Internal periodic waves in fluids with exponential density distribution along depth

Abstract

This paper aims to investigate internal waves of permanent form in fluids of infinite depth and with exponential density distribution along depth. The Dubreil-Jacotin-Long transformation is adopted to deduce the governing equations and boundary conditions of the internal wave motion. Homotopy analysis method is used to solve this problem. Dispersion relation between the phase velocity and wave-number k at a given wave height is achieved. Furthermore, the relation between dispersion and wave height over exponential distribution factor is also obtained by homotopy-Padé approximation. Results show that the phase velocity depends much on the exponential distribution factor, while the wave height makes very little difference. With regard to the periodic wave forms, strong deformation occurs near the bottom and there the trough of the internal waves tends to be flattened, especially when the wave height is large. Dynamic pressure and velocity field of the fluid are also investigated at the end of the paper.