On the hydrodynamic stability of pulsatile flow in a plane channel

Abstract

A linear stability analysis is undertaken for plane pulsatile Poiseuille flow. The stability picture is described in terms of two distinct ranges of the Womersley number, Wo, which is the ratio of pulsatile to viscous forces. The low-frequency range, termed precritical, has dominant viscous effects, while the high-frequency range, termed postcritical, has dominant inertial effects. A critical Womersley number, Wocr=1.107, is identified, where viscous and inertial forces are in balance. In the precritical range, viscous forces become rapidly dominated by impulse forces, resulting in a sharp drop of the critical Reynolds number with increasing Wo. In the postcritical range, inertial forces become increasingly dominant over impulse forces, resulting in flow stabilization. In the limits Wo→0 and Wo→∞, the flow recovers the stability characteristics of the steady base flow, independently of the pressure amplitude. In other words, pulsating the flow is always destabilizing. The results reported in the postcritical range are in agreement with existing theoretical and experimental works.