层结流体在缓变地形、耗散与热源作用下的Rossby孤立波

发布时间：2018-03-02 02:34

本文关键词： 非齐次KdV-Burgers方程 β效应缓变地形耗散热外源　出处：《内蒙古大学》2016年硕士论文　论文类型：学位论文

【摘要】：Rossby孤立波是大气与海洋运动的主要波动之一,本文在层结流体准地转位涡方程,以及含有缓变地形下边界条件的基础上,用摄动方法与时空伸长变化得到层结流体中Rossby孤立波振幅满足的非线性方程.本文首先在直角坐标系下导出了推广的β效应(即Rossby参数β是纬度变量y的函数)的层结流体准地转位涡方程与带有缓变地形hB1(t)的下边界条件,进行无量纲化处理,得到无量纲化的控制方程与边界条件,然后引入G-M(Gardner-Morikawa)变换滤去快变量x,t；利用小参数展开得到各阶摄动方程；用正交模方法讨论各阶问题,最后利用消奇异条件讨论Rossby孤立波在缓变地形、耗散与热源作用下Rossby孤立波振幅在慢变量ξ,τ下的演变规律.在准地转位涡方程的基础上,对地球流体中Rossby孤立波含有缓变地形、耗散与热源做了一些研究,主要内容如下：第一章介绍了地球流体中有关Rossby波的研究现状、研究方法与选题背景.第二章给出了有关处理地球流体的一些近似模式,并推导了推广的β平面近似下的正压模式、层结模式下地球流体的准地转方程以及带有缓变地形的下边界条件.第三章采用推广的β-平面近似模式,将β平面近似f=f_0+β_0y(β_0是常数),进一步化为f=f0+β0(y)y这里β0(y)是纬度变量y的非线性函数,这样的近似可以更好的描述大气与海洋的运动,尤其在中高纬度地区.在下边界条件中考虑有缓变地形存在并利用扰动展开与时空伸长变化推导了Rossby孤立波振幅满足的Kortewege-de Vries-Burgers(KdV-Burgers)方程与Modify Kortewege-de Vries(mKdV)方程的结论.第四章对本文所做工作的总结与展望.
[Abstract]:Rossby solitary wave is one of the main waves of atmospheric and oceanic motion. This paper is based on the quasi geostrophic vorticity equation of stratified fluid and the boundary conditions under slowly varying terrain. The nonlinear equation of Rossby solitary wave amplitude in stratified fluid is obtained by using perturbation method and space-time elongation variation. In this paper, the generalized 尾 effect (that is, Rossby parameter 尾 is a function of latitude variable y) is derived in a rectangular coordinate system. The quasi-geostrophic vorticity equation of stratified fluid and the lower boundary conditions with slowly varying terrain hb1. The dimensionless governing equation and boundary condition are obtained by dimensionless treatment, and then G-Me Gardner-Morikawa-transform is introduced to filter the fast variable xt; the perturbation equation of each order is obtained by using small parameter expansion; and the problems of each order are discussed by orthogonal mode method. Finally, the evolution law of the amplitude of Rossby solitary wave under slowly changing topography, dissipation and heat source is discussed by using the condition of eliminating singularity. On the basis of quasi geostrophic vorticity equation, the Rossby solitary wave in earth fluid contains slowly varying topography. Some studies on dissipative and heat sources are carried out. The main contents are as follows: in Chapter 1, the current research situation, research methods and background of Rossby wave in earth fluid are introduced. In chapter 2, some approximate models for dealing with earth fluid are given. The barotropic model under the generalized 尾 plane approximation, the quasi geostrophic equation of the earth fluid under the stratified model and the lower boundary conditions with slowly changing terrain are derived. In chapter 3, the generalized 尾-plane approximation model is adopted. If the 尾 plane is approximated to ff0 尾 0yth (尾 _ S _ 0 is a constant, further reduced to f _ f _ 0 尾 _ 0y) is a nonlinear function of the latitude variable y, such an approximation can better describe the motion of the atmosphere and the ocean. Especially in the middle and high latitudes, the existence of slowly varying terrain is taken into account in the lower boundary conditions, and the conclusions of Kortewege-de Vries-Burgersn KdV-Burgers equation and Modify Kortewege-de VriesmKdV) equation satisfying the amplitude of Rossby solitary wave are derived by using perturbation expansion and space-time elongation variation. In chapter 4th, the results of the Kortewege-de Vries-Burgersberg equation and the Modify Kortewege-de VriesmKdV equation are derived. Summary and prospect of the work done in this paper.
【学位授予单位】：内蒙古大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175.29

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