Linear stability analysis of Poiseuille flow in a rectangular duct

Abstract

A laminar flow of a viscous incompressible fluid with a constant pressure gradient (Poiseuille flow) is considered in a rectangular duct for different values of cross-sectional aspect ratio. A new method, significantly more efficient than the known ones, is proposed and justified for computing the critical Reynolds number of such a flow. The dependence of the critical Reynolds number on the cross-sectional aspect ratio is numerically studied. A theoretical justification of the obtained dependence is proposed