层结大气中非线性椭圆余弦波和孤立波的研究

在前文采用半地转近似和行波法来研究层结大气中的非线性波动的基础上，进一步探讨非线性方程及其级数近似方程的解的稳定性，波动解的存在条件和波动的一些特征。研究指出，在平衡点附近，将非线性方程用其级数近似方程代替是可行的、合理的。在初始拟能满足一定的条件下，椭圆余弦波和孤立波是存在的。文中还求得了椭圆余弦波解的周期、ｘ向波长和振幅以及孤立波的宽度和振幅。并指出，孤立波的宽度和振幅不但与波速有关，还与β因子和层结稳定度有关，而且在相同的某条件下，西行的混合Ｒｏｓｓｂｙ－重力孤立波比起东行的惯性重力孤立波来，宽度要小但振幅却大。

A STUDY ON THE NON-LINEAR CNOIDAL WAVES AND SOLITARY WAVES IN THE STRATIFIED ATMOSPHERE

On the basis of the works of Tan et al. (1988) and Xu (1996) on the nonlinear waves in the stratified atmosphere by using the methods of the semi-geostrophic approximation and the travelling wave solution, the stability of the solutions of the non-inear equation and its approximate series equation, the existence condition of the wave solution and some characteristics of the waves are discussed in this paper. The results are: (1) near the equilibrium point, substituting the solution of nonlinear equation with that of its approximate series equation is reasonable; (2) the solutions of the cnoidal waves and solitary waves are existant when the initial enstrophy satisfy certain conditions; (3) the period, wavelength inx-direction, amplitude of the cnoidal waves, and the wave-width, amplitude of solitary waves are obtained; (4) the wave-width and amplitude of the solitary waves are concernd with notonly the wave velocity but also the Rossby parameterand the stratification stability.Under the certain condition, the wavewidth of the mixed Rossby-ravity solitary wave moving westward is less than that of inertial gravity solitary wave moving eastward, butthe amplitude is bigger.