完整Coriolis力作用下非线性Rossby波的精确解

从包含完整Coriolis力的Boussinesq近似的斜压大气运动方程组出发，利用半地转近似导出β效应和地球旋转水平分量f_H=2Ωcosφ共同作用下的大气非线性Rossby波动所满足的KdV方程，求得了椭圆余弦波解和孤立波解.结果分析表明，若扰动与纬度有关，Coriolis参数分量f_H将影响波动传播的频率特征，并加强水平散度对斜压Rossby波的作用；如果扰动与纬度无关，则 Coriolis 参数分量f_H的影响消失.

Exact solutions to the nonlinear Rossby waves with a complete representation of the Coriolis force

A horizontal component of the earth′s rotation is included in a set of Boussinesq fluid equations, which have a constant horizontal component of the Coriolis parameter, while the vertical component varies with latitude. The nonlinear Rossby waves described by the KdV equation are derived. Its periodic-wave and soliton solution are also obtained. The results show that the f_H=2Ωcosφ effect can be important if the perturbations are functions of the latitude. We also find that when the perturbations are independent of latitude, the f_H effect disappears.