Surface tension effects an the nonlinear behavior of long waves in a two layer flow

The propagation of long waves of finite amplitude at the interface of two v iscous fluids in the presence of interfacial tension is examined. The effec t of capillarity on the shape of the waves at the interface of two superpos ed fluids is investigated for a wide range of density differences, viscosit y ratios and imposed pressure gradients. It is found that in planar geometr y surface tension stabilizes the interfacial disturbances. Attention is giv en to the case in which the upper fluid is more dense and comprises a thin film above the lower fluid. With the heavier fluid on the top the flow patt ern is always unstable when surface tension effects are neglected. In this case the interfacial waves do not grow forever and reach a finite amplitude only when the interfacial tension is greater than a critical value.