We unravel the nonmodal stability of a three-dimensional nonstratified Poiseuille flow in a saturated hyperporous medium constrained by impermeable rigid parallel plates. The primary objective is to broaden the scope of previous studies that conducted modal stability analysis for two-dimensional disturbances. Here, we explore both temporal and spatial transient disturbance energy growths for three-dimensional disturbances when the Reynolds number and porosity of the material are high, based on evolution equations with respect to time and space, respectively. Modal stability analysis reveals that the critical Reynolds number for the onset of shear mode instability increases as porosity increases. Moreover, the Darcy viscous drag term stabilizes shear mode instability, resulting in a delay in the transition from laminar flow to turbulence. In addition, it demonstrates the suppression of three-dimensional shear mode instability as the spanwise wavenumber increases, thereby confirming the statement of Squire’s theorem. By contrast, nonmodal stability analysis discloses that both temporal and spatial transient disturbance energy growths curtail as the effect of the Darcy viscous drag force intensifies. But their maximum values behave like O(Re2) for a fixed porous material, where Re is the Reynolds number. However, for different porous materials, the scalings for both temporal and spatial transient disturbance energy growths are different. Furthermore, increasing porosity also suppresses both temporal and spatial disturbance energy growths. Finally, we observe that temporal transient disturbance energy growth becomes larger for a spanwise perturbation, while spatial transient disturbance energy growth becomes larger for a steady perturbation when angular frequency vanishes. The initial disturbance that excites the largest temporal energy amplification generates two sets of alternating high-speed and low-speed elongated streaks in the streamwise direction.

中文翻译：

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通过多孔介质的泊肃叶流的非模态稳定性分析


我们揭示了三维非分层泊赛叶流在受不渗透刚性平行板约束的饱和多孔介质中的非模态稳定性。主要目标是扩大以前对二维扰动进行模态稳定性分析的研究范围。在这里，我们分别基于关于时间和空间的演化方程，探讨了当材料的雷诺数和孔隙率较高时，三维扰动的时间和空间瞬态扰动能量增长。模态稳定性分析表明，剪切模式不稳定性的临界雷诺数随着孔隙率的增加而增加。此外，达西粘性阻力项稳定了剪切模式的不稳定性，导致从层流到湍流的过渡延迟。此外，它还证明了随着翼展波数的增加，三维剪切模式不稳定性的抑制，从而证实了 Squire 定理的陈述。相比之下，非模态稳定性分析表明，随着达西粘性阻力效应的增强，时间和空间瞬态干扰能量的增长都会减少。但它们的最大值与固定多孔材料的 O（Re2） 类似，其中 Re 是雷诺数。然而，对于不同的多孔材料，时间和空间瞬态干扰能量增长的尺度是不同的。此外，孔隙率的增加也会抑制时间和空间扰动能量的增长。最后，我们观察到，当角频率消失时，时间瞬态扰动能量增长会随着翼展方向的扰动而变大，而空间瞬态扰动能量的增长会随着稳定扰动的增加而变大。 激发最大时间能量放大的初始扰动在流向方向上产生两组交替的高速和低速拉长条纹。