Abstract
This paper describes the third-order solution for the nonlinear internal and surface progressive water wave in a two-layer fluid. We use the perturbation method to develop a mathematical derivation. In the previous studies, the second- and third-order solutions derived by Umeyama (2002) and Song (2004) can not satisfy the boundary conditions. The present third-order asymptotic solution which satisfies the governing equation and boundary conditions is obtained. The numerical results demonstrate the influence of the ratio density and thickness of the two fluids on the interfacial and surface profiles as well as the wave frequency. The wave elevations at the free surface and the interface are calculated in different wave conditions under the thicknesses and densities ratio between the upper and lower layers in two-layer fluids. This simple theoretical solution can be used to analyze the different dynamic mechanisms between a interfacial wave induced by the given surface wave (IWSW) and a surface wave induced by the given interfacial wave (SWIW). The effect of on the wave height of SWIW is shown in Fig1. The height of SWIW is directly proportional to . However, the effect of on the wave height of IWSW is opposite. The height of SWIW and are in inverse proportion relation (see Fig. 2).
Highlights
We consider a two-layer fluid system in which the flow motion is irrotational and the fluids are homogeneous incompressible, inviscid of different density
The origin of the axes will be located in the undisturbed interface; the subscript I and II denote the upper layer and the lower layer
We have shown a way to by which the different dynamic mechanism between IWSW and SWIW can be described in general
Summary
We consider a two-layer fluid system in which the flow motion is irrotational and the fluids are homogeneous incompressible, inviscid of different density. Shows a two-layer fluid system that is stably stratified. The origin of the axes will be located in the undisturbed interface; the subscript I and II denote the upper layer and the lower layer. I and t ) denote hI , and those of the lower layer are velocity potentials in the upper and LII lower layers, so that they satisfying the continuity equation lead to the Laplace equations as follows:. The wave motion described above has to satisfy the boundary conditions at the bottom, density interface and free surface, respectively. On an immovable and impermeable uniform bottom, the no-flux bottom boundary condition gives IIy 0, at y hII
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
