A Set Of Boussinesq-type Equations Of Interfacial Internal Waves In Threelayer Density-Stratified Fluids With The Shear Flow

In oceans, lakes and other water bodies, the density stratification is very common,and it is particularly complex and sometimes clearly multi-layered in the real oceans. The interfacial internal waves, which occur at the interfaces of the stable density stratified fluid systems, are not uncommon. In order to correctly describe the wave law in the ocean interior, it is necessary to investigate the interfacial internal waves in the multi-layer density stratified fluids. Investigation on interfacial internal waves has a very important meaning not only on many their own phenomena, but also has a directive significance for us to understand the functions for the internal mixing in oceans and the change of climate and environment, and the applications in the ocean engineering,military affairs and so on.In this thesis, based on the assumption of a small wave steepness and the inviscid and incompressible on the water mass, the three-layer density stratified fluid systems with the mean shear flows are considered. With the Nwogu’s methods, the strongly nonlinear interfacial internal waves in the three-layer density stratified fluid systems are studied. A set of Boussinesq-type equations of interfacial internal waves in the threelayer density-stratified fluids with the shear flows is given using the horizontal velocities component at arbitrary distances from the still water level as the velocity variables, and the nonlinear interactions between the interfacial internal waves and the shear flows are revealed. The main contents are as follows:In the introduction, the background and the meaning of studying the interfacial internal waves in the shear flows, the present research current situation and the main contents of this thesis are briefly summarized.In the first chapter, the basic equations and boundary conditions of the interfacial internal waves in the three-layer density stratified fluids with the mean shear flows are given, and the dimensionless for them is accomplished by using the Choi’s methods.In the second chapter, the depth-integration of the non-dimensional equations for three-layer fluids is carried on respectively, and a set of Boussinesq-type equations of the strongly nonlinear interfacial internal waves in the shear flows is obtained with the Nwogu’ method.In the third chapter, the summary of research results for this thesis is given, and the outlook for further work is pointed out.