Nonlinear progressive internal gravity wave on fluid of trapezoidal bottom

In the present paper we discuss a theoretical model for the interfacial profiles of progressive nonlinear waves which result from introducing a trapezoidal obstacle, of finite height, attached to the bottom below the flow of a stratified, ideal, two layer fluid, bounded from above by a rigid boundary. Assuming a very large horizontal length compared with the vertical height allows us to apply the shallow-water approximation theory, and, consequently, a nonlinear perturbation method is presented to construct per power series the analytical solution for the interfacial profiles of the progressive waves. The dependence of the interfacial profile on the trapezoidal obstacle size, as well as its dependence on some flow parameters, such as the ratios of depths and densities of the two fluids, have been studied and illustrated.