Nonlinear internal wave at the interface of two-layer liquid due to a moving hydrofoil

This paper is concerned with the internal wave at the interface of two layers of liquids due to a hydrofoil in the lower layer liquid. The two-layer fluid is assumed moving parallel to the interface at different velocities. The stratified flow is modeled based on the incompressible potential flow theory, with the nonlinear boundary conditions at the interface. Boundary integral equations are formulated for the fully nonlinear interfacial wave generated by the hydrofoil. The numerical model results in a set of nonlinear algebra equations, which are solved using the quasi-Newton method. We show that the quasi-Newton method is more efficient than Newton’s method, which is often used for solving these types of equations in the literature. The wave profiles were analyzed in terms of the location and thickness of the hydrofoil, the Froude number, and the ratio of the densities of the two fluids. The computations show that the interfacial wave amplitude showed a trend first of increase and then of decrease with the distance between the hydrofoil and the still interface.