中层大气Rossby波与惯性重力波的非线性相互作用 （Ⅰ）相互作用方程

从包含Ｒｏｓｓｂｙ波和惯性重力波的大气运动方程组出发，采用弱非线性相互作用近似，推导出耗散大气中这两种尺度相差很大的波动之间的非线性相互作用方程．以此为基础，得到了描述窄角谱Ｒｏｓｓｂｙ波包和惯性重力波包的非线性时空演变规律的三波相互作用方程．数值分析表明，当一个Ｒｏｓｓｂｙ波包与两个惯性重力波包发生相互作用时，两个惯性重力波包之间进行快速的能量交换，同时与Ｒｏｓｓｂｙ波包之间进行缓慢的能量传输．从时间尺度上讲，惯性重力波可以看作Ｒｏｓｓｂｙ波包运动的背景噪声，因此上述非线性相互作用过程可以理解为大尺度Ｒｏｓｓｂｙ波包与背景噪声之间的能量交换过程．

THE NONLINEAR INTERACTION BETWEEN ROSSBY WAVE AND INERTIAL-GRAVITY WAVE IN THE MIDDLE ATMOSPHERE （Ⅰ）THE EQUATIONS OF NONLINEAR INTERACTION

Starting from the shallow-water equations which contain Rossby wave(RW) and inertial-gravity wave (IGW), a set of equations depicting the nonlinear interactions of RW and IGW in the dissipative atmosphere,whose temporal scales have verylarge difference, are derived in the frame of weak nonlinear theory.RW and IGW are departed from the coupling equations, the nonlinear interactions among waveswith different type can be studied from the interaction equations.When a RWpackets propagates through the atmosphere in which there are two IGW packets,the two IGWs exchange energy between themselves rapidly and they exchange theirenergies with RW simultaneously in a much slower rate.The temporal scales of IGWsare so small comparing to that of RW, the IGWs can be viewed as the ambient noise to the motion of RW. From this point, the nonlinear interaction among a RWand two IGWs can be understood as the course of energy exchanging between large scale RW and ambient noise.