对称不稳定的非线性问题和对称型重力惯性波的非线性周期解

The Nonlinear Problem of Symmetric Instability and the Periodic Solution of Symmetric Inertia-Gravitational Wave

本文利用密度的空间分布不均匀性引入非线性项，从准动量无辐散模式出发导出了一个自治的二阶非线性系统，应用这个系统讨论了非线性项对对称不稳定以及对称型重力惯性波非线性周期解的作用。从本系统的一次近似系统可得到类似Hoskins于1974年得到的结论，同样可导出对称不稳定的位涡判据。由于本系统是一有限次的非线性系统，故应用Poincare形式级数法可证明非线性周期解的存在性，并可求得周期解的一系列近似解。

In this paper, the nonlinear terms are introduced by means of the nonhomogeneous spatial distri-bution of density. An autonomous nonlinear system is derived from the moment nondivergent model.With this system we discuss the effect of nonlinear tCrms on the symmetric instability and symmetric pe-riodic solution. The conclusion obtained from its first-order approximation systom is similar to thatproposed by Hoskins in l974, and the potential vorticity criterion of symmetric instability is also ob-tained. By the Poincare series method, we prove the existence of the nonlinear periodic solution becausethis nonlinear system is a limitod order one. A series of approximate periodic solutions are alsoobtained.