中文摘要：

采用水平方向的显式算法与垂直方向的隐式算法相结合的时间分裂法，建立了二维可压缩大气中重力波非线性传播的数值模式．用本模式对小振幅重力波传播过程的模拟结果与线性重力波理论预测的结果吻合很好，从而验证了本模式的正确性．我们用此模式模拟了有限振幅重力波在非线性传播过程中的饱和与破碎，结果表明，（1）翻转出现在饱和之前，但向破碎演化仍需要一段时间，由于非线性波-波和波-流相互作用使得非线性数值模拟的饱和高度（出现时间）高（早）于线性饱和理论预测的结果；（2）重力波在不稳定之前已经有能量向背景场中转移，破碎直接导致非线性波-波相互作用，造成能量向小尺度短波上转移；（3）背景风场的加速方向，形成射流的方向与重力波的水平传播方向一致，表明重力波与背景流的非线性相互作用加剧了背景风剪切和不稳定性的发展．

英文摘要：

A time splitting numerical model is developed in this paper, which combined the explicit algorithm in the horizontal direction and the implicit algorithm in the vertical direction, and used to simulate the nonlinear propagation of the gravity wave （GW） in a 2-dimensional compressible atmo- sphere. Numerical simulation of the nonlinear propagation of the small amplitude GW is presented by using this model. The numerical results coincide well with linear theory and indicate that the numerical model is correct. The saturation and breakdown of the nonlinear propagation of the finite amplitude GW is simulated by using the model. The results show that： （1） The overturn appears before the saturation of GW, however, it requires a long time （nearly 1.5 periods of the GW） to induce the GW breakdown. The height （time） of instability predicted by linear saturation theory is higher （latter） than the corresponding results obtained from nonlinear numerical simulation because of the nonlinear wave-wave and wave-flow interaction. （2） The nonlinear wave-flow interaction produces energy transforring from the GW to mean flow prior to instability. The nonlinear wave-wave interaction is induced by the breakdown of GW directly. （3） The direction of the horizontal mean wind acceleration, the jet and the horizontal propagation of GW are consistent and indicate that the nonlinear wave-flow interaction accelerate the formation of horizontal mean wind shear and the development of the instability.