层结流体中在热外源和β效应地形效应作用下的非线性Rossby孤立波

发布时间：2018-06-04 07:41

本文选题：Rossby波 + 热外源　；参考：《内蒙古大学》2016年硕士论文

【摘要】：Rossby波存在于大尺度的流体中,因此它在大气和海洋的运动研究中是非常重要的.我们通过理论和观察,获得了Rossby波最基本的特征和性质,它满足准地转近似和静态平衡.在层结流体中,前人研究了均匀大气中的长波并且得到了KdV方程,但是这个是限定于切变速度要比基本平均纬向流小很多的.这里β近似采用f=f0+β(y)y代替一般的f=f0+β_0y(β_0是一个常数),用非线性函数β(y)替代了β近似中的常数β_0.特别是在中高纬地区,这样更能保证大气和海洋中描述运动的精确性.Helfrich口Pedlosky通过构造纬向流在时间尺度方面的关联性,获得了方程的强迫项,这种强迫是由地形和外源引起的.这里我们取一个基本切变流,其中Vaisala-Brunt频率N和z变量有关.对于层结流体而言,从带有地形、热外源耗散的下边界条件以及带有热外源的准地转位涡方程开始,使用小参数展开方法和多尺度时空伸长变换推导出了具有热外源、β效应和地形效应的强迫Rossby孤立波方程,得到孤立Rossby振幅满足的带有地形与热外源的非齐次非线性的Schr(?)dinger 方程.通过分析Rossby孤立波振幅的变化,指出了热外源、p效应和地形效应都是诱导Rossby孤立波产生的重要因素,给出了切变基本流下地形、热外源和层结流体中Rossby的相互作用.
[Abstract]:Rossby waves exist in large scale fluids, so they are very important in the study of atmospheric and oceanic motion. The basic characteristics and properties of Rossby waves are obtained by means of theory and observation, which satisfy the quasi-geostrophic approximation and static equilibrium. In stratified fluid, long waves in homogeneous atmosphere are studied and KdV equation is obtained, but the shear velocity is much smaller than the basic average zonal current. In this case, the 尾 approximation is replaced by f=f0 尾 tiao y instead of the ordinary f=f0 尾 tit _ 0 (尾 _ 0 is a constant, and the nonlinear function 尾 _ (y) is used to replace the constant 尾 _ S _ 0 in the 尾 -approximation. Especially in the middle and high latitudes, the accuracy of describing motion in atmosphere and ocean. Helfrich mouth Pedlosky obtains the forced term of the equation by constructing the correlation of zonal current in time scale, which is caused by topography and exogenous factors. Here we take a basic shear flow where the Vaisala-Brunt frequency N and z variables are related. For stratified fluids, we start with the lower boundary conditions with topography, the dissipation of heat source and the quasi geostrophic vortex equation with heat source. The forced Rossby solitary wave equations with thermal, 尾 and topographic effects are derived by using the method of small parameter expansion and multiscale space-time elongation transformation. The nonhomogeneous nonlinear Schr(?)dinger equations with topographic and thermal exogenous are obtained, which satisfy the isolated Rossby amplitudes. By analyzing the amplitude variation of Rossby solitary wave, it is pointed out that both thermal and topographic effects are important factors in inducing Rossby solitary wave, and the interaction between thermal source and Rossby in stratified fluid under the basic shear flow is given.
【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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