剪切流中三层密度分层流体界面内波的Boussinesq方程

发布时间：2019-01-15 21:21

【摘要】：在海洋、湖泊等水体中,密度成层现象非常普遍,真实海洋中密度成层现象尤其复杂,有时明显呈多层成层状态.发生在密度稳定分层流体界面处的界面内波在这些流体系统并不少见.为了正确描述海洋内部的运动规律,开展多层密度成层流体界面内波的研究非常必要.它的研究不仅对界面内波本身的很多现象有重要意义,而且还对人们了解界面内波在海洋内部混合和环境气候变化中的作用以及界面内波在海洋工程和海洋军事上的应用等方面具有指导意义.本文基于波陡很小的假设,考虑均匀剪切流场中不可压缩和无粘性的三层密度分层流体系统.采用类似于Nwogu的方法,讨论剪切流存在时三层密度分层流体系统中的强非线性界面内波,以任意水深处的水平速度分量为速度变量,给出了界面内波的Boussinesq方程,揭示了波流之间的非线性相互作用.主要内容如下:绪论,简要概述了剪切流中界面内波的研究意义和背景,目前的研究现状和本文的主要研究内容.第一章,给出剪切流中三层密度分层流体界面内波的基本方程以及边界条件,并且利用Choi的方法对其进行无量纲化.第二章,分别对三层流体所满足的无量纲化方程进行深度积分,采用Nwogu的方法得到剪切流中强非线性界面内波所满足的Boussinesq方程.第三章,总结本文的研究结果,并提出进一步的研究工作展望.
[Abstract]:The phenomenon of density stratification is very common in the ocean, lake and other water bodies, but the phenomenon of density stratification in the real ocean is especially complicated, and sometimes it appears to be multilayered. Interfacial waves occurring at the interface of density-stable stratified fluids are not uncommon in these fluid systems. In order to describe the law of ocean motion correctly, it is necessary to study the interfacial wave of multi-layer density stratified fluid. Its research is not only of great significance to many phenomena of interfacial internal waves, It is also helpful to understand the role of interfacial internal waves in ocean internal mixing and environmental climate change, as well as the application of interfacial internal waves in ocean engineering and marine military affairs. Based on the assumption that the wave steepness is very small, the incompressible and viscidity stratified fluid system with incompressible and non-viscous density in the uniform shear flow field is considered in this paper. By using a method similar to Nwogu, the strongly nonlinear interfacial internal waves in a three-layer density stratified fluid system in the presence of shear flow are discussed. The Boussinesq equation of the interfacial internal wave is given with the horizontal velocity component of any depth of water as the velocity variable. The nonlinear interaction between waves and currents is revealed. The main contents are as follows: introduction, the research significance and background of interfacial internal waves in shear flow, the current research situation and the main research contents of this paper are briefly summarized. In the first chapter, the basic equations and boundary conditions of interfacial internal waves of three layer density stratified fluid in shear flow are given, and they are dimensionless by using Choi's method. In the second chapter, the dimensionless equations satisfied by three-layer fluid are integrated in depth, and the Boussinesq equation of strongly nonlinear interfacial internal waves in shear flow is obtained by using Nwogu's method. The third chapter summarizes the research results of this paper and puts forward the prospect of further research.
【学位授予单位】：内蒙古工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175;O357

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