海-气耦合气候系统非线性扰动模式的周期正解

陈丽娟; 鲁世平; 徐晶

doi:10.21656/1000-0887.370188

海-气耦合气候系统非线性扰动模式的周期正解

doi: 10.21656/1000-0887.370188

南京信息工程大学数学与统计学院, 南京 210044

基金项目: 国家自然科学基金(11271197)；江苏省普通高校研究生科研创新计划项目(CXLX13_502)

详细信息

作者简介:
陈丽娟（1973—），女，副教授，博士(通讯作者. E-mail: cljung@sohu.com).

中图分类号: O175
计量
- 文章访问数: 917
- HTML全文浏览量: 142
- PDF下载量: 625
- 被引次数: 0
出版历程
- 收稿日期: 2016-06-14
- 修回日期: 2016-08-02
- 刊出日期: 2017-04-15

Positive Periodic Solutions to the Nonlinear Disturbed Model for Sea-Air Coupling Climate Systems

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P.R.China

Funds: The National Natural Science Foundation of China(11271197)

摘要

摘要: 与ENSO相关的热带大尺度海-气相互作用是影响全球气候年际变化的主要过程之一.该文从一个海-气相互作用方程组出发，推广了一个具有一般形式的海气耦合气候系统非线性扰动模式.运用拓扑度理论，从数学上严格证明了一定条件下该模式存在周期正解的结果，并分析了所得结果潜在的应用价值.海-气相互作用研究，有助于理解气候变化过程，为气候模拟和预报提供理论基础.
- 海-气耦合 /
- 非线性 /
- 周期正解
Abstract: The focus was given on the tropical large-scale ocean-atmosphere interaction associated with ENSO, which was considered as one of the most important mechanisms for the global inter-annual climate variability. From a group of sea-air coupling equations, a nonlinear disturbed model was built for sea-air coupling climate systems. Based on the continuation theorem of Mawhin’s coincidence degree, the existence of positive periodic solutions to a class of nonlinear problems was discussed. A strict proof of the existence of positive periodic solutions to the model was obtained, and the potential application value of the result was expected. The study of air-sea interaction, which helps to understand the process of climate variability, provides a theoretical basis for climate simulation and prediction.
- sea-air coupling /
- nonlinear /
- positive periodic solution

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参考文献(21)

[1]	CHAO Ji-ping, YUAN Shao-yu, CHAO Qing-chen, et al. A date analysis study on the evolution of the El Nio/La Nia cycle[J]. Advances in Atmospheric Sciences,2002,19(5): 837-844.
[2]	Teng H, Wang B. Interannual variations of the boreal summer intraseasonal oscillation in the Asian-Pacific region[J]. Journal of Climate,2003,16: 3571-3584.
[3]	Lin A, Li T. Energy spectrum characteristics of boreal summer intraseasonal oscillations: climatology and variations during the ENSO developing and decaying phases[J]. Journal of Climate,2008,21: 6304-6320.
[4]	Yang B, Wang Y, Wang B. The effect of internally generated inner-core asymmetries on tropical cyclone potential intensity[J]. Journal of the Atmospheric Sciences,2007,64: 1165-1188.
[5]	Zhuo G, Zeng Q. Predictions of ENSO with a coupled atmosphere-ocean general circulation model[J]. Advances in Atmosphere Sciences,2001,18(4): 587-603.
[6]	Luo J, Masson S, Behera S, et al. Extended ENSO predictions using a fully coupled ocean-atmosphere model[J]. Journal of Climate,2008,21: 84-93.
[7]	Yu J, Liu W T, Mechoso C R. An SST anomaly dipole in the northern subtropical Pacific and its relationships with ENSO[J]. Geophysical Research Letters,2000,27(13): 1931-1934.
[8]	Zhou T, Yu R, Li Z. ENSO-dependent and ENSO-independent variability over the mid-latitude North Pacific: observation and air-sea coupled model simulation[J]. Advances in Atmosphere Sciences,2002,19(6):1127-1147.
[9]	王雯, 徐燕, 鲁世平. 厄尔尼诺-南方涛动时滞海气振子耦合模型的周期解[J]. 物理学报, 2011,60(3): 030205.(WANG Wen, XU Yan, LU Shi-ping. The periodic solutions of a delayed sea-air oscillator coupling model for the ENSO[J]. Acta Physica Sinica,2011,60(3): 030205.(in Chinese))
[10]	LU Shi-ping, ZHENG Liang, CHEN Li-juan. Homoclinic solutions for a class of second order neutral function differential systems[J]. Acta Mathematica Scientia,2013,33(5): 1361-1374.
[11]	LIN Wan-tao, LIN Yi-hua, MO Jia-qi. Asymptotic solving method for a sea-air oscillator model of atmospheric physics[J]. Chinese Physics B,2012,21(1): 010204.
[12]	MO Jia-qi, LIN Wan-tao, LIN Yi-hua. Asymptotic solution for the El Nino time delay sea-air oscillator model[J]. Chinese Physics B,2011,20(7): 070205.
[13]	林万涛, 林一骅, 石兰芳, 等. 一类厄尔尼诺-南方涛动耦合振子动力学模型的震荡近似解[J]. 物理学报, 2013,62(14): 140202.(LIN Wao-tao, LIN Yi-hua, SHI Lan-fang, et al. Vibrating approximate solution for a class of El Nino-southern coupled oscillation dynamic model[J]. Acta Physica Sinica,2013,62(14): 140202.(in Chinese))
[14]	Mller J D, Shapiro L J. Influences of asymmetric heating on hurricane evolution in the MM5[J]. Journal of the Atmospheric Sciences, 2005,62: 3974-3992.
[15]	Hong C, Li T. The extreme cold anomaly over southeast Asia in February 2008: Roles of ISO and ENSO[J]. Journal of Climate,2009,22: 3786-3801.
[16]	Zhang R, Zebiak S E. An embedding method for improving interannual variability simulations in a hybrid coupled model of the tropical Pacific Ocean-atmosphere system[J]. Journal of Climate,2004,17: 2794-2812.
[17]	陈丽娟, 鲁世平. 零维气候系统非线性模式的周期解问题[J]. 物理学报, 2013,62(20): 200201.(CHEN Li-juan, LU Shi-ping. The problem of periodic solution of nonlinear model in zero-dimensional climate system[J]. Acta Physica Sinica,2013,62(20): 200201.(in Chinese))
[18]	陈丽娟, 鲁世平, 徐晶. 海气耦合随机-动力气候模式的周期解问题[J]. 应用数学和力学, 2015,36(10): 1085-1094. (CHEN Li-juan, LU Shi-ping, XU Jing. The periodic solution of stochastic-dynamic climate model with sea-air interaction[J]. Applied Mathematics and Mechanics,2015,36(10): 1085-1094.(in Chinese))
[19]	林振山. 海-气相互作用系统可能性态的研究[J]. 大气科学, 1991,15(4): 43-51.(LIN Zhen-shan. Studying of the behaviours and states of the sea-atmosphere climatic system[J]. Scientia Atmospherica Sinica,1991,15(4): 43-51.(in Chinese))
[20]	林振山. 气候建模·诊断和预测的研究[M]. 北京: 气象出版社, 1996.(LIN Zhen-shan. Climate Modeling: A Study of Diagnosis and Prediction [M]. Beijing: China Meteorological Press, 1996.(in Chinese))
[21]	Gaines R E, Mawhin J L. Coincidence Degree and Nonlinear Differential Equations [M]. Berlin: Springer, 1977.