Investigation of stability of a laminar flow in a parallel-plate channel filled with a fluid saturated porous medium

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Instability of a laminar flow in a parallel-plate channel filled with a fluid saturated porous medium is investigated on the basis of a modified Orr-Sommerfeld equation. This equation takes into account three drag terms: the Darcy term that describes friction between the fluid and the porous matrix, the Forchheimer quadratic drag term that describes a form drag due to the solid obstacles, and the Brinkman term, which is a viscous term similar to the Laplacian term in the Navier-Stokes equations. Numerical analysis is carried out using the collocation method. The dependence of the critical Reynolds number on porosity and permeability of the porous medium is analyzed numerically.