The Study Of Nonlinear Stability Of The Atmospheric Motions

Recently, the stability of atmospheric motion has been considered a central issue in fluid mechanics. Some progresses have been made at home and abroad in this area, such as reference [1]-[12]. But there are still some problems are not been solved well, mainly the linear stability and nonlinear stability criteria for some models are not totally consistent, it is difficult to extend linear stability criteria to nonlinear stability criteria. The linear equation has been used to solve the stability problem usually, but this stability only makes sense in the case of small perturbation. The key problem solved in this paper is the stability of the nonlinear motion.This paper attempts to remove the difference between linear stability criterion and nonlinear stability criteria. There are four parts in this paper. The first part introduce the background and significance of the research problem.The second part introduces the prior knowledge. The third section, analyses relevant theories with the main line of nonlinear stability of atmospheric motion. The fourth part, firstly used the characteristic function we derivate A general three-dimensional quasi-geostrophic model of the nonlinear stability criterion for the application of broader (Cy>1), then we applied it in Eady model to prove the nonlinear stability criterion and the linear stability criterion is entirely consistent.