标题： 关于Stokes层中的内循环不稳定性 显示英文标题

标题： On the intracyclic instability in Stokes layers

摘要： 时变流体动力学在自然现象和工业应用中起着至关重要的作用。理解这些动态系统内的流动不稳定性与转变对于预测和控制它们的非定常行为至关重要。时变流动的一个经典例子是斯托克斯层。为了研究该流动中的转变机制，我们采用了有限时间李雅普诺夫指数（FTLE）来展示线性能量放大机制可能解释过渡态斯托克斯层内的循环内不稳定性，并通过与轴向湍流强度实验测量结果的良好比较加以支持。这补充了文献中已有的应用于斯托克斯层的理论，包括弗洛凯分析和瞬时/瞬间分析，这些理论难以准确捕捉到这一实验观察结果。FTLE 分析与瞬态增长分析密切相关，后者被形式化为一个优化问题，即随着时间推移扰动能量的增长优化问题。我们发现，随着有限斯托克斯层变得更加受限，能量放大效应减弱，并且振荡频率对最大瞬态增长具有非单调影响。基于这些结果，我们建议未来的实验研究验证这一线性机制。 显示英文摘要

摘要： Time-dependent fluid dynamics plays a crucial role in both natural phenomena and industrial applications. Understanding the flow instabilities and transitions within these dynamical systems is essential for predicting and controlling their unsteady behaviour. A classic example of time-dependent flow is the Stokes layer. To study the transition mechanism in this flow, we employ the Finite-Time Lyapunov Exponent (FTLE) to demonstrate that a linear energy amplification mechanism may explain the intracyclic instability in the transitional Stokes layer, supported by favourable comparisons with experimental measurements of axial turbulence intensity. This complements existing theories applied to the Stokes layer in the literature, including the Floquet analysis and the instantaneous/momentary analyses, which have struggled to capture this experimental observation accurately. The FTLE analysis is closely related to the transient growth analysis, formulated as an optimisation problem of the disturbance energy growth over time. We found that the energy amplification weakens as the finite Stokes layer becomes more confined and the oscillating frequency has a non-monotonic effect on the maximum transient growth. Based on these results, we recommend future experimental studies to validate this linear mechanism.