地形效应条件下正压流体的能量守恒
发布时间：2019-04-28 15:57
【摘要】：大气的能量循环是大气科学研究领域的一个重要分支,大气能量守恒在海洋学和气象学中已经被广泛应用.在这篇论文中我们讨论了两类正压流体模式的方程组.首先我们讨论旋转浅水模式,推导出了具有地形效应的控制方程,得到了该方程满足大气能量(动能和势能,不考虑水汽)守恒的结论,进一步分析了地形效应对大气能量的转换和分配的影响.然后我们基于正压准地转大气模式,研究了大气能量受地形效应的影响.起初,通过分析尺度法,将正压方程组无量纲化,再者,确定一个合适的小参数,利用摄动展开依次得到无量纲化的正压方程组的零级和一级近似方程.从而获悉了在地形效应条件下的正压准地转位涡方程.最终通过新得到的正压准地转位涡方程推导了能量守恒这一结论.并进一步站在能量角度阐释了一列均匀西风是如何受地形效应影响的.
[Abstract]:Atmospheric energy cycle is an important branch of atmospheric science. Conservation of atmospheric energy has been widely used in oceanography and meteorology. In this paper, we discuss the equations of two kinds of barotropic fluid models. Firstly, we discuss the rotating shallow water model, derive the governing equation with topographic effect, and obtain the conclusion that the equation satisfies the conservation of atmospheric energy (kinetic energy and potential energy, regardless of water vapor). The influence of terrain effect on the conversion and distribution of atmospheric energy is further analyzed. Then, based on the barotropic quasi-geostrophic model, the effects of topography on the atmospheric energy are studied. At first, the barotropic equation system is dimensionless by analyzing the scale method. Furthermore, a suitable small parameter is determined and the zero-order and first-order approximate equations of the dimensionless barotropic equation system are obtained by means of perturbation expansion. Thus, the barotropic quasi-geostrophic vorticity equation under topographical effect is obtained. Finally, the conclusion of energy conservation is derived from the new barotropic quasi-geostrophic vorticity equation. Furthermore, from the point of view of energy, it explains how a series of uniform westerlies are affected by terrain effect.
【学位授予单位】：内蒙古大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2467764
[Abstract]:Atmospheric energy cycle is an important branch of atmospheric science. Conservation of atmospheric energy has been widely used in oceanography and meteorology. In this paper, we discuss the equations of two kinds of barotropic fluid models. Firstly, we discuss the rotating shallow water model, derive the governing equation with topographic effect, and obtain the conclusion that the equation satisfies the conservation of atmospheric energy (kinetic energy and potential energy, regardless of water vapor). The influence of terrain effect on the conversion and distribution of atmospheric energy is further analyzed. Then, based on the barotropic quasi-geostrophic model, the effects of topography on the atmospheric energy are studied. At first, the barotropic equation system is dimensionless by analyzing the scale method. Furthermore, a suitable small parameter is determined and the zero-order and first-order approximate equations of the dimensionless barotropic equation system are obtained by means of perturbation expansion. Thus, the barotropic quasi-geostrophic vorticity equation under topographical effect is obtained. Finally, the conclusion of energy conservation is derived from the new barotropic quasi-geostrophic vorticity equation. Furthermore, from the point of view of energy, it explains how a series of uniform westerlies are affected by terrain effect.
【学位授予单位】：内蒙古大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
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