Instability and transition in an elementary porous medium are investigated via global linear stability analysis and numerical simulation. The porous medium is presented by a representative elementary volume (REV) which consists of a staggered array of square cylinders. The stability analysis indicates the first critical Reynolds number at Re cr 84. Two unstable modes are captured from the linear stability analysis: a two-dimensional oscillatory mode and a three-dimensional stationary mode. A series of analyses based on direct and adjoint methods is conducted on both the unstable modes. The energy analysis shows that lift-up and converging flow effects are both responsible for the unstable modes. In the numerical simulation, the averaged fluctuation profiles exhibit similar spatial distributions as the perturbation kinetic energy from the three-dimensional mode, which confirms the prediction from the stability analysis. In addition, we observe stationary counter-rotating streamwise vortices since subcritical Reynolds number, which is a consequence of lift-up instability.

中文翻译：

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基本多孔介质中的不稳定性和转变

通过整体线性稳定性分析和数值模拟研究了基本多孔介质中的不稳定性和跃迁。多孔介质由代表性基本体积（REV）表示，该基本体积由方形圆柱体的交错阵列组成。稳定性分析表明在Re cr 84处的第一个临界雷诺数。线性稳定性分析中捕获了两个不稳定模式：二维振荡模式和三维平稳模式。对两种不稳定模式都进行了一系列基于直接和伴随方法的分析。能量分析表明，升力和汇流效应都是造成不稳定模式的原因。在数值模拟中 平均波动分布表现出与三维模式扰动动能相似的空间分布，这证实了稳定性分析的预测。此外，由于亚临界雷诺数，我们观察到静止的逆流向旋涡，这是提升不稳定性的结果。