地形边界变化条件下的浅水方程求解及其动力学特征

项目名称： 地形边界变化条件下的浅水方程求解及其动力学特征

项目编号： No.41465002

项目类型： 地区科学基金项目

立项/批准年度： 2015

项目学科： 天文学、地球科学

项目作者： 达朝究

作者单位： 西北民族大学

项目金额： 50万元

中文摘要： 由于自然变化和人为因素影响，地形高度会发生变化，进而导致大气环流、局地气候乃至全球气候的变化。本项目针对地形高度变化的事实，深入探讨地形对大气影响的动力过程。将地形变化分为两部分：固有地形项和随时间变化的扰动项；视后者为一小项，对此做小参数展开，运用波动力学边界条件处理方法和微分方程处理技巧，研究地形变化条件下的浅水方程。通过数学推导，由浅水方程导得含地形变化效应的涡度方程，并得到涡度振幅演变满足的KdV方程，对于分层流体则是mKdV方程。我们将引进新的求解KdV方程的方法并加以改进，使之更适合于含地形附加项的KdV方程。研究重点将放在mKdV方程上，该方程至今少有研究。通过求KdV方程的解析解和数值计算，揭示地形变化对大气环流以及阻高、冷涡的影响。研究成果有助于深化了解大气动力过程，可为现有气候模式的陆面过程提供动力学依据。

中文关键词： KdV方程；扰动；浅水方程；地形边界

英文摘要： Due to the natural variation and the anthropogenic factors, the altitude of the topographic boundary maybe changed, which may influence the circulation of atmosphere, and then change the local and global climate. The research project based on the fact of changing terrain, discusses the dynamics process of the effect upon the atmosphere. The topography is divided into two parts, the natural terrain and the disturbance term, the latter one is considered as a small quantity. Small parameter expansion is applied to study, using the method of treatment the boundary condition of the wave dynamics and the skill of the boundary condition of differential equation, we discuss the shallow water wave equation. Through the mathematical derivation, this research obtains the vorticity equation involving the change of the topographic boundary, and can get the KdVequation for the evolution of the amplitude of the vorticity(mKdV equation stands for the stratified fluid). We introduce a new method to solve the KdV equation, and will make this method better to adapt to the KdV equation which contains the topographic boundary. The research emphasis is the mKdV equation, which has been less studied so far. From the analytical solution and the numerical solution of the KdV equation, the influence of the topographic boundary upon the circulation of atmosphere, the blocking high and the cold vortex can be shown. The results can not only help to understand the atmosphere dynamical process, but also can offer scientific basis for the climate model.

英文关键词： KdV equation;disturbance;shallow water equation;topographic boundary