完整Coriolis力作用下非线性Rossby波的精确解

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

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fH=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fH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fH的影响消失.

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 fH =2Ω cosφ effect can be important if the perturbations are functions of the latitude. We also find that when the perturbations are independent of latitude, the fH effect disappears.