Stability of a plane Poiseuille flow in a three-layered anisotropic porous-fluid channel

The modal and non-modal stability analysis of plane Poiseuille flow through a three-layer channel containing a centered anisotropic porous layer parallel to the channel walls is investigated. The channel is confined by solid impermeable walls and governed by the volume-averaged Navier-Stokes equation in the porous layer and the Navier-Stokes equation in fluid layers. At porous-fluid interfaces, continuity of stress and velocity is employed, while no-slip conditions are used at impermeable walls. A modal stability analysis is performed to comprehend the long-time flow transition characteristics. Note that the eigenvalue-based modal stability analysis only describes the asymptotic fate of the perturbation and thus fails to capture the short-term characteristics of the flow. In contrast, the non-modal stability analysis determines the perturbation response at a short time and the transient growth of the perturbations. The present study shows that the system parameters, such as porosity, anisotropic permeability, and porous layer thickness, significantly affect the long- and short-time stability characteristics of the flow that leads to energy growth. The present analysis provides a valuable means to control the flow instability of a multi-layer porous system having anisotropic permeability.