The role of the critical layer in the stability of viscous shear flow

Abstract

The critical layer affects the stability of a variety of shear flows at the lowest order. This article studies the influence of the critical layer in boundary layers and in the parallel flow of miscible fluids, and concludes that the convective as well as the viscous terms of the Navier-Stokes equation can contribute towards the dominance of the critical layer. The result may be stabilizing or destabilizing depending on the balance between different terms in the stability equation.