Dynamics of nonlinear three-dimensionalwaves on the interface between two fluids in a channel with low-sloping bottom and top

A combined approach is proposed to describe the transformation of three-dimensional disturbances of the interface between two incompressible immiscible fluids of different densities contained in a channel with fixed rigid top and bottom. It is assumed that the wavelengths are moderately large, the amplitudes are small but finite, the top and the bottom can be gently sloping, and capillary effects are small. The system of equations derived is applicable for modeling disturbances simultaneously scattering in arbitrary horizontal directions. Some typical wave problems are numerically solved and the effect of governing parameters is shown.