The Analytical Solution Of Sea-air Coupled Model For El Ni(?)o/La Ni(?)a-Southern Oscillation

With the global warming and the increase of extreme weather phenomena,the climate variability has already become a central issue which was attended by the people all over the world. El Nino/La Nina&Southern Oscillation(ENSO) event is a complex nonlinear system, its happening seriously affect the global climate and ecology. It brought many disasters, on the global economic development and human life have seriously affected. Thus,the study about ENSO cycle has important significance. Although the ENSO event's research had already made great progress, the process of ENSO event still couldn't be accurately forecasted.Therefore, its mechanism of exploration and prevention of study are concern objects to the current international academic.Due to the complexity and nonlinear of the air-sea interaction, the method of numerical simulation be used extensively, and achieved gratifying achievements. However the numerical method cannot give expression of the solution of the ENSO air-sea coupling system, it is difficult to make an analysis of global properties. And its research only in limited precision.Explanation of ENSO's basic physical significance demands a analytical theory mode. This thesis mainly use the homotopy mapping method, perturbation method and variational iteration method to the asymptotic solution of the tropical sea-air coupling oscillator model.Major results of this thesis are:1,Study of sea-air coupled model for El Nino/La Nina-Southern oscillation by using the homotopic mapping method.1) A box model of the interhemispheric thermohaline circulation (THC) in the disturbed sea-air for globe climate is considered. By using the homotopic mapping method, a class of nonlinear model is studied. And the approximate solution is obtained.From the comparison of accuracy, we can conclude that the obtained solution by using the homotopic mapping method has a finer approximate degree.Then,compares their curves can be seen can be seen that the approximate solution by using the homotopy mapping method and the exact solution of the equation have smaller error.2) A class of oscillator for the El Ni~no/La Ni~na-southern oscillation model is considered. By using the homotopic mapping method, developing nonlinear terms to the power series in p, we compare the coefficients of the same power in p for both sides of the equations,we have the coefficients of zeroth order power in p. Using the same method, we can obtain a higher order approximate solution.It is shown that, the solution by using the homotopic mapping method has a good accuracy.2,Study of sea-air coupled model for El Nino/La Nina-Southern oscillation based on the variational iteration method.1) A solving problem for the Lorenz system in atmospheric dynamics system is considered. Firstly, a set of variational iteration is constructed by using the generalized variation principle. Then, the initial approximate solution is decided. Finally, using the variational iteration, we can find every approximation Xn(T0), Yn(T0),Zn(T0) for corresponding model. Its limit function X(T0)=(?)Xn(T0), Y(T0)=(?)Yn(T0), Z(T0)=(?)Zn(T0) is exact solution of disturbed Lorenz system.2) A sea-air oscillator model of the nonlinear coupling system is studied.Using the variational iteration principle,a series of corresponding functional is constructed.Then the Lagrange operators are selected. Finally, using the generalized variational iteration method,the approximate sequences of a series of solutions for the sea-air oscillator model are obtained. It can be prooved that the approximate sequences by using the generalized variational iteration are uniform convergence in research scope,therefore, limit function is a group of solution of system. Meanwhile,using the variational principle and selecting Lagrange operators reasonably, the convergence speed of corresponding sequence are ensured.3,A class of coupled system of the El Ni no/La Ni na-Southern Oscillation mechanism is studied.Using the perturbed theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behavior of solution for corresponding problem is considered.Then, we compare the values of Tnum from the numerical calculation and Tper from the asymptotic disturbed expansion at different values of T(℃) and t(yr), we can see that the first approximate disturbed solution Tper obtained using the perturbation method has a good accuracy and the smaller theτ, the better and the accuracy is. The perturbation method is a valid method.These optimal methods are approximate analytic methods, which differs from the general numerical method. The expansions of solution can analytic operation sequentially. And then we can also diversify qualitative and quantitative behaviors for corresponding physical quantities,and thereby further to discuss the atmospheric physics of the coupled sea-air oscillators model for globe climate,And found its law, thus further to understand it, and forecast it.The innovation of this thesis consists in(1) The numerical method cannot give expression of the solution of the ENSO air-sea coupling system, it is difficult to make an analysis of global properties.The method used in this thesis is a kind of approximate analytic method, which can get the movement rule of nonlinear system, it helps to deepen us understanding the ENSO oscillation forming mechanism and irregularities source.(2) Using the homotopy mapping method, perturbation method and variational iteration method to Processing the nonlinear term of ENSO phenomenon, mapping the complex nonlinear atmospheric dynamics problems for simple linear problem.