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

Abstract

By using a two‐dimentional full‐implicit‐continuous‐Eulerian scheme, numerical simulation for nonlinear propagation of Gaussian gravity‐wave packets in a compressible and isothermal atmosphere are carried out. The numerical analyses show that for an initially given upgoing gravity‐wave packet whose disturbance velocity is much less than ambient wind velocity, although there exists nonlinear interaction, during the propagation, the whole wave packet 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 the wave packet passes. After a long time propagation (several periods), wave‐associated perturbation and energy can still concentrate in a limited region 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 gravity 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 propagate almost freely along their rays, and the nonlinear effect will only lower the propagation velocity of the wave‐associated energy. While gravity‐wave packets propagate in a nonisothermal atmosphere, the nonlinear propagation paths of wave energy depart clearly from the ray paths derived from the linear gravity wave theory under the WKB approximation, which indicates that the linear gravity‐wave theory under the WKB approximation can not predict the nonlinear propagation of gravity‐wave packet in a nonisothermal atmosphere.