MIXED ROSSBY-GRAVITY CNOIDAL WAVE UNDER THE CONDITION OF SEMI-GEOSTROPHIC APPROXIMATION

Under the codition of semi-geostrophic approximation,incorporating the travelling wave solution,the single variable equation of the verticle velocity is obtained by use of the vorticity equation,divergence equation,continuity equation and adiabatic equation in the stratified atmosphere. To find the solution of the single varible equation which can be reduced to the KdV equation,the nonlinear cnoidal wave and solitary wave are obtained. These waves have two frequences,so it can be seen that there are two nonlinear waves in the stratified atmosphere,one is the inertial gravity cnoidal wave which propagates eastwardly,the other is the mixed Rossby-gravity cnoidal wave which character is situated between the Rossby cnoidal wave and the inertial gravity cnoidal wave which propagates westwardly. The phase velocities of these cnoidal waves have relations with not only their wave numbers and amplitudes,but also the β effect and the static stabilities. The lower the latitude,the slower the phase velocity of the waves is;the more stable the atmospheric stratification,the faster the phase velocity is.