High-order Boussinesq Equations Of The Strong Nonlinear Waves In Shear Flows

Because of the factors such as the wind and the water body self movement, waves are formed on the surface of the sea and lakes, and at the same time, the density stratified phenomenon also occurs in the sea and lakes. This phenomenon is extremely common and very complex in the real ocean, and is usually the density continuous stratification. In order to more accurately describe the motion law in the water body, it is necessary to explore the interfacial waves in multi-layer density stratified fluids. Investigation on them is not only helpful for us to explain the various phenomena of the interfacial waves, but also has important directive significance to the study of the internal factors in the ocean and the environmental and climatic change, and the development of ocean engineering, military affairs and so on. The research of surface waves on the single-layer fluid and interfacial internal waves in two-layer density stratified fluids may play an important role in the investigation of interfacial waves in density continuous stratified fluids, so the study on them has fundamental significance.In this thesis, based on the ratio of characteristic water depth to the characteristic water length, the single-layer fluid system and the two-layer density stratified fluid system with uniform shear flows are discussed, which are inviscid and incompressible. With the method similar to Nwogu’s, the strong nonlinear surface waves on the single-layer fluid and the strong nonlinear interfacial internal waves in two-layer density stratified fluids are investigated under uniform shear flows by using the velocities at arbitrary depths as the velocity variables. Finally, the forth-order Boussinesq equations are derived for the surface waves and the interfacial internal waves.