Instabilities caused by oscillating accelerations normal to a viscous fluid-fluid interface

The case of two incompressible viscous fluids (with different densities) which meet at a planar interface and are subject to an externally imposed oscillating acceleration directed normal to the interface is studied. The linear evolution of perturbations to the basic-state flow is investigated. It is found that the critical Stokes-Reynolds number and the most unstable perturbation wavelengths are insensitive to the degree of density and viscosity differences between the two fluids.