of large datasets. First, the efficiency and accuracy of sDMD are compared to the classical DMD, using a publicly available test dataset that consists of velocity field snapshots obtained by direct numerical simulation of a wake flow behind a cylinder. Streaming DMD not only reliably reproduces the most important dynamical features of the flow; our calculations also highlight its advantage in terms of the required computational resources. We subsequently use sDMD to analyse three different turbulent flows that all show some degree of large-scale coherence: rapidly rotating Rayleigh--Bénard convection, horizontal convection and the asymptotic suction boundary layer. Structures of different frequencies and spatial extent can be clearly separated, and the prominent features of the dynamics are captured with just a few dynamic modes. In summary, we demonstrate that sDMD is a powerful tool for the identification of spatio-temporal structures in a wide range of turbulent flows.

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