Abstract
The stability of the interface between two viscous fluids is considered when the depth of the lower fluid is much less than the depth of the upper fluid. A long wavelength perturbation scheme is used to solve the linear stability problem and the equation governing the nonlinear evolution of the interface is deduced. The exact dispersion relation is derived for arbitrary values of wavelength and then simplified for large wavelength values. It is found that the flow is always linearly unstable when the lower fluid is also the more viscous fluid.