The interaction between capillary waves near a charged liquid-liquid interface with a tangential discontinuity of the velocity field

Abstract

The evolution of capillary waves in a system of two liquid layers with a charged interface and the upper layer with a free surface and finite thickness translating at a constant velocity parallel to the semi-infinite lower layer is studied numerically within the framework of a linear mathematical model of capillary wave motion. The interacting waves generated at the free surface of the upper layer and at the interface give rise to an oscillatory instability of the interface, in addition to the Kelvin-Helmholtz instability. The new instability arises if the upper layer velocity is sufficiently small. The increment of oscillations depends on the density ratio of the liquids, velocity magnitude, and the charge at the interface.