Nonlinear analysis of interaction between finite-amplitude capillary waves in a layered inhomogeneous liquid

The nonlinear capillary wave motion in a two-layer liquid with a free surface is analytically investigated accurate to the second order of smallness in ratio of the wave amplitude to the layer thickness. The layers differ in physicochemical properties. A capillary analogue to the “dead water” effect is observed in the system in both linear and quadratic approximations. In the absence of an electric charge at the interfaces, internal nonlinear resonance interaction between capillary waves is also absent regardless of the place of their origination. When there is a charge at the interlayer boundary, capillary waves resonantly interact with each other.