纬向切变基流中的非线性正压Rossby波

在半地转近似下，用相角函数方法得到了包含纬向基流及其切变的非线性常微分方程。利用常微分方程解的拓扑性质的定性理论，直接得到该方程存在有限振幅的周期波解与孤立波解即非线性正压Ｒｏｓｓｂｙ波解存在的条件，由此分析了纬向切变基流对波解存在的影响。最后利用函数逼近法求得了非线性正压Ｒｏｓｓｂｙ波解的显式表达式。结果表明，纬向切变基流对波的影响不仅表现在波的存在方面，而且还表现在波的形态方面，反映了波的非线性特点和基流对波动的作用。

THE EFFECTS OF LATITUDINAL SHEARING FLOW ON NONLINEAR BAROTROPIC ROSSBY WAVES

nder the condition of semi-geostrophical approximation and by means of the phase function method, the non-linear ordinary differential equation with latitudinal shearing flow is obtained. Then the conditions for the existence of limited amplitude periodical and isolated wave solutions are directly obtained on the basis of the qualitative theory of ordinary differential equations. It is proved that latitudinal shearing flow affects not only the existence but also the formation of waves, which indicates the non-linear features of waves and the influence of basic flows on undulations.