Several Kinds Of Models Describing Rossby Solitary Waves And Their Properties

In recent years,along with the people of the earth's fluid mechanics and in-depth study of atmospheric dynamics,a series of achievements,among them,the research of Rossby solitary waves as a kind of special and important branch,has important theoretical significance and research value.Rossby waves,also known as planetary wave,are the most representative wave phenomenon associated with the shape and rotation of the earth.This paper adopts the method of combining the theoretical analysis and numerical simulation,are established under the condition of barotropic and baroclinic atmosphere,a few class description Rossby solitary waves equation of different model,and carries on the further research.In the chapter 1,the theoretical origin of Rossby isolated waves is introduced,and the background and significance of the research are discussed.In addition,we also introduced the research status of Rossby isolated waves theory at home and abroad,and listed the results that have been achieved in this field.In the chapter 2,we study the model of enveloping Rossby isolated waves describing(2+1)-dimensional coupling.First of all,based on the positive pressure of the fluid quasigeostrophic vorticity equation,using the perturbation method and the elongation of time and space transformation,deduce the description(2+1)-dimensional coupling envelope Rossby solitary wave model,the coupled nonlinear schrodinger equation(CNLS).Further solutions of the model using the trial function method,the equation of the solution as we know,the coupling of the two solitary waves will exist in the process of interaction process of amplitude offset each other,but because in the absence of solitary wave under the condition of dissipation of energy conservation,after two wave in interaction and broadcast their own direction.In addition,starting from the concept of optical soliton communication in the field of chirp,research in the field of positive pressure air,Rossby wave propagation in the process of nonlinear effect and dispersion effect caused by the chirp,it is concluded that when the parameters for a particular value,two effect caused by chirp cancel each other out.In the chapter 3,in view of the ocean and the atmosphere of algebraic Rossby solitary waves,using the perturbation method and the small parameter perturbation expansion method,get a new class of describing three dimensional algebraic Rossby solitary waves generation and evolution of the model,namely the ZK-BO equation.The exact solution of ZK-BO equation is obtained based on the test method.Through numerical simulation and comparison,it can be found that the wavelength of the three-dimensional Rossby isolated waves is shorter and the amplitude of wave is higher.In addition,the effects of dissipation on the evolution of isolated waves and the fission of isolated waves are studied.Through theory and image analysis,we can draw the following conclusion:algebraic solitary wave split into four different solitary wave,and in the same direction of propagation of large amplitude solitary wave propagation velocity is smaller than the amplitude of solitary wave propagation speed,so the distance between the solitary waves is more and more big.In the chapter 4,first of all,based on the description of the baroclinic atmosphere condition basic equations of fluid motion,using perturbation method and a small parameter perturbation expansion method deduces the integer order mKdV equations show that,and then using semi-inverse and variational method get a new model under the definition of Riemann-liouville derivative,namely fractional mKdV equations show that space and time.In addition,the conservation law of mKdV equation is studied by using Lie group analysis,and several different kinds of solutions are obtained by using the method.We summarize predecessors for Rossby research of solitary wave,found that the fractional order partial differential equation in this area also play an important role,and research for the partial differential equations of fractional order for us to further understand the movement of fluid in the Marine atmosphere open a new window.Summarizing the above research contents,this paper gives a summary and prospect in chapter 5.