A Ginzburg-Landau model for linear global modes in open shear flows
A Ginzburg-Landau model for linear global modes in open shear flows
复制标题
开放剪切流中线性全局模态的 Ginzburg-Landau 模型
DOI：
10.1017/jfm.2020.691
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发表时间：
2020
影响因子：
3.7
通讯作者：
Li Larry K. B.
中科院分区：
文献类型：
--
作者：
Gupta Vikrant;He Wei;Wan Minping;Chen Shiyi;Li Larry K. B.
金兹堡-朗道方程 (GLE) 可以对非平衡系统（包括流体力学中的系统）的几个关键特征进行现象学建模。然而，它在实际流量中的有效性仍然值得怀疑。在这里，我们证明线性 GLE 可以被公式化，使其具有与开放剪切流中的线性全局稳定性问题相同的 Wentzel-Kramers-Brillouin (WKB) 近似。我们使用 GLE 对三种不同尾流的线性全局模式进行建模，发现它可以准确捕获 WKB 近似中的一阶线性增长率和频率。此外，我们发现它还可以提供直接特征向量和伴随特征向量的形状以及最大结构敏感性区域。所提出的模型仅需要基本流程作为输入，但可以提供稳健的预测并且计算成本低廉。除了为基于 GLE 的控制策略开辟新的可能性之外，所提出的模型还使得精确的稳定性计算成为可能，即使对于一些计算上难以处理的开放剪切流也是如此。
The Ginzburg–Landau equation (GLE) can phenomenologically model several key features of non-equilibrium systems including those in fluid mechanics. Its validity in real flows, however, remains questionable. Here, we show that the linear GLE can be formulated such that it has the same Wentzel–Kramers–Brillouin (WKB) approximation as for the linear global stability problem in open shear flows. We use the GLE to model the linear global modes of three different wakes and find that it can accurately capture the linear growth rate and frequency to first order in the WKB approximation. Furthermore, we find that it can also provide the shapes of the direct and adjoint eigenvectors and the regions of maximal structural sensitivity. The proposed model requires only the basic flow as input, but gives robust predictions and is computationally inexpensive. As well as opening up new possibilities for GLE-based control strategies, the proposed model makes accurate stability calculations possible, even for some computationally intractable open shear flows.