This paper deals theoretically with the problem of the hydrodynamic stability of a stratified flow of a viscous fluid. The primary flow consists of two laminar streams of viscous fluids of different densities flowing in opposite directions between two parallel inclined planes under the action of gravity. The effect of surface tension at the interface of the two fluids is included in the formulation of the problem.

Since instability can be expected to occur at low Reynolds numbers when the inclination is nearly vertical, the solution of the Orr–Sommerfeld equations is developed as a power series in the transverse space co-ordinate. It is shown that for the vertical case, the flow is unstable for all values of the Reynolds number. Surface tension is found to influence both the direction and celerity of the disturbance. Results are also given for inclinations slightly away from the vertical, where small critical Reynolds numbers do exist.