Linear stability analysis of Poiseuille flow in porous medium with small suction and injection

TL;DR

This paper analyzes how small suction and permeability influence the linear stability of Poiseuille flow in porous media, revealing stabilizing effects through a modified Orr-Sommerfeld framework.

Contribution

It introduces a modified Orr-Sommerfeld equation for porous media flow and highlights the importance of velocity normalization in stability analysis.

Findings

Small suction Reynolds number stabilizes flow.

Permeability parameter has a stabilizing effect.

Normalization of wall-normal velocity is crucial.

Abstract

We investigate the effect of small suction Reynolds number and permeability parameter on the stability of Poiseuille fluid flow in a porous medium between two parallel horizontal stationary porous plates . We have shown that the perturbed flow is governed by an equation named modified Orr-Sommerfeld equation. We find also that the normalization of the wall-normal velocity with characteristic small suction (or small injection) velocity is important for a perfect command of porous medium fluid flow stability analysis. The stabilizing effect of the parameters in general and small suction Reynolds number and permeability parameters in particular on the linear stability are found.