正压大气中地转偏差引起的非线性Rossby波

正压大气中的非线性波动的研究业已在60年代开始,70年代到80年代取得了丰硕的成果。在我国巢纪平等(1980)首先讨论了旋转大气中的正压Rossby椭圆余弦波。之后刘式适、黄思训等也做了大量的工作。特别是刘式适等,鉴于以前的工作多采用多尺度方法,比如约化摄动法,而这种方法中的G-M变换本身就意味着将要导出的结果。考虑到长波的弱非线性近似,将非线性项在平衡点附近展开为Taylor级数,求得了方程的非线性近似解。黄思训等认为应用展开法只能求得原方程的近似解,问题的解析解尚未找到。于是利用类似的模式导出了方程的解析解,且给出了存在非线性

THE NONLINEAR WAVES PRODUCED BY GEOSTROPHIC DEVIATION IN BAROTROPIC ATMOSPHERE

In this paper the nonlinear waves that are produced by geostrophic deviation in the barotropic atmosphere with the semi-geostrophic approximation (or geostrophic momentum approximation) are discussed. The analytical solution of this barotropic model is obtained. It is shown that the condition which brought elliptical function into existence is and the condition which brought solitary into existence is a=± If we defined M=a/ ,the above conditions changed into and M=±1.