【作者】 周伟；

【导师】 张志跃；

【作者基本信息】 南京师范大学 ， 计算数学， 2013， 硕士

【摘要】 本文给出了一种求解球面上二维准地转模型的方法,即傅里叶有限体积元法.这种方法不仅守恒,计算效率高,而且有效地解决了极点问题.在这个模型的基础上,我们利用无导数优化算法求出了条件非线性最优扰动,并研究了不同波长的初始扰动对位涡拟能的发展的影响.数值试验表明,在扰动较小的情况下,位涡拟能在短时间内都是呈现出线性,但随着时间的发展,这种线性特征消失,说明在短时间内线性模式可以代替非线性模式,但随着时间发展切线性模式不再适用.更多还原

【Abstract】 In this thesis, we describe a new Fourier finite volume element method for solving the two-dimensional quasi-geostrophic equations on a sphere. This method is conservative and efficient. the pole problem is resolved at the same time. In addition, based on the two-dimensional quasi-geostrophic model, perturbation is found by the derivative free methods. The influence of different initial disturbances on the development of enstrophy is studied. It can be found from the experiments that, enstrophy development presents a linear development in a short time. However, as time goes on, this phenomenon disappears. It can be concluded that nonlinear mode can be replaced by tangent linear model in a short time. But in a long time, the tangent linear model lose effectiveness.更多还原