扰动厄尔尼诺/拉尼娜-南方涛动模型的解

谢峰; 林一骅; 林万涛; 莫嘉琪

doi:10.7498/aps.60.010201

摘要

厄尔尼诺/拉尼娜-南方涛动(ENSO)是一个包括在赤道太平洋中海-气交互作用的年际现象. 本文创建一个求解ENSO模型非线性方程的近似方法. 并在这基础上借助同伦映射方法研究了一类ENSO模型振子模型的近似解与精确解. 同时讨论了近似解的精度. 从得到的结果看出,同伦映射方法能够用于分析ENSO模型在赤道东太平洋中的SST异常和气-海振荡的温跃层深度异常.

关键词:

非线性 /
同伦映射 /
摄动 /
ENSO模型

The EI Ni o/La Ni a and the Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific Ocean-atmosphere interactions. This paper, aims at creating an approximate solving method of nonlinear equation for the ENSO models. And based on a class of oscillator of ENSO models, employing the method of homotopic mapping, the approximate and exact solutions of the corresponding problem is studied. The accuracy of approximate solution is discussed. It is proved from the results that homotopic method can be used for analyzing the SST anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for ENSO model.

Keywords:

作者及机构信息

(1)LASG,中国科学院大气物理研究所,北京 100029; (2)东华大学理学院,上海 201620; 上海高校计算科学E-研究院SJTU研究所,上海 200240; (3)上海高校计算科学E-研究院SJTU研究所,上海 200240; 安徽师范大学数学系,芜湖 241003

基金项目: 国家自然科学基金(批准号:40876010,10701023), 中国科学院知识创新工程重要方向项目(批准号:KZCX2-YW-Q03-08), 公益性行业科研专项(批准号:GYHY200806010), LASG国家重点实验室专项经费, 中央高校基本科研业务费重点项目(批准号:2010B08-2-1), 上海市教育委员会E-研究院建设计划项目(批准号:E03004)和浙江省自然科学基金(批准号:Y6090164) 资助的课题.

Authors and contacts

(1)College of Science, Donghua University, Shanghai 201620, China; Division of Computational Science, E-Institutes of Shanghai Universities, at SJTU, Shanghai 200240, China; (2)Division of Computational Science, E-Institutes of Shanghai Universities, at SJTU, Shanghai 200240, China; Anhui Normal University, Wuhu 241003, China; (3)LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China

参考文献

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[2]	McCreary J P, Anderson D L T 1984 Mon. Wea. Rev. 112 934
[3]	Cane M A, Zebiak S E 1985 228 1084
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[31]	Liu S K, Fu Z T, Liu S D 2002 Chin. Phys. Sin. 2002 51 10 (in Chinese) [刘式适、付遵涛、刘式达、赵强 2002物理学报51 10]
[32]	Lin W T, Ji Z Z, Wag B 2003 Chinese Science Bulletin 48 999
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[36]	Mo J Q, Lin W T 2005 Chin. Phys. 14 875
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[40]	de Jager E M, Jiang F 1996 The Theory of Singular Perturbation (Amsterdam: North-Holland Publishing Co)
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[42]	Hovhannisyan G, Vulanovic 2008 Nonlinear Stud. 15 297
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[45]	Mo J Q, Zhang W J, He M 2007 Acta Phys. Sin. 56 1843 (in Chinese) [莫嘉琪、张伟江、何铭 2007 物理学报 56 1843]
[46]	Mo J Q, Zhang W J, Chen X F 2007 Acta Phys. Sin. 56 6169 (in Chinese) [莫嘉琪、张伟江、陈贤峰 2007 物理学报 56 6689]
[47]	Mo J Q 2009 Acta Phys. Sin. 58 695 (in Chinese) [莫嘉琪 2009 物理学报 58 695]
[48]	Mo J Q, Yao J S 2009 Acta Phys. Sin. 58 7419 (in Chinese) [莫嘉琪、姚静荪 2009 物理学报 58 7419]
[49]	Mo J Q 2009 Acta Phys. Sin 58 2930 (in Chinese) [莫嘉琪 2008 物理学报 58 2930]
[50]	Mo J Q, Cheng Yan 2009 Acta Phys. Sin. 58 4379 (in Chinese) [莫嘉琪、陈燕 2009 物理学报 58 4379]
[51]	Mo J Q 2009 Science in China,Ser. G 52 1007
[52]	Mo J Q, Chen X F 2010 Acta Phys. Sin. 50 1403 (in Chinese) [莫嘉琪、陈贤蜂 2010 物理学报 501403]
[53]	Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys.B 19030202
[54]	Mo J Q 2010 Chin. Phys. B 19 010203
[55]	Liao S J, Chang A T 1998 ASME J.Appl. Mech. 65 914
[56]	Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method (New York: CRC Press Co)
[57]	Jin F F 1997 J. Atmos. Sci. 54 811
[58]	Wang C 2001 Advances in Atmospheric Sciences 18 674

施引文献

[1]	Bjerknes J A 1996 Tellus. 18 820
[2]	McCreary J P, Anderson D L T 1984 Mon. Wea. Rev. 112 934
[3]	Cane M A, Zebiak S E 1985 228 1084
[4]	Anderson D L T, McCreary J P 1985 J. Atmos. Sci. 42 615
[5]	Zebiak S E, Cane M A 1987 Mon. Wea. Rev. 115 2262
[6]	Schopf P S, Suarez M J 1988 J. Atmos. Sci. 45 549
[7]	Philander S G, Lau N C, Pacanowski R C 1989 Philos. Trans. Roy. Soc. London Ser. A 329 167
[8]	Latif M, Sterl A, Maier-Reimer E 1993 J. Climate 6 700
[9]	Neelin J D 1989 Philos. Trans. Roy. Soc. London Ser. A 329 189
[10]	Neelin J D 1990 J. Atmos. Sci. 47 674
[11]	Bjerknes J 1969 Mon. Wea. Rev. 97 163
[12]	Neelin J D, Latif M, Jin F F 1994 Annu. Rev. Fluid Mech. 26 617
[13]	McWilliams J C, Gent P R 1991 J. Atmos. Sci. 35 962
[14]	Lau K M 1981 J. Atmos. Sci. 38 248
[15]	McCreary J P 1983 Mon. Wea. Rev. 111 370
[16]	Philander S G. H, Yamagata T, Pacanowski R C 1984 J. Atmos. Sci. 41 604
[17]	Gill A E 1985 Elsevier Oceanography Series 40 303
[18]	Yamagata T 1985 Elsevier Oceanography Series 40 637
[19]	Hirst A C 1986 J. Atmos. Sci. 43 606
[20]	Xie S P, Kubikawa A, Hanawa K 1989 J. Climate 2 946
[21]	Wakata, Y, Sarachik E S 1991 J. Atmos .Sci. 48 2060
[22]	Jin F F, Neelin J D 1993 J. Atmos. Sci. 50 3523
[23]	Jin F F, Neelin J D, Ghil M 1994 Science 264 70
[24]	Wang C, Weisberg R H, Virmani J I 1999 J. Geophys. Res. 104 5131
[25]	Wang B, Wang Y 1996 J. Climate 9 1586
[26]	Cane M A, Munnich M, Zebiak S E 1990 J. Atmos. Sci. 47 1562
[27]	Wang B, Fang Z 1996 J. Atmos. Sci. 53 2786
[28]	Wang B, Barcilon A, Fang Z 1999 J. Atmos. Sci. 56 5
[29]	Dai XG, Wang A H, Chou J F 2001 Chin. Phys. Sin. 50 606 (in Chinese) [戴新刚、王爱慧、丑纪范 2001 物理学报 50 606]
[30]	Feng G L, Dong W J, Jia X J 2002 Chin. Phys. Sin. 51 1181 (in Chinese) [封国林、董文杰、贾晓静、曹鸿兴 2002物理学报51 1181]
[31]	Liu S K, Fu Z T, Liu S D 2002 Chin. Phys. Sin. 2002 51 10 (in Chinese) [刘式适、付遵涛、刘式达、赵强 2002物理学报51 10]
[32]	Lin W T, Ji Z Z, Wag B 2003 Chinese Science Bulletin 48 999
[33]	Lin W T, Mo J Q 2003 Chinese Science Bulletin 48(Ⅱ) 5
[34]	Mo J Q, Lin W T 2004 Acta Phys. Sin. 53 996 (in Chinese) [莫嘉琪、林万涛 2004 物理学报 53 996]
[35]	Mo J Q, Lin W T 2004 Acta Phys. Sin. 53 996 (in Chinese) [莫嘉琪、林万涛 2004 物理学报 53 996]
[36]	Mo J Q, Lin W T 2005 Chin. Phys. 14 875
[37]	Mo J Q, Lin W T, Wang H 2009 Acta Math. Sin. 29 101 (in Chinese) [莫嘉琪、林万涛 2009 物理学报 59 101]
[38]	Mo J Q, Lin W T 2008 Chin. Phys. B 17 370
[39]	Mo J Q, Lin W T 2008 Chin. Phys. B 17 743
[40]	de Jager E M, Jiang F 1996 The Theory of Singular Perturbation (Amsterdam: North-Holland Publishing Co)
[41]	Sagon G 2008 Nonlinearity 21 1183
[42]	Hovhannisyan G, Vulanovic 2008 Nonlinear Stud. 15 297
[43]	Barbu L, Cosma 2009 J. Math. Anal. Appl. 351 392
[44]	Ramos M 2009 J. Math. Anal. Appl. 352 246
[45]	Mo J Q, Zhang W J, He M 2007 Acta Phys. Sin. 56 1843 (in Chinese) [莫嘉琪、张伟江、何铭 2007 物理学报 56 1843]
[46]	Mo J Q, Zhang W J, Chen X F 2007 Acta Phys. Sin. 56 6169 (in Chinese) [莫嘉琪、张伟江、陈贤峰 2007 物理学报 56 6689]
[47]	Mo J Q 2009 Acta Phys. Sin. 58 695 (in Chinese) [莫嘉琪 2009 物理学报 58 695]
[48]	Mo J Q, Yao J S 2009 Acta Phys. Sin. 58 7419 (in Chinese) [莫嘉琪、姚静荪 2009 物理学报 58 7419]
[49]	Mo J Q 2009 Acta Phys. Sin 58 2930 (in Chinese) [莫嘉琪 2008 物理学报 58 2930]
[50]	Mo J Q, Cheng Yan 2009 Acta Phys. Sin. 58 4379 (in Chinese) [莫嘉琪、陈燕 2009 物理学报 58 4379]
[51]	Mo J Q 2009 Science in China,Ser. G 52 1007
[52]	Mo J Q, Chen X F 2010 Acta Phys. Sin. 50 1403 (in Chinese) [莫嘉琪、陈贤蜂 2010 物理学报 501403]
[53]	Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys.B 19030202
[54]	Mo J Q 2010 Chin. Phys. B 19 010203
[55]	Liao S J, Chang A T 1998 ASME J.Appl. Mech. 65 914
[56]	Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method (New York: CRC Press Co)
[57]	Jin F F 1997 J. Atmos. Sci. 54 811
[58]	Wang C 2001 Advances in Atmospheric Sciences 18 674

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