The Evolutionary Characteristic And Interaction Of Nonlinear Vortex Rossby Waves

In the paper, we have investigated the nonlinear Vortex Rossby waves in the atmosphere. It is found by use of the WKB method the wave packet is governed by nonlinear schr(o|¨)dinge equation. It is shown by numerical calculations that the value of its outward-propagating speed is about O(10°m/s), almost to be consistent with observational one of spiralrain bands of tropical cyclone from the Vortex Rossby wave. Thus it is significative to study the evolutionary characteristic of nonlinear Vortex Rossby wave, the existence of the solutions, the periodic waves solutions and the stability and the numerical format. There are five parts in the thesis.First, by the use of WKB method that evolutionary characteristic of nonlinear Vortex Rossby wave is governed by nonlinear schr(o|¨)dinge equation and the interaction between two wave packets is governed by coupled nonlinear Schrodinger equations:Second, for the coupled nonlinear Schrodinger equations, adopted the method of integral estimate, we prove that the condition of the existence for the solutions are: (2) the initial conditions satifyThird, the periodic waves solutions and their stability of the equations are investigated and the criteria for stability and instability are obtained.Fourth, we give the format of four-point scheme for the coupled nonlinear Schro dinger equat ions:*" )B, +-Z-B, = 0B, =0 , B,AA,J sh J r=oIf the conditions satisfy AJ0 e H\0 < b < \oj■ | < M, and 0 < qj (svs2) < Rfa +s2),Sj e[0,oo), the format of four-point implicit scheme is proved to be stable.Furthermore the error is 0{t + h2).Fifth, it is shown by numerical calculations that the value of its outward-propagating speed is about O(10° m/s), almost to be consistent with observational one of spiralrain bands of tropical cyclone from the vortex Rossby wave. It is the reason that many scholars can find the development and matainance of spiralrain bands from vortex Rossby wave.