The Third-order Progressive Wave So-Lutions In The Lagrangian Description For Interfacial Waves In Three-layer Density-stratified Fluids

Interfacial waves widely exist in the ocean interior,and it is usually studied with a two-layer density-stratified model.However,there are usually multi-layer in the real ocean.In order to understand the state of water movement under complex multi-layer conditions,it is necessary to study the interfacial waves in multi-layer density-stratified fluid systems.Investigation on the motion of the interfacial wave can deepen understanding of the pattern of the internal waters motion of the oceans in multi-layer fluids,and it also is a very important guiding significance in the underwater navigation,disaster prediction,marine engineering,marine military and other disciplines.On the one hand,the study of the interfacial waves in three-layer density-stratified fluid system can generalize the research of the traditional three-layer density-stratified fluid system;on the other hand,it can lay the foundation for studying the more complex multi-layer density-stratified layer system.So,it is extremely essential for the study of interfacial waves in three-layer density-stratified fluid.In this paper,by the perturbation method,the interfacial wave in three-layer density-stratified fluids are studied in Lagrangian description.On the condition of the upper free surface and the upper rigid boundary,the third-order asymptotic solution of the velocity potential in each layer fluid?the third-order wave solution of the interfacial waves?the mass transport velocity?wave frequency?Lagrangian mean level of the particle and the particle trajectory are given in no current,respectively.The results shown that the discontinuitise at the interfaces appear for the mass transport velocity,wave frequency,Lagrangian mean leve of the particle and the particle trajectory.But when the boundary is rigid,the discontinuitise may disappear if the water depth ratio and the density ratio of the three layer fluids satisfy certain conditions.Finally,the research is extended to that which is in the uniform current,and the same result is obtained.