This review discusses a recently developed optimization technique for analyzing the nonlinear stability of a flow state. It is based on a nonlinear extension of nonmodal analysis and, in its simplest form, consists of finding the disturbance to the flow state of a given amplitude that experiences the largest energy growth at a certain time later. When coupled with a search over the disturbance amplitude, this can reveal the disturbance of least amplitude—called the minimal seed—for transition to another state such as turbulence. The approach bridges the theoretical gap between (linear) nonmodal theory and the (nonlinear) dynamical systems approach to fluid flows by allowing one to explore phase space at a finite distance from the reference flow state. Various ongoing and potential applications of the technique are discussed.

中文翻译：

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非线性非模态稳定性理论

这篇综述讨论了最近开发的一种用于分析流动状态非线性稳定性的优化技术。它基于非模态分析的非线性扩展，并且以其最简单的形式包括找到对给定振幅的流动状态的扰动，该扰动在特定时间后经历最大的能量增长。当与对扰动幅度的搜索相结合时，这可以揭示最小幅度的扰动——称为最小种子——用于过渡到另一种状态，如湍流。该方法通过允许人们探索与参考流动状态有限距离处的相空间，弥合了（线性）非模态理论和（非线性）动力学系统方法之间的理论差距。讨论了该技术的各种正在进行和潜在的应用。