A framework for input-output analysis of wall-bounded shear flows
A framework for input-output analysis of wall-bounded shear flows
复制标题
壁面剪切流输入输出分析框架
DOI：
10.1017/jfm.2019.418
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发表时间：
2019
影响因子：
3.7
通讯作者：
Ahmadi M
中科院分区：
文献类型：
--
作者：
Ahmadi M
我们提出了一个新的框架来评估输入输出放大特性的非线性模型的壁有界剪切流，受到平方可积和持续扰动。我们专注于在一个方向上的空间不变的流量，其基流可以描述的多项式，如流向恒定的通道，库埃特和管流。我们的方法是基于控制理论中的耗散不等式的概念，并提供了一个统一的方法来检查流的性能，如能量增长，最坏情况下的扰动放大和稳定的持续激励（即输入到状态的稳定性）。它也使直接分析的非线性偏微分方程，而不是离散形式的方程，从而消除截断误差的可能性。我们演示了如何数值计算的输入-输出特性的流（凸）优化问题的解决方案。我们应用我们的理论和计算工具，平面库埃特，渠道和管道流动。我们的研究结果表明，所提出的框架导致的结果是一致的，在文献中获得的理论和实验放大缩放。
We propose a new framework to evaluate input–output amplification properties of nonlinear models of wall-bounded shear flows, subject to both square integrable and persistent disturbances. We focus on flows that are spatially invariant in one direction and whose base flow can be described by a polynomial, e.g. streamwise-constant channel, Couette and pipe flows. Our methodology is based on the notion of dissipation inequalities in control theory and provides a single unified approach for examining flow properties such as energy growth, worst-case disturbance amplification and stability to persistent excitations (i.e. input-to-state stability). It also enables direct analysis of the nonlinear partial differential equation rather than of a discretized form of the equations, thereby removing the possibility of truncation errors. We demonstrate how to numerically compute the input–output properties of the flow as the solution of a (convex) optimization problem. We apply our theoretical and computational tools to plane Couette, channel and pipe flows. Our results demonstrate that the proposed framework leads to results that are consistent with theoretical and experimental amplification scalings obtained in the literature.