A numerical study of nonlinear propagation of a gravity-wave packet in compressible atmosphere

By using a two-dimensional full-implicit-continuous-Eulerian scheme, numeri cal simulation for nonlinear propagation of Gaussian gravity-wave packets i n a compressible and isothermal atmosphere are carried out. The numerical a nalyses show that for an initially given upgoing gravity-wave packet whose disturbance velocity is much less than ambient wind velocity, although ther e exists nonlinear interaction, during the propagation, the whole wave pack et and the wave-associated energy keep moving upward, while the wave front keeps moving downward. Wave-associated perturbation velocity increases with the increasing height, and the mean flow shows obvious enhancement when th e wave packet passes. After a long time propagation (several periods), wave -associated perturbation and energy can still concentrate in a limited regi on that is comparable in size to that given initially. The propagation path of wave energy coincides well with the ray path predicted by the linear gr avity wave theory, but the magnitude of wave energy propagation velocity is evidently smaller than the group velocity derived from the linear gravity wave theory. This indicates that once gravity waves are generated, they pro pagate almost freely along their rays, and the nonlinear effect will only l ower the propagation velocity of the wave-associated energy. While gravity- wave packets propagate in a nonisothermal atmosphere, the nonlinear propaga tion paths of wave energy depart clearly from the ray paths derived from th e linear gravity wave theory under the WKB approximation, which indicates t hat the linear gravity-wave theory under the WKB approximation can not pred ict the nonlinear propagation of gravity-wave packet in a nonisothermal atm osphere.