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arXiv 2602.09137physics.flu-dynmath.APmath.DSmath.OC
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从斜波强迫到涡旋强化：一种基于扰动的频域响应框架

From oblique-wave forcing to streak reinforcement: A perturbation-based frequency-response framework

University of Southern California（南加州大学）；University of Minnesota（明尼苏达大学）

Dušan Božić, Anubhav Dwivedi, Mihailo R. Jovanović

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39 pages, 30 figures
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AI总结：

本文提出一种基于扰动的频域响应框架，分析亚临界过渡中湍流放大机制，揭示斜波强迫通过升力机制生成涡旋，并探讨非模放大、涡旋生成与模不稳定性之间的统一描述。

摘要：

我们开发了一种基于扰动的频域响应框架，用于分析亚临界过渡中壁耦合剪切流中放大机制的核心。通过系统地将扰动关于强迫幅度展开，建立线性共振分析与高阶非线性相互作用之间的严格对应关系。在二次项中，不稳斜波的二次相互作用通过升力机制生成稳定的流体涡旋。我们证明这些涡旋的空间结构由流体方向常数共振算子的第二个输出奇异函数捕获。在更高阶次中，斜波与诱导涡旋之间的非线性耦合作为结构化强迫作用于层流线性化动力学，产生额外涡旋成分，其相对相位决定主导阶涡旋响应的增强或衰减。我们的分析识别出一个临界强迫幅度，标志着弱非线性区域的崩溃，此后直接数值模拟显示持续的不稳定性。我们证明这种崩溃与二次不稳定性 onset 相吻合，揭示了驱动涡旋生成的非线性相互作用也驱动经典过渡理论中的模增长。所得到的框架提供了机制透明且计算高效的过渡描述，将非模放大、涡旋生成和模不稳定性统一在由纳维-斯托克斯方程直接推导的单一公式中。

英文摘要：

We develop a perturbation-based frequency-response framework for analyzing amplification mechanisms that are central to subcritical routes to transition in wall-bounded shear flows. By systematically expanding the input-output dynamics of fluctuations about the laminar base flow with respect to forcing amplitude, we establish a rigorous correspondence between linear resolvent analysis and higher-order nonlinear interactions. At second order, quadratic interactions of unsteady oblique waves generate steady streamwise streaks via the lift-up mechanism. We demonstrate that the spatial structure of these streaks is captured by the second output singular function of the streamwise-constant resolvent operator. At higher orders, nonlinear coupling between oblique waves and induced streaks acts as structured forcing of the laminar linearized dynamics, yielding additional streak components whose relative phase governs reinforcement or attenuation of the leading-order streak response. Our analysis identifies a critical forcing amplitude marking the breakdown of the weakly nonlinear regime, beyond which direct numerical simulations exhibit sustained unsteadiness. We show that this breakdown coincides with the onset of secondary instability, revealing that the nonlinear interactions responsible for streak formation also drive the modal growth central to classical transition theory. The resulting framework provides a mechanistically transparent and computationally efficient description of transition that unifies non-modal amplification, streak formation, and modal instability within a single formulation derived directly from the Navier-Stokes equations.

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