Several Kinds Of Atmospheric Solitary Wave Models And Applications In Severe Weather Phenomena

In recent years,severe weather often occurs,causing great damage to people's lives.Therefore,more and more people pay attention to the problem of severe weather,and the research on Marine atmosphere is carried out accordingly.With the rapid development of science and technology,the study of nonlinear waves in the ocean has attracted the attention of scholars at home and abroad.Two important branches,Rossby solitary waves and gravity solitary waves,have become the focus of research,which have important practical significance.In this thesis,multi-scale analysis and perturbation method are used to establish Rossby solitary waves model and gravity solitary waves model under different fluid states.According to the above models,the generation and evolution rules of solitary waves is explored,the disastrous weather phenomenon caused by squall lines is explained,and the physical mechanism of squall lines formation is discussed.The thesis consists of five chapters.In the chapter 1,the physical background and significance of Rossby solitary waves and gravity solitary waves are briefly introduced,and the research status of Rossby solitary waves and gravity solitary waves at home and abroad is analyzed.In the chapter 2,based on quasi-geostrophic vorticity equation with complete Coriolis under positive pressure,the mZK equation describing the generation and evolution of solitary waves is obtained by using multi-scale analysis and perturbation method.According to the semi-inverse method and the fractional variation principle,the time-space fractional mZK equation is obtained.In order to further study the properties of the time-space fractional mZK equation,the conservation laws of time-space fractional mZK equation under the Riemann-Liouville fractional derivative and Caputo fractional derivative are studied respectively according to the lie symmetry analysis,nonlinear self-adjoint and similarity reduction.Based on the conservation laws,the generation and evolution of Rossby solitary waves in the ocean and atmosphere are discussed.In the chapter 3,starting from the basic equations describing the baroclinic non-static equilibrium atmosphere,and considering the matching at the boundary,a new kind of algebraic gravity solitary wave and a new Boussinesq-BO model are obtained by using the multi-scale analysis and perturbation method.Compared with the classical solitary wave model,the algebraic gravity solitary wave model can describe the propagation of solitary wave in two directions,which is more consistent with the actual state of the ocean and atmosphere.Through the analysis of Boussinesq-BO equation,the conservation law of mass,momentum and energy are obtained.Finally,the exact solution of Boussinesq-BO equation is obtained by using the trial function method.In the chapter 4,squall lines in the atmosphere are briefly described firstly.Squall lines can cause a series of disastrous weather,thus it is of great value to study the squall line.Then,according to the exact solution and conservation laws of Boussinesq-BO equation,the relation between the fission process of gravity solitary waves and squall lines is discussed.Finally,it is conclude that the fission of gravity solitary wave is one of the possible physical mechanisms leading to the formation of squall lines.The research of this part will lay a solid theoretical foundation for improving the accuracy of weather forecast.In the chapter 5,the whole thesis is summarized and the future work is also prospected.