层结大气中重力惯性波的非线性周期解

本文在动量无辐散近似下的层结大气中,考虑密度空间分布的不均匀性引入非线性项,并假设解为行波形式,得到了一个二阶非线性系统。应用本系统不仅可以得到刘式适等(1984)所得到的一切结果,而且可以证明一次近似系统存在周期解时,非线性系统也存在周期解,且避免了应用级数展开时所带来的一些数学问题。文中还讨论了非线性系统的一系列近似解。

THE NONLINEAR PERIODIC SOLUTION OF INERTIA-GRAVITATIONAL WAVE IN STRATIFIED ATMOSPHERE

In the stratified atmosphere in which the moment nondivergent approximation was applied, the nonlinear term was introduced because of the nonhomogeneous spatial distribution of density. The solution to be of the form of progressive wave is considered and obtained a two-order nonlinear equation. By means of this system, all results which were derived by Liu Shikuo(1984) were obtained.Moreover, it can be proved that there existed periodic solution in the nonlinear system when there existed periodic solution in the one-order approximation system, and some mathematic problems that were caused by using series expansion were linear system is avoided. In this paper, a series of approximatic solution of nonalso discussed.