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GENERALIZED VARIATION ITERATION SOLUTION OF AN ATMOSPHERE-OCEAN OSCILLATOR MODEL FOR GLOBAL CLIMATE

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Journal of Systems Science & Complexity 2011年第2期24卷 271-276页

作者： Jiaqi MO wantao lin Anhui Normal University Wuhu 241000 China Division of Computational Science E-Institutes of Shanghai Universities at Shanghai Jiaotong University Shanghai 200240 China State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamic Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China

A box model of the interhemispheric thermohaline circulation （THC） in atmosphere-ocean for global climate is considered. By using the generalized variational iteration method, the approximate solution of a simplified nonlinear model is studied. The generalized variational iteration method is an analytic method, and the obtained analytic solution can be operated sequentially. The authors also diversify qualitative and quantitative behaviors for corresponding physical quantities.

关键词： Approximate solution atmosphere-ocean E1 Nino-Southern oscillation variational iteration.

Approximate Solution for Mechanism of Thermally and Wind-driven Ocean Circulation

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Chinese Geographical Science 2010年第5期20卷 383-388页

作者： MO Jiaqi lin wantao lin Yihua Anhui Normal University Wuhu 241000 China State Key Laboratory of Numerial Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China Division of Computational Science E-Institutes of Shanghai Universities at Shanghai Jiaotong University Shanghai 200240 China

The thermally and wind-driven ocean circulation is a complicated natural phenomenon in the atmospheric physics. Hence we need to reduce it using basic models and solve the models using approximate methods. A non-linear model of the thermally and wind-driven ocean circulation is used in this paper. The results show that the zero solution of the linear equation is a stable focus point, which is the path curve trend origin point as time (t) trend to infinity. By using the homotopic mapping perturbation method, the exact solution of the model is obtained. The homotopic mapping perturbation method is an analytic solving method, so the obtained solution can be used for analytic operating sequentially. And then we can also obtain the diversified qualitative and quantitative behaviors for corresponding physical quantities.

关键词： global climate atmosphere-ocean oscillation homotopic mapping approximate solution

Dissipative Travelling Wave Solution for El Nio Tropic Sea-air Coupled Oscillator

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Chinese Geographical Science 2010年第3期20卷 275-280页

作者： WEN Zhaohui lin wantao lin Yihua MO Jiaqit Institute of Applied Mathematics School of Statistics and Applied Mathematics Anhui University of Finance and Economics Bengbu 233030 China State Key Laboratory of Numerical Modeling for Atmospheric and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China Anhui Normal University Wuhu 241000 China Division of Computational Science E-Institutes of Shanghai Universities at Shanghai Jiaotong Uinversity Shanghai 200240 China

El Nifio and Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific sea-air interactions. An asymptotic method of solving equations for the ENSO model is proposed. Based on a class of oscillator of ENSO model and by employing a simple and valid method of the variational iteration, the coupled system for a sea-air oscillator model of interdecadal climate fluctuations is studied. Firstly, by introducing a set of functionals and computing the variationals, the Lagrange multipliers are obtained. And then, the generalized variational iteration expressions are constructed. Finally, by selecting appropriate initial iteration, and from the iterations expressions, the approximations of solution for the sea-air oscillator ENSO model are solved successively. The approximate dissipative travelling wave solution of equations for corresponding ENSO model is studied. It is proved from the results that the method of the variational iteration can be used for analyzing the sea surface temperature anomaly in the equatorial Pacific of the sea-air oscillator for ENSO model.

关键词： El Nifio-Southem Oscillator model variational iteration sea-air oscillator

Perturbed Solving Method for Interdecadal Sea-air Oscillator Model

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Chinese Geographical Science 2012年第1期22卷 42-47页

作者： MO Jiaqi lin Yihua lin wantao CHEN Lihua Department of Mathematics Anhui Normal University Wuhu 241003 China Division of Computational Science E-Institutes of Shanghai Universities at Shanghai Jiaotong University Shanghai 200240 China State Key Laboratory of Numerical Modeling for Atmospheric Sciencens and Geophysical Fluid Dynamic Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China Department of Mathematics and Computer Science Fuqing Branch of Fujian Normal University Fuqing 350300 China

A coupled system of the interdecadal sea-air oscillator model is studied. The E1 Nifio-southem oscillation （ENSO） atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The oscillator model is involved with the variations of both the eastern and western Pacific anomaly pat- terns. This paper proposes an ENSO atmospheric physics model using a method of the perturbation theory. The aim is to create an asymptotic solving method for the ENSO model. Employing the perturbed method, the asymptotic solution of corresponding problem is obtained, and the asymptotic behaviour of the solution is studied. Thus we can obtain the prognoses of the sea surface temperature anomaly and related physical quantities.

关键词： nonlinear equation perturbation E1 Nifio-southern oscillator model interdecadal sea-air oscillator

Homotopic Mapping Solving Method for Perturbed Mechanism of Western Boundary Undercurrents in Equator Pacific

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Chinese Geographical Science 2006年第4期16卷 347-350页

作者： MO Jiaqi WANG Hui lin wantao Department of Mathematics Anhui Normal University Wuhu 241000 China Division of Computational Science E-Instilutes of Shanghai Universities Shanghai Jiaotong University Shanghai 200240 China Department of Mathematics Huzhou Teachers College Huzhou 313000 China Chinese Academy of Meteorological Sciences Beijing 100081 China LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China

The perturbed boundary undercurrent is an exceptional event in the tropical atmosphere and ocean. It is a complicated nonlinear system. Its appearance badly affects not only natural conditions such as climate and environment, but also global economic development and human living, and brings about many calamities. Thus there is very attractive study on its rules in the international academic circles. Many scholars made more studies on its local and whole behaviors using different methods, such as self-anamnestic principle, Fokker-Plank Equation method, higher order singular pedigree and predictable study, rapid change on boundary, indeterminate adaptive control, multi-eogradient method and so on. Nonlinear perturbed theory and approximate method are very attractive studies in the international academic circles. Many scholars considered a class of nonlinear problems for the ordinary differential equation, the reaction diffusion equations, the boundary value of elliptic equation, the initial boundary value of hyperbolic equation, the shock layer solution of nonlinear equation and so on. In this paper, a class of perturbed mechanism for the western boundary undercurrents in the equator Pacific is considered. Under suitable conditions, using a homotopic mapping theory and method, we obtain a simple and rapid arbitrary order approximate solution for the corresponding nonlinear system. For example, a special case shows that using the homotopic mapping method, there is a high accuracy for the computed value. It is also provided from the results that the solution for homotopic mapping solving method can be used for analyzing operator for perturbed mechanism of western boundary undercurrents in the equator Pacific.

关键词： undercurrent perturbation approximate solution equator Pacific

Singularly Perturbed Solution of Coupled Model in Atmosphere-ocean for Global Climate

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Chinese Geographical Science 2008年第2期18卷 193-196页

作者： MO Jiaqi lin wantao WANG Hui Department of Mathematics Anhui Normal University Wuhu 241000 China Division of Computational Science E-Institutes of Shanghai Universities at SJTU Shanghai 200240 China Huzhou Teachers College Huzhou 313000 China LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China Chinese Academy ofMeteorological Sciences Beijing 100081 China

A box model of the interhemispheric thermohaline circulation (THC) in atmosphere-ocean for global cli-mate is considered. By using the multi-scales method, the asymptotic solution of a simplified weakly nonlinear model is discussed. Firstly, by introducing first scale, the zeroth order approximate solution of the model is obtained. Sec-ondly, by using the multi-scales, the first order approximate equation of the model is found. Finally, second order ap-proximate equation is formed to eliminate the secular terms, and a uniformly valid asymptotic expansion of solution is decided. The multi-scales solving method is an analytic method which can be used to analyze operation sequentially. And then we can also study the diversified qualitative and quantitative behaviors for corresponding physical quantities. This paper aims at providing a valid method for solving a box model of the nonlinear equation.

关键词： atmosphere-ocean El Nino-Southern Oscillation singular perturbation approximate solution

Spatial and temporal variation characteristics of ocean waves in the South China Sea during the boreal winter

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Acta Oceanologica Sinica 2015年第1期34卷 23-28页

作者： ZHU Geli lin wantao ZHAO Sen CAO Yanhua State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric PhysicsChinese Academy of Sciences Department of Mathematics and Physics North China Electric Power University University of Chinese Academy of Sciences

The spatial and temporal variation characteristics of the waves in the South China Sea （SCS） in the boreal winter during the period of 1979/1980-2011/2012 have been investigated based on the European Centre for Medium-range Weather Forecasts interim （ERA-Interim） reanalysis dataset. The results show that the lead- ing mode of significant wave height anomalies （SWHA） in the SCS exhibits significant interannual variation and a decadal shift around the mid-1990s, and features a basin-wide pattern in the entire SCS with a center located in the west of the Luzon Strait. The decadal change from a weak regime to a strong regime is mainly associated with the enhancement of winter monsoon modulated by the Pacific decadal oscillation （PDO）. The interannual variation of the SWHA has a significant negative correlation with the E1 Nino Southern Oscillation （ENSO） in the same season and the preceding autumn. For a better understanding of the physi- cal mechanism between the SCS ocean waves and ENSO, further investigation is made by analyzing atmo- spheric circulation. The impact of the ENSO on the SWHA over the SCS is bridged by the East Asian winter monsoon and Pacific-East Asian teleconnection in the lower troposphere. During the E1 Nino （La Nino）, the anomalous Philippine Sea anticyclone （cyclone） dominates over the Western North Pacific, helps to weaken （enhance） East Asian winter monsoon and then emerges the negative （positive） SWHA in the SCS.

关键词： ocean waves interannual variability South China Sea ENSO PDO

Variational iteration solving method for El Nio phenomenon atmospheric physics of nonlinear model

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Acta Oceanologica Sinica 2005年第5期24卷 35-38页

作者： MO Jiaqi WANG Hui lin wantao lin Yihua Anhui Normal University Wuhu 241000 China Division of Computional Science E-Institute of Shanghai Universities Shanghai Jiaotong University Shanghai 200240 China Chinese Academy of Meteorological Sciences Beijing 100081 China State Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmosheric Physics Chinese Academy of Sciences Beijing 100029 China

A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conceptual oscillator model should consider the variations of both the eastern and western Pacific anomaly patterns. An E1 Niйo atmospheric physics model is proposed using a method for the variational iteration theory. Using the variational iteration method, the approximate expansions of the solution of corresponding problem are constructed. That is, firstly, introducing a set of functional and accounting their variationals, the Lagrange multiplicators are counted, and then the variational iteration is defined, finally, the approximate solution is obtained. From approximate expansions of the solution, the zonal sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the sea-air oscillation for E1 Niйo atmospheric physics model can be analyzed. E1 Niйo is a very complicated natural phenomenon. Hence basic models need to be reduced for the sea-air oscillator and are solved. The variational iteration is a simple and valid approximate method.

关键词： nonlinear variational iteration method E1 Niйo phenomenon

A new method for judging the computational stability of the difference schemes of nonlinear evolution equations

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Chinese Science Bulletin 2000年第15期45卷 1358-1361页

作者： lin wantao Jl Zhongzhen WANG Bin YANG Xiaozhong State Key Laboratory of Numerical Modeling for Atmospheric Science and Geophysical Fluid Dynamics Institute of Atmospheric PhysicsChinese Academy of SciencesBeijing 100029China North China Electric Power University Beijing 102206China

For the non-conservative difference schemes of nonlinear evolution equations with aperiodic boundary conditions, taken one-dimensional nonlinear advection equation as an example, a new method for judging the computational stability is given. It is proved to be practical and effective through several numerical examples. The stability criteria obtained by this method are really the necessary conditions of computational stability.

关键词： nonlinear evolution equation difference scheme computational stability heuristic analysis.