损耗大气中重力波的非线性相互作用理论

基于中高层大气重力波动力学是由非线性过程和损耗过程共同决定的物理思想,本文采用弱非线性相互作用近似,推导出损耗大气中重力波的非线性相互作用方程.这组方程是研究固定相位和随机相位重力波相互作用问题的出发点.通过引入平均振幅,我们得到了损耗情况下离散重力波的三波相互作用方程,该方程描述了重力波波包非线性时空演变的规律.作为该方程的一个具体应用,我们考虑了由于波-波相互作用产生的不稳定性.当一大尺度大振幅的主重力波通过大气传播时,非线性相互作用可能导致两个次级波振幅随时间指数增长.由于分子损耗和频率失配,主波的振幅必须大于一个阈值,这种指数增长才可能出现.共振条件满足时,阈值变为最小.频率失配还会导致次级波本征频率发生改变,改变的大小是频率失配值的一半.

A THEORY ON NONLINEAR INTERACTION OF GRAVITY WAVES IN A DISSIPATIVE ATMOSPHERE

In the light of an idea that the dynamics of gravity waves in the middle and upper atmosphere is determined jointly by nonlinear interaction and molecular disspation, a set of equations depicting the nonlinear interactions of gravity waves in a dissipative atmosphere is derived in the frame of weak nonlinear theory. The equations can be used to study both interactions of fixed-phase and random-phase gravity wave packets. Starting from the equations we investigate the interaction of three discrete gravity wave packets. When an intense large-scale primary gravity wave propagates through the dissipative atmosphere, it likely decays into secondary waves through three wave interactions. The amplitudes of the secondary waves grow exponentially. The molecular dissipation and frequency dismatch yield a threshold value of horizontal fluid velocity associated with primary wave, only above this threshold the exponential growth of the amplitudes of the secondary waves can set in. The threshold value takes its mininum under the condition of resonance. The frequency dismatch leads to a variation in the intrinsic frequencies of the secondary waves. The magnitude of the variation is just a half of the dismatch value.