By using a full-implicit-continuous-Eulerian (FICE) scheme and taking a set of basic atmospheric motion equations in spherical coordinates as governing equations, z fully nonlinear numerical model for the dynamics of the middle and upper atmosphere is established to numerically study the nonlinear global propagations and amplitude growths of large-scale gravity wave packets. The simulation results show that the newly established model can successfully exhibit the essential characteristics of the global propagations of gravity waves: wave energies propagate upward along the ray paths derived from the hnear gravity wave theory, and wave disturbance amplitudes increase with the increasing heights. During the upward propagation of gravity wave packets, there occurs evident enhancement of background wind along the propagation direction. Moreover, our simulation demonstrates that Earth rotation has little influences on the wave energy propagations and amplitude growths. However, the primary nonlinear curvature terms (uvr tan0 and -u2r tan0) play an important role in the growths of gravity wave amplitudes, which causes a evident latitudinal dependence of wave amplitude growth. In the Northern Hemisphere, with the same spatial scales and initial zonal dislurbance amplitudes, the waves propagating in lower-latitude regions have larger disturbance amplitudes.

By using a two-dimensional, full-implicit-continuous-Eulerian (FICE) scheme, we simulated the nonlinear propagation and evolution of gravity wave paekels in a compressible, nonisothermal and dissipative atmosphere. The numerical results show that when an upgoing gravity wave packet is generated in the lower mesosphere, it can propagate along gs ray path until it reaches lower thermosphere. However, upon reaching the lower thennosphere, the wave packet and associated energy propagate ahnost horizontally, which departs obviously from the prediction of linear gravity wave theory under WKB approximation in the nondissipative case. Further discussion indicates that the influences of nonlinearity and background temperature are not strong enough to restrict completely the upward energy propagation of the wave packet and that the influence of constant molecular viscosity on the characteristics (energy propagation path and wave parameters) of gravity waves is insignificant. It is the vertical inhomogeneity of molecular viscosity that causes the restriction of upward energy propagation of the gravity wave packet Moreover, througheut propagation, the donlgrant vertical wavelength of the wave packet decreases with time, as it is affected by the joint actions of nonlinearity, background temperature, and dissipation. These results indicate that the molecular viscosity, especially the vertical inhomogeneity of molecular viscosity, plays an important talc in the nonlinear propagation of gravity wave packets.

By using a two-dimentional fug-implicit-continuous-Euleri&n scheme, numerical sLm ulation for nonlinear propagation of Gaussian gravity-wave packets in a compressible and isothermal a~osphere are carried out. The numerical analyses show that for an inkiaUy given upgomg 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 nonlsothermal atmosphere, the nonlinar propagation paths of wave energy depart clearly from the ray paths derived from the Fncer gravity wave theory under the WKB approximation, which indicates that the linear gravity-wave theory under the UKB approximation can not predict the nonlinear propagation of gravity-wave packet in a nonisothennal atmosphere.