Linear wave interaction at the charged fluid-fluid interface under tangential discontinuity of the velocity field

Capillary wave flow in a two-layer fluid with the upper layer moving parallel to the charged interface at a constant velocity is treated within a linear mathematical model. Interaction between waves excited on the free surface of the upper layer and at the interface results not only in classical Kelvin-Helmholtz instability (at low velocities of the upper layer) but also in oscillatory instability of the interface. The instability increment depends on the fluid density ratio, translational velocity, and charge density at the interface.