The Nonlinear Evolvement And Stability Study Of Vortex Rossby Waves

Since the research on the spread and evolution of Vortex Rossby Waves is thekey problem to study the movement of the typhoon, this paper study the nonlinearatmosphere dynamic equation by using a model in the polar coordinate according tothe theory of atmosphere dynamics. It is found by the WKB method that the packetof nonlinear Vortex Rossby wave which is effected by Rossby parameterβisgoverned by the nonlinear Schr(?)dinger equation and we solve the Schr(?)dingerequation under the condition that has practical meanings. It is Shown that the Rossbyparameterβis important in the spread of the Vortex Rossby waves and makes themovement of the Vortex Rossby waves steady-going, we get the conclusion that therange of the theoretical value of its out ward-propagating speed is consistent with theobservational one of spiral rain bands.In addition, we study the stability of Vortex Rossby waves when the Rossbyparameterβis regarded, we get some new determinant basis of the stability ofVortex Rossby waves.