We study physical mechanisms that trigger transient growth in a high-speed spatially developing laminar boundary layer that interacts with an oblique shock wave. We utilize an approach based on power iteration, with the global forward and adjoint linearized equations, to quantify the transient growth in compressible boundary layers with flow separation. For a Mach 5.92 boundary layer with no oblique shock wave, we show that the dominant transient response consists of oblique waves, which arise from the inviscid Orr mechanism, the lift-up effect, and the first-mode instability. We also demonstrate that the presence of the oblique shock wave significantly increases transient growth over short time intervals through a mechanism that is not related to a slowly growing global instability. The resulting response takes the form of spanwise periodic streamwise elongated streaks, and our analysis of the linearized inviscid transport equations shows that base-flow deceleration near the reattachment location contributes to their amplification. The large transient growth of streamwise streaks demonstrates the importance of nonmodal effects in the amplification of flow perturbations and identifies a route for the emergence of similar spatial structures in transitional hypersonic flows with shock-wave/boundary-layer interactions.

中文翻译：

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斜冲击波/边界层相互作用在5.92马赫时的瞬态生长分析

我们研究触发与倾斜冲击波相互作用的高速空间发展层流边界层中瞬态增长的物理机制。我们利用基于功率迭代的方法，使用全局正向和伴随线性化方程，通过流动分离来量化可压缩边界层的瞬态增长。对于没有斜激波的马赫数5.92边界层，我们证明了主要的瞬态响应由斜波组成，斜波由不粘的Orr机理，升力效应和一阶不稳定性引起。我们还证明了倾斜冲击波的存在通过与缓慢增长的全球不稳定性无关的机制在短时间间隔内显着增加了瞬态增长。所得的响应采取展向方向周期性流向细长条纹的形式，并且我们对线性无粘性运输方程的分析表明，在重新连接位置附近的基流减速有助于其放大。流向条纹的大量瞬时增长证明了非模态效应在放大流动扰动中的重要性，并确定了在具有冲击波/边界层相互作用的过渡高超声速流动中出现类似空间结构的途径。