We investigate the temporal stability analysis of a two-layer flow inside a channel that is driven by pressure. The channel consists of a fluid layer overlying an inhomogeneous and anisotropic porous layer. The flow contains a Couette component due to the movement of the horizontal impermeable upper and lower walls binding the two layers. These walls of the channel move at an identical speed but in opposite directions. The flow dynamics for the porous medium are modelled by the Darcy-Brinkman equations, and the Navier-Stokes equations are employed to describe the motion within the fluid layer. The hydrodynamic instability of infinitesimal disturbance is investigated using Orr-Sommerfeld analysis. The corresponding eigenvalue problem is derived and solved numerically using the Chebyshev polynomial-based spectral collocation method. Results reveal that stability features are strongly affected by the axial and spatial permeability variations of the porous medium. Further, the ratio of the depth of the fluid layer to the porous layer and the strength of the Couette component play a crucial role. The destabilization of the perturbed system is noticed by strengthening the Couette flow component. The combined impact of increasing the anisotropy parameter and depth ratio, decreasing Darcy number, and reducing the inhomogeneity factor stabilizes the system. This facilitates us to have greater control over the instability characteristics of such fluid-porous configuration by suitably adjusting various flow parameters. The outcome will be beneficial in relevant applications for enhancing or suppressing the instability of perturbation waves, as preferable.

中文翻译：

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Couette-Poiseuille 流的线性稳定性分析：覆盖各向异性和不均匀多孔层的流体层


我们研究了由压力驱动的通道内两层流的时间稳定性分析。该通道由覆盖不均匀且各向异性多孔层的流体层组成。由于结合两层的水平不可渗透的上壁和下壁的运动，该流包含库埃特分量。这些通道壁以相同的速度但方向相反地移动。多孔介质的流动动力学通过 Darcy-Brinkman 方程进行建模，并采用 Navier-Stokes 方程来描述流体层内的运动。使用奥尔-索末菲分析研究了无穷小扰动的水动力不稳定性。使用基于切比雪夫多项式的谱配置方法导出并数值求解相应的特征值问题。结果表明，稳定性特征受到多孔介质的轴向和空间渗透率变化的强烈影响。此外，流体层与多孔层的深度之比以及库埃特组件的强度起着至关重要的作用。通过加强库埃特流分量可以注意到扰动系统的不稳定。增加各向异性参数和深度比、降低达西数以及降低不均匀因子的综合影响使系统稳定。这有助于我们通过适当调整各种流动参数来更好地控制这种流体多孔结构的不稳定性特征。该结果将有益于增强或抑制扰动波不稳定性的相关应用（如优选）。