Dynamic behavior of an internal solitary wave oscillating over variable bathymetry

This study analyzes the interfacial wave motion of a stratified two-layer fluid in a three-dimension domain. The proposed analytical solution considers the relationship between nonlinearity and frequency dispersion, but ignores viscous effects. The governing equations based on the Navier-Stokes equations are formed to simulate internal solitary wave (ISW) propagation over a variable seabed. In addition to numerical results, theoretical formulations are established to obtain analytical solutions. Numerical results indicate that at a given ratio of the height of a submarine ridge and the lower layer thickness, a depression-type ISW would generate a larger trailing oscillation than an elevation-type ISW. An elevation-type ISW is apparently evolved, while a depression-type ISW propagates on a trapezoidal shelf in a depth ratio, where the upper layer is thicker than the lower layer