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.