Instability of a plane Poiseuille flow bounded between inhomogeneous anisotropic porous layers

The linear stability analysis of a plane Poiseuille flow in a channel with anisotropic and inhomogeneous porous layers is performed. The generalized Darcy equation, along with the Navier-Stokes equation, governs the flow in the porous-fluid-porous channel. The Beaver-Joseph interface condition is assumed, which considers the coupling between the flows in the porous and fluid layers. The spectral collocation method is employed to solve the Orr-Sommerfeld type eigenvalue problem for the amplitude of the disturbances of arbitrary wavenumbers. The effect of anisotropy and inhomogeneous permeability on the stability characteristics is addressed in detail. The stability characteristics of the anisotropy parameter (the ratio of permeability in the streamwise and the transverse direction) and the inhomogeneity function are presented in detail.