Nonlinear Rossby Waves In Rotation Flows

Based on perturbation method an WKB method as well as the quasi-geostrophoic potential vorticity equation in the rotational stratified coordinate system,we analyzed the Rossby waves with a balance among forcing dissipation,topographic effect and nonlinear effect in barotropic atmosphere and in stratified atmosphere which there is the vertical shear of the basic flow in.In consequence,we obtained a nonlinear Schrodinger equation with complex coefficients and an envelope solitary wave solution when the wave number of Rossby envelope solitary waves is 1 or2.Accordingly,we analyzed the Rossby solitary waves with the influence of vertical shear of basic flow stratification effect ? effect topographic effect and forcing dissipation.Particularly,based on the nonlinear Schrodinger equation we can analyze qualitatively the stability of stratified atmosphere,come to the conclusion of the influence of dissipation on the stability.We also obtained longitude structure of Rossby envelope solitary waves from 1 and 2 order approximate equations.