The convective nature of instability in plane Poiseuille flow

Abstract

By numerical solution of the Orr–Sommerfeld equation for complex frequency and complex wavenumber for a wide range of Reynolds numbers R and by asymptotic analysis for large R, it is shown that there is no absolute instability in a two-dimensional plane Poiseuille flow for any R and that the flow is convectively unstable for Rc <R<∞, where Rc is the critical Reynolds number.