Linear stability theory of two-layer fluid flow in an inclined channel

Abstract

The linear stability of the two-layer flow of immiscible, incompressible fluids in an inclined channel is considered. In the long-wave limit, mechanisms for linear instability, and the consequences of competition between mechanisms, are identified. For arbitrary wave numbers, air–water and olive oil–water systems are considered, in order to determine the influence of the channel thickness and the mean interfacial height on the stability of the flow. This paper characterizes those physical situations in which the primary instability is to long-wave interfacial disturbances. The odd Orr–Sommerfeld shear mode within the water layer, which is necessarily stable in plane Poiseuille flow, is found to grow and even be the dominant mode of instability for the olive oil–water system. The consequences beyond linear stability are discussed.