The role of density discontinuity in the inviscid instability of two-phase parallel flows

Abstract

We re-examine the inviscid instability of two-phase parallel flows with piecewise linear velocity profiles. Although such configuration has been theoretically investigated, we employ the concept ofwaves resonance to physically interpret the instability mechanism as well as the essential role of density discontinuity in the flow. Upon performing linear stability analysis, we demonstrate the existence of neutrally stable "density" and "density-vorticity" waves which are emerged due to the density jump in the flow, in addition to the well-known vorticity waves. Such waves are capable of resonating with each other to form unstable modes in the flow. Although unstable modes in this study are classified as the "shear instability" type, we demonstrate that they are not necessarily of theRayleigh type. The results also showthat the density can have both stabilizing and destabilizing effects on the flow stability.We verify that the difference in the resonating pair of neutral waves leads to such distinct behavior of the density variation. © 2014 AIP Publishing LLC.