In shock wave/boundary layer interactions, two mechanisms have been recognized to drive the low-frequency unsteadiness of the reflected shock: upstream boundary layer forcing and downstream feedback. The current work presents a quantitative analysis of the causal mechanisms underlying such flow unsteadiness. The analysis is based on a large-eddy simulation database covering approximately 300 cycles of the low-frequency shock fluctuations in a Mach 2 turbulent boundary layer. This time span enables the accurate application of frequency-domain system identification methods targeting such low frequencies. The evaluation of the spectrum in the interaction zone indicates that the broadband low-frequency unsteadiness is predominantly two-dimensional and can be isolated via spanwise averaging. Empirically derived transfer functions are computed using the averaged flow field and indicate the occurrence of a feedback between the locations downstream of the flow separation and the shock fluctuations. The results indicate that this mechanism dominates over the upstream forcing of the interaction region. Accordingly, the computed transfer functions are also used as an estimation tool to predict the shock motion accurately; for the largest streamwise separation between input and output signals, correlations above 0.6 are observed between predictions and raw data. Computation of spectral proper orthogonal decomposition modes reveals the existence of upstream traveling waves in the leading spectral mode at the main shock frequency; higher frequencies do not exhibit this trend. Furthermore, the spectral modes obtained using selected flow regions downstream of the shock enable the reconstruction of a significant portion of the energy in the interaction zone. Finally, a linear stability analysis is conducted using the mean turbulent flow, showing the existence of upstream traveling waves. Evaluation of a vortex sheet model indicates that these upstream traveling modes are of acoustic nature. The predicted modes from this local analysis present a compelling match against the spectral modes, both in terms of the shape and phase speed of the fluctuations. The combined analysis of the techniques indicates that downstream disturbances are the dominant cause of shock oscillations in the present configuration, leading to shock motion by upstream traveling acoustic modes.

中文翻译：

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冲击波/湍流边界层相互作用的因果关系

在冲击波/边界层相互作用中，已经认识到有两种机制可以驱动反射冲击的低频不稳定：上游边界层强迫和下游反馈。当前的工作对这种流动不稳定的因果机制进行了定量分析。该分析基于一个大涡模拟数据库，该数据库涵盖了 2 马赫湍流边界层中大约 300 个低频冲击波动周期。该时间跨度能够准确应用针对此类低频的频域系统识别方法。对相互作用区频谱的评估表明，宽带低频不稳定主要是二维的，可以通过展向平均来隔离。使用平均流场计算经验导出的传递函数，并指示流动分离下游位置和冲击波动之间反馈的发生。结果表明，这种机制支配了相互作用区域的上游强迫。因此，计算出的传递函数也被用作估计工具来准确预测冲击运动；对于输入和输出信号之间的最大流向分离，在预测和原始数据之间观察到高于 0.6 的相关性。谱固有正交分解模态计算揭示了在主激波频率的超前谱模态中存在上游行波；更高的频率没有表现出这种趋势。此外，使用激波下游的选定流动区域获得的频谱模式能够重建相互作用区中的大部分能量。最后，使用平均湍流进行线性稳定性分析，显示上游行波的存在。涡流片模型的评估表明这些上游行进模式具有声学性质。这种局部分析的预测模式与光谱模式在波动的形状和相位速度方面呈现出令人信服的匹配。对这些技术的综合分析表明，下游扰动是当前配置中激波振荡的主要原因，导致上游行进声模式引起激波运动。