Spectral proper orthogonal decomposition and resolvent analysis of near-wall coherent structures in turbulent pipe flows
Spectral proper orthogonal decomposition and resolvent analysis of near-wall coherent structures in turbulent pipe flows
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DOI：
10.1017/jfm.2020.445
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发表时间：
2020-04
影响因子：
3.7
通讯作者：
Leandra I. Abreu;A. Cavalieri;P. Schlatter;R. Vinuesa;D. Henningson
中科院分区：
文献类型：
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作者：
Leandra I. Abreu;A. Cavalieri;P. Schlatter;R. Vinuesa;D. Henningson
摘要采用高阶谱元法直接数值模拟了摩擦雷诺数$Re_{\tau} = 180$和$550$时紊流管内的相干结构。利用光谱固有正交分解（SPOD）对数据库进行分析，确定了能量优势的相干结构，其中大部分是条纹和准流向涡。为了理解如何对这种结构进行建模，使用求解算子的奇异值分解计算了谐波强迫的线性流动响应，使用平均场作为基流。计算了几种频率和波数组合的SPOD和解析分析，从而可以绘制出湍流管道流动中SPOD模式和广泛相关尺度下的最佳响应之间的相似性。为了探索两种方法一致的物理原因，在解析分析中引入了一个抬升机制指标，当最优作用力由墙向分量和方位角分量主导时，该指标被激活，相关响应对应于流向速度条纹。在参数空间的大范围内，观测到主导的SPOD模式和解析模式之间有很好的一致性。在该区域，在解析分析中发现了显著的增益分离，这可能归因于与抬升机制相关的强放大，这里被理解为非线性强迫项，导致流向涡旋的出现，进而形成高振幅条纹。对于这两个雷诺数，所观察到的一致性通常是缓冲层中具有大能量的结构。结果表明，解析分析作为一种相关的降阶模型，适用于壁面湍流中相干结构，特别是与近壁面湍流涡旋和条纹相对应的流向细长结构。
Abstract Direct numerical simulations, performed with a high-order spectral-element method, are used to study coherent structures in turbulent pipe flow at friction Reynolds numbers $Re_{\tau } = 180$ and $550$. The database was analysed using spectral proper orthogonal decomposition (SPOD) to identify energetically dominant coherent structures, most of which turn out to be streaks and quasi-streamwise vortices. To understand how such structures can be modelled, the linear flow responses to harmonic forcing were computed using the singular value decomposition of the resolvent operator, using the mean field as a base flow. The SPOD and resolvent analysis were calculated for several combinations of frequencies and wavenumbers, allowing the mapping out of similarities between SPOD modes and optimal responses for a wide range of relevant scales in turbulent pipe flows. In order to explore physical reasons behind the agreement between both methods, an indicator of lift-up mechanism in the resolvent analysis was introduced, activated when optimal forcing is dominated by the wall-normal and azimuthal components, and associated response corresponds to streaks of streamwise velocity. Good agreement between leading SPOD and resolvent modes is observed in a large region of parameter space. In this region, a significant gain separation is found in resolvent analysis, which may be attributed to the strong amplification associated with the lift-up mechanism, here understood as nonlinear forcing terms leading to the appearance of streamwise vortices, which in turn form high-amplitude streaks. For both Reynolds numbers, the observed concordances were generally for structures with large energy in the buffer layer. The results highlight resolvent analysis as a pertinent reduced-order model for coherent structures in wall-bounded turbulence, particularly for streamwise elongated structures corresponding to near-wall streamwise vortices and streaks.