Dissipative Travelling Wave Solution for El Niño Tropic Sea-air Coupled Oscillator

WEN Zhaohui; LIN Wantao; LIN Yihua; MO Jiaqi

doi:10.1007/s11769-010-0275-x

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WEN Zhaohui, LIN Wantao, LIN Yihua, MO Jiaqi. Dissipative Travelling Wave Solution for El Niño Tropic Sea-air Coupled Oscillator[J]. Chinese Geographical Science, 2010, 20(3): 275-280. doi: 10.1007/s11769-010-0275-x

Citation:

WEN Zhaohui, LIN Wantao, LIN Yihua, MO Jiaqi. Dissipative Travelling Wave Solution for El Niño Tropic Sea-air Coupled Oscillator[J]. Chinese Geographical Science, 2010, 20(3): 275-280. doi: 10.1007/s11769-010-0275-x

Dissipative Travelling Wave Solution for El Niño Tropic Sea-air Coupled Oscillator

doi: 10.1007/s11769-010-0275-x

1.
Institute of Applied Mathematics, School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, China;
2.
State Key Laboratory of Numerical Modeling for Atmospheric and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China;
3.
Anhui Normal University, Wuhu 241000, China;
4.
Division of Computational Science, E-Institutes of Shanghai Universities at Shanghai Jiaotong Uinversity, Shanghai 200240, China

Funds: Under the auspices of National Natural Science Foundation of China (No.40876010);Main Direction Program of Knowledge Innovation Programs of Chinese Academy of Sciences (No.KZCX2-YW-Q03-08);R & D Special Fund for Public Welfare Industry (meteorology) (No.GYHY200806010);LASG State Key Laboratory Special Fund;Foundation of E-Institutes of Shanghai Municipal Education Commission (No.E03004);Natural Science Foundation of Zhejiang Province (No.Y6090164)

Received Date: 2009-12-25
Rev Recd Date: 2010-02-21
Publish Date: 2010-04-01

Abstract

El Niño 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.
- El Niñ,
- o-Southern Oscillator model,
- variational iteration,
- sea-air oscillator

References

[1]	An S I,Wang B,2000.Interaction change of the structure of the ENSO mode and its impact on ENSO frequency.Journal of Climate,13(12):2044-2055.
[2]	Bobkova A S,2005.The behavior of solutions of miltidimensional singularly perturbed systems with one fast variable.Differential Equations,41(1):22-32.DOI:10.1007/s10625-005-0131-4
[3]	de Jager E M,Jiang Furu,1996.The Theory of Singular Perturbation.Amsterdam:North-Holland Publishing.
[4]	Gu Daifang,Philander S G H,1997.Interdecadal climate fluctuations that depend on exchanges between the tropics and extratropics.Science,275(7):805-807.DOI:10.1126/sciance.275.5301.805
[5]	He Jihuan,2002.Approximate Nonlinear Analytical Methods in Engineering and Sciences.Zhengzhou:Henan Science and Technology Publisher.(in Chinese)
[6]	He Jihuan,2006.Some asymptotic methods for strongly nonlinear equations.International Journal of Modern Physics,B20(10):1141-1199.
[7]	Lin Wantao,Ji Zhongzhen,Wang Bin,2002.A comparative analysis of computational stability for linear and non-linear evolution equations.Advances in Atmospheric Sciences,19(4):699-704.
[8]	Lin Wantao,Mo Jiaqi,2004.Asymptotic behavior of perturbed solution for simple coupled ocean-atmosphere model for ENSO.Chinese Science Bulletin,48(Ⅱ):5-7.
[9]	Lin Yihua,Ceng Qingcun,1999.Kelvin waves in a simple air-sea coupled model in the tropics.Progress in Natural Science,9(3):211-215.
[10]	Lin Yihua,Ji Zhongzhen,Zeng Qingcun,1999.Meridional wind forced low frequency disturbances in the tropical ocean.Progress in Natural Science,9(7):532-538.
[11]	Marques I,2006.Existence and asymptotic behavior of solutions for a class of nonlinear elliptic equations with Neumann Ondition.Nonlinear Analysis,61(1):21-40.
[12]	McPhaden M J,Zhang D,2002.Slowdown of the meridional overturning circulation in the upper Pacific Ocean.Nature,415(3):603-608.DOI:10.10381415603a
[13]	Mo Jiaqi,2009a.Analytic solution for a class of generalized Sine-Gordon perturbation equation.Acta Physics Sinica,58(5):2930-2933.(in Chinese)
[14]	Mo Jiaqi,2009b.A class of homotopic solving method for ENSO model.Acta Mathematica Scientia,29(1):101-109.
[15]	Mo Jiaqi,2009c.Approximate solution of homotopic mapping to solitary for generalized nonlinear KdV system.Chinese Physics Letter,26(1):010204.
[16]	Mo Jiaqi,2009d.A variational iteration solving method for a class of generalized Boussinesq equations.Chinese Physics Letter,26(6):060202.
[17]	Mo Jiaqi,2009e.Homotopic mapping solving method for gain fluency of laser pulse amplifier.Science in China(Ser.G),39(5):568-661.
[18]	Mo Jiaqi,Lin Wantao,2008a.Asymptotic solution for a class of sea-air oscillator model for El-Nino-southern oscillation.Chinese Physics,17(2):370-372.
[19]	Mo Jiaqi,Lin Wantao,2008b.The homotopic method of travelling wave solution for El Nino tropic sea-air coupled oscillator.Chinese Physics,17(3):743-746.
[20]	Mo Jiaqi,Wang Hui,Lin Wantao,2006a.Singularly perturbed solution of a sea-air oscillator model for the ENSO.Chinese Physics,15(7):1450-1453.
[21]	Mo Jiaqi,Wang Hui,Lin Wantao,2006b.Homotopic method of solving a class of El Nino/La Nino Southern Oscillation sea-air oscillator.Chinese Physics,15(9):1927-1931.
[22]	Mo Jiaqi,Wang Hui,Lin Wantao et al.,2006c.Varitional iteration method foe solving the mechanism of the equatorial eastern El Ni(n)o-Southern Oscillation.Chinese Physics,15(4):671-675.
[23]	Mo Jiaqi,Lin Wantao,Wang Hui,2007a.Variational iteration solving method of a sea-air oscillator model for the ENSO.Progress in Natural Science,17(2):230-232.
[24]	Mo Jiaqi,Lin Wantao,Wang Hui,2007b.Variational iteration method for solving perturbed mechanism of western boundary undercurrents in the Pacific.Chinese Physics,16(4):951-964.
[25]	Ni Weiming,Wei Juncheng,2006.On positive solution concentrating on spheres for the Gierer-Meinhardt system.Journal of Differential Equations,221(1):158-189.
[26]	Nonaka M,Xie Shangping,McCreary J P,2001.Decadal variations in the subtropical cells and equatorial Pacific SST.Geophysical Research Letters,220(7):1116-1119.
[27]	Wang Bin,2002.A comparative analysis of computational stability for linear and non-linear evolution equations.Advances in Atmospheric Sciences,219(4):699-704.

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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

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Dissipative Travelling Wave Solution for El Niño Tropic Sea-air Coupled Oscillator

1. Institute of Applied Mathematics, School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, China;

2. State Key Laboratory of Numerical Modeling for Atmospheric and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China;

3. Anhui Normal University, Wuhu 241000, China;

4. Division of Computational Science, E-Institutes of Shanghai Universities at Shanghai Jiaotong Uinversity, Shanghai 200240, China

Received Date: 2009-12-25

Rev Recd Date: 2010-02-21

Publish Date: 2010-04-01

Key words:

Abstract: El Niño 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.

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Reference (27)

[1]	An S I,Wang B,2000.Interaction change of the structure of the ENSO mode and its impact on ENSO frequency.Journal of Climate,13(12):2044-2055.
[2]	Bobkova A S,2005.The behavior of solutions of miltidimensional singularly perturbed systems with one fast variable.Differential Equations,41(1):22-32.DOI:10.1007/s10625-005-0131-4
[3]	de Jager E M,Jiang Furu,1996.The Theory of Singular Perturbation.Amsterdam:North-Holland Publishing.
[4]	Gu Daifang,Philander S G H,1997.Interdecadal climate fluctuations that depend on exchanges between the tropics and extratropics.Science,275(7):805-807.DOI:10.1126/sciance.275.5301.805
[5]	He Jihuan,2002.Approximate Nonlinear Analytical Methods in Engineering and Sciences.Zhengzhou:Henan Science and Technology Publisher.(in Chinese)
[6]	He Jihuan,2006.Some asymptotic methods for strongly nonlinear equations.International Journal of Modern Physics,B20(10):1141-1199.
[7]	Lin Wantao,Ji Zhongzhen,Wang Bin,2002.A comparative analysis of computational stability for linear and non-linear evolution equations.Advances in Atmospheric Sciences,19(4):699-704.
[8]	Lin Wantao,Mo Jiaqi,2004.Asymptotic behavior of perturbed solution for simple coupled ocean-atmosphere model for ENSO.Chinese Science Bulletin,48(Ⅱ):5-7.
[9]	Lin Yihua,Ceng Qingcun,1999.Kelvin waves in a simple air-sea coupled model in the tropics.Progress in Natural Science,9(3):211-215.
[10]	Lin Yihua,Ji Zhongzhen,Zeng Qingcun,1999.Meridional wind forced low frequency disturbances in the tropical ocean.Progress in Natural Science,9(7):532-538.
[11]	Marques I,2006.Existence and asymptotic behavior of solutions for a class of nonlinear elliptic equations with Neumann Ondition.Nonlinear Analysis,61(1):21-40.
[12]	McPhaden M J,Zhang D,2002.Slowdown of the meridional overturning circulation in the upper Pacific Ocean.Nature,415(3):603-608.DOI:10.10381415603a
[13]	Mo Jiaqi,2009a.Analytic solution for a class of generalized Sine-Gordon perturbation equation.Acta Physics Sinica,58(5):2930-2933.(in Chinese)
[14]	Mo Jiaqi,2009b.A class of homotopic solving method for ENSO model.Acta Mathematica Scientia,29(1):101-109.
[15]	Mo Jiaqi,2009c.Approximate solution of homotopic mapping to solitary for generalized nonlinear KdV system.Chinese Physics Letter,26(1):010204.
[16]	Mo Jiaqi,2009d.A variational iteration solving method for a class of generalized Boussinesq equations.Chinese Physics Letter,26(6):060202.
[17]	Mo Jiaqi,2009e.Homotopic mapping solving method for gain fluency of laser pulse amplifier.Science in China(Ser.G),39(5):568-661.
[18]	Mo Jiaqi,Lin Wantao,2008a.Asymptotic solution for a class of sea-air oscillator model for El-Nino-southern oscillation.Chinese Physics,17(2):370-372.
[19]	Mo Jiaqi,Lin Wantao,2008b.The homotopic method of travelling wave solution for El Nino tropic sea-air coupled oscillator.Chinese Physics,17(3):743-746.
[20]	Mo Jiaqi,Wang Hui,Lin Wantao,2006a.Singularly perturbed solution of a sea-air oscillator model for the ENSO.Chinese Physics,15(7):1450-1453.
[21]	Mo Jiaqi,Wang Hui,Lin Wantao,2006b.Homotopic method of solving a class of El Nino/La Nino Southern Oscillation sea-air oscillator.Chinese Physics,15(9):1927-1931.
[22]	Mo Jiaqi,Wang Hui,Lin Wantao et al.,2006c.Varitional iteration method foe solving the mechanism of the equatorial eastern El Ni(n)o-Southern Oscillation.Chinese Physics,15(4):671-675.
[23]	Mo Jiaqi,Lin Wantao,Wang Hui,2007a.Variational iteration solving method of a sea-air oscillator model for the ENSO.Progress in Natural Science,17(2):230-232.
[24]	Mo Jiaqi,Lin Wantao,Wang Hui,2007b.Variational iteration method for solving perturbed mechanism of western boundary undercurrents in the Pacific.Chinese Physics,16(4):951-964.
[25]	Ni Weiming,Wei Juncheng,2006.On positive solution concentrating on spheres for the Gierer-Meinhardt system.Journal of Differential Equations,221(1):158-189.
[26]	Nonaka M,Xie Shangping,McCreary J P,2001.Decadal variations in the subtropical cells and equatorial Pacific SST.Geophysical Research Letters,220(7):1116-1119.
[27]	Wang Bin,2002.A comparative analysis of computational stability for linear and non-linear evolution equations.Advances in Atmospheric Sciences,219(4):699-704.

Dissipative Travelling Wave Solution for El Niño Tropic Sea-air Coupled Oscillator

doi: 10.1007/s11769-010-0275-x

Abstract

References

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通讯作者: 陈斌, bchen63@163.com

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