识别驱动线性和非线性不稳定性的活动流区
Identifying the active flow regions that drive linear and nonlinear instabilities
摘要：
探索了一种分析不稳定振荡流的新框架。在线性设置中，非平行流中的时间增长扰动表示线性流算子的不稳定本征模。在非线性环境中，有限振幅的自维持周期振荡通常被描述为非线性全局模式。在这两种情况下，流动动力学可以被定性为内源性的，而不是由外部强迫驱动的放大器流的外源性行为。本文引入了内点概念，定义了整体频率和增长率对流算子变化的灵敏度。定义在线性和非线性环境中的内点，表征了局部流动区域对全局特征动力学的贡献。它以简单的方式计算为直接流动状态的时间导数与伴随模式之间的局部逐点内积。本研究演示了两个典型的例子，金斯堡-朗道方程和圆柱体的尾流，如何分析的基础上的endotraction可用于物理讨论的机制，驱动全球不稳定性。结果表明，与早期的“造波机”的定义在文献中发现是一致的，但目前的形式主义，使一个更详细的讨论：振荡频率和增长率之间有明确的区别，和个人的贡献，从各个方面的流动运营商可以被隔离和单独讨论。[截断]
英文摘要：
A new framework for the analysis of unstable oscillator flows is explored. In linear settings, temporally growing perturbations in a non-parallel flow represent unstable eigenmodes of the linear flow operator. In nonlinear settings, self-sustained periodic oscillations of finite amplitude are commonly described as nonlinear global modes. In both cases the flow dynamics may be qualified as being endogenous, as opposed to the exogenous behaviour of amplifier flows driven by external forcing. This paper introduces the endogeneity concept, a specific definition of the sensitivity of the global frequency and growth rate with respect to variations of the flow operator. The endogeneity, defined both in linear and nonlinear settings, characterizes the contribution of localized flow regions to the global eigendynamics. It is calculated in a simple manner as the local point-wise inner product between the time derivative of the direct flow state and an adjoint mode. This study demonstrates for two canonical examples, the Ginzburg-Landau equation and the wake of a circular cylinder, how an analysis based on the endogeneity may be used for a physical discussion of the mechanisms that drive a global instability. The results are shown to be consistent with earlier 'wavemaker' definitions found in the literature, but the present formalism enables a more detailed discussion: a clear distinction is made between oscillation frequency and growth rate, and individual contributions from the various terms of the flow operator can be isolated and separately discussed. [Truncated]
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