Propagation of an atmospheric gravity wave (AGW) in a wind field is studied by numerical simulation. Two models are applied: the first is a linear model to check with the gravity wave theory; the second is a quasi-nonlinear model to study the characteristics of the secondary waves produced by the interactions between two gravity wave packets. The magnitudes and directions of the vertical phase and group velocities obtained by linear simulation are consistent with the prediction of linear gravity wave theory. That is, the vertical propagation velocities of the phase and the energy of an AGW are always opposite to each other. In the quasi-nonlinear model, two primary waves are forced to oscillate at the ground level with their group velocities upward and phase velocities downward, which creates two secondary waves by the interaction between the primary waves. The smaller one is found to have group velocity upward and phase velocity downward just the same as that of the two primary waves. The group velocity of the larger one is found to be downward always, while its phase velocity is upward when the primary waves in the source region are still oscillating and becomes downward after the primary waves stop oscillation. The result reveals that the smaller one is a production of a resonant interaction; while the larger one is the production of a non-resonant interaction. Both secondary waves do not follow the dispersion relation of the linear theory. The result of this simulation confirms our previous observation that the vertical phase and group velocities of a non-linear AGW are not necessarily in the opposite direction.
