The Third-order Standing Wave Solutions In Eulerian Description For Interfacial Waves In Three-layer Density-stratified Fluids

The interfacial wave is the fluctuation occurring at the interface between different density fluid,and it is more common in the oceans and lakes,for example,the stormy waves formed by the wind blowing through the water surfaces,the ship's waves caused by a ship running in the water,the tsunamis occurred during an underwater earthquake and so on are all interfacial waves.The study for interfacial waves can not only discover its mechanism of formation and evolution,but also has important guiding significance to the investigation for the general internal waves in oceans and lakes.The interfacial waves are divided into the progressiving wave and the standing wave.At present,there are many research achievements for the interfacial progressive waves at the interfaces of multilayer density-stratified fluids,but the interfacial standing waves in the density-stratified fluids are usually investigated with two layer density-stratified fluid model.So it is necessary to study the interfacial standing waves for multilayer density stratified fluid.In this thesis,the interfacial standing waves for three layer density stratified fluids are discussed based on the small amplitude wave theory.Suppose that the fluids are irrotational,inviscid and incompressible,and that the bottom is rigid boundary.By using the perturbation expansion method,the velocity potentials for each layer and the third-order standing wave solutions of interfacial waves are given for the upper rigid boundary condition and the upper free surface condition,respectively.It is noted that the first-order asymptotic solutions are linear wave solutions,and the second-order asymptotic solutions are determined by the first-order asymptotic solutions,the second-order nonlinear modification and the second-order nonlinear interactions between the interfacial waves,and the third-order asymptotic solutions are composed by the first-order asymptotic solutions,the second-order asymptotic solutions,the third-order nonlinear modification and the third-order nonlinear interactions between the interfacial waves,and the first-order solutions,the second-order solutions and third-order solutions are all dependent on the depth and the density of each layer.