Recovery of the inherent dynamics of noise-driven amplifier flows
Recovery of the inherent dynamics of noise-driven amplifier flows
复制标题
恢复噪声驱动放大器流的固有动态
DOI：
10.1017/jfm.2016.266
复制
发表时间：
2016
影响因子：
3.7
通讯作者：
P. Schmid
中科院分区：
文献类型：
--
作者：
J. Inigo;D. Sipp;P. Schmid
噪声放大器流量的不稳定是由上游环境扰动驱动和维持的。使用在统计稳定状态下拍摄的快照执行动态模式分解提取出边际稳定的动态模式，其模拟持续的动态，但错过了这些流的实际内在稳定行为。在这项研究中，我们提出了一种替代的数据驱动技术，试图识别内在的线性稳定行为并将其与驱动项分开。该技术使用系统识别算法从时间相关的输入输出数据中提取流的简化状态空间模型。这样的模型可以根据上游传感器的测量准确预测速度场（输出）的值，该传感器捕获传入扰动（输入）的影响。该方法在受 Tollmien-Schlichting 不稳定性影响的二维边界层上进行说明，这是流动充当噪声放大器的典型示例。所识别模型的谱与文献中报道的全阶系统的结果非常吻合。然而，由于噪声放大器流中特征值谱的鲁棒性较差，这种比较似乎只是定性的。因此，我们提倡使用上游传感器和流动动力学之间的频率响应，这被证明是一个稳健的量。频率响应针对全阶计算进行了验证，并与局部空间稳定性分析进行了很好的比较。
Unsteadiness in noise amplifier flows is driven and sustained by upstream environmental perturbations. A dynamic mode decomposition performed with snapshots taken in the statistically steady state extracts marginally stable dynamic modes, which mimic the sustained dynamics but miss the actual intrinsic stable behaviour of these flows. In this study, we present an alternative data-driven technique which attempts to identify and separate the intrinsic linear stable behaviour from the driving term. This technique uses a system-identification algorithm to extract a reduced state-space model of the flow from time-dependent input–output data. Such a model accurately predicts the values of the velocity field (output) from measurements of an upstream sensor that captures the effect of the incoming perturbations (input). The methodology is illustrated on a two-dimensional boundary layer subject to Tollmien–Schlichting instabilities, a canonical example of flow acting as a noise amplifier. The spectrum of the identified model compares well with the results reported in literature for the full-order system. Yet the comparison appears to be only qualitative, due to the poor robustness properties of eigenvalue spectra in noise-amplifier flows. We therefore advocate the use of the frequency response between the upstream sensor and the flow dynamics, which is revealed to be a robust quantity. The frequency response is validated against full-order computations and compares well with a local spatial stability analysis.