大气科学中的对称性
Symmetries in atmospheric sciences
摘要：
简要回顾了对称性方法在大气科学中的一些应用。特别是，重点放在利用经典的Lie对称性的方法来获得类的精确解，从大气模型。正压涡度方程说明了这一点。此外，部分不变的解决方案的建设的可能性进行了讨论。另一点是讨论如何利用对称性来联系不同类型的微分方程。这是说明与球和位涡方程。最后，利用离散对称性导出了E.洛伦兹（Lorenz，1960）以合理的数学方式提出了这一观点。
英文摘要：
Selected applications of symmetry methods in the atmospheric sciences are reviewed briefly. In particular, focus is put on the utilisation of the classical Lie symmetry approach to derive classes of exact solutions from atmospheric models. This is illustrated with the barotropic vorticity equation. Moreover, the possibility for construction of partially-invariant solutions is discussed for this model. A further point is a discussion of using symmetries for relating different classes of differential equations. This is illustrated with the spherical and the potential vorticity equation. Finally, discrete symmetries are used to derive the minimal finite-mode version of the vorticity equation first discussed by E. Lorenz (1960) in a sound mathematical fashion.
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