The dynamics of an oscillating shear layer when confined is enriched by retarded actions whose physical modeling is not trivial. We present a nonlinear delayed saturation feedback model, which allows us to correctly reproduce the complex shear layer spectra observed experimentally in open cavity flows in the incompressible limit. The model describes the evolution of the amplitude of the shear layer instabilities and considers two hydrodynamic feedback mechanisms directly related to the confinement introduced by the walls. One is associated with reflections of instability waves on the vertical cavity walls and the other to intracavity recirculation flow. These feedback mechanisms provide retarded actions with time lags that are used in the delay differential equation and allow the computation of the model parameters on physical grounds. The frequency components of six experimental cases in different flow regimes are well recovered by the dynamical model. The results show that the model with a single feedback mechanism produces monoperiodic oscillations of the amplitude, while the interplay of two purely hydrodynamic feedback mechanisms allow quasiperiodicity to develop.

中文翻译：

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不可压缩开孔流动的非线性延迟反馈模型

局限性时，振荡剪切层的动力学特性会因其物理建模并非无关紧要的延迟动作而变得更加丰富。我们提出了一个非线性延迟饱和反馈模型，该模型可以让我们正确地再现在不可压缩极限的开腔流中实验观察到的复杂剪切层谱。该模型描述了剪切层不稳定性幅度的演变，并考虑了两种与壁引入的约束直接相关的流体动力反馈机制。一种与垂直腔壁上不稳定波的反射相关，另一种与腔内再循环流相关。这些反馈机制为延迟微分方程提供了具有时滞的延迟动作，并允许基于物理理由计算模型参数。通过动力学模型可以很好地恢复六个实验案例在不同流态下的频率分量。结果表明，具有单个反馈机制的模型会产生振幅的单周期振荡，而两个纯流体动力反馈机制的相互作用使得准周期性得以发展。