弱频散条件下大气运动的非线性演变过程

NONLINEAR EVOLUTION OF WEAKLY-DISPERSIVE ATMOSPHERIC MOTIONS

研究非线性过程对大气运动影响的一个常用方法是在一定条件下,将大气运动力学方程化为一些熟知的典型非线性演变方程,再利用数学中已有的结果进行讨论。Long、Redekopp等从地转涡度方程出发,证明了迭加在带状切变气流中的长的Rossby波的演变可以用著名的Kdv方程来描述。

Based on conservative equation of potential vorticity, it is proved that the atmospheric nonlinear evolution in weak frequency-dispersion condition is usually governed by KdV equation and the forms of weak frequency dispersion conditions are discussed. Some previous researches on derivation of KdV equation from different specified atmospheric motions are actually the special cases of the general form in this paper. The KdV equation can be resolved by numerical method. The results present that the initial disturbance in limited domain will develop the isolated wave under one given condition and a series of frequency-dispersing waves under other given conditions.