Stability of Two-Layer Viscous Stratified Flow Down an Inclined Plane

Abstract

The stability of flow down an inclined plane is investigated for the case of a stratified fluid system consisting of two layers of viscous fluids of different densities. This problem is an extension of the works of Benjamin and Yih for a homogeneous fluid; thus their results are a special case of the solution for this more general problem. Reynolds numbers for the bifurcation point of the neutral curve are found for various ratios of density and depth of the two layers. For the purpose of comparing the relative stability between different configurations, a stability index is defined. It is found that the two‐layer flow is more stable or unstable than the homogeneous case of equal total depth, depending on whether the upper fluid is lighter or heavier than the lower one.