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Volume 5 Issue 3

Jul.  1988

Article Contents

NONLINEAR RESONANCE INTERACTIONS AND INDEX CYCLES IN THE ATMOSPHERE


doi: 10.1007/BF02656750

  • A barotropic spectral model is used to study the planetary-scale motions of an atmosphere whose wave ensemble modes are externally driven. Pertubations are induced by a barotropic analogue of thermal driving and by Ekman friction, bottom topography, and the vanished internal dissipation. The use of complete spectral expansions without truncation leads to that the nonlinear coupling equations between the low-index mode and the high-index mode are obtained by means of the random phase approximation and the projec-tion operator techniques. The nonlinear coupling equations are entirely equivalent to the Volterra systems in ecology.In the phase-plane, the orbits of the nonlinear coupling equations are the family of closed curves, indicat-ing a bound, and periodic motion. The qualitative behaviors of low-index and high-index modes as functions of time picture the motion of atmospheric flows, with exchanges of energy between the low-index mode and the high-index mode by nonlinear resonance interaction. It is suggested that the phenomenon of blocking be exponentially grown of the low-index mode, the atmospheric motion then evolved to the high-index mode due to relaxation process. The results therefore lead to a plausible hypothesis concerning index cycles in the atmosphere discussed by Lorenz’s early works.
  • [1] XU Xingkui, Jason K. LEVY, 2011: The Impact of Agricultural Practices in China on Land-Atmosphere Interactions, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 821-831.  doi: 10.1007/s00376-010-0007-2
    [2] ZENG Xiaodong, WANG Aihui, ZENG Qingcun, Robert E. DICKINSON, Xubin ZENG, Samuel S. P. SHEN, 2006: Intermediately Complex Models for the Hydrological Interactions in the Atmosphere-Vegetation-Soil System, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 127-140.  doi: 10.1007/s00376-006-0013-6
    [3] Shaofeng LIU, Michael HINTZ, Xiaolong LI, 2016: Evaluation of Atmosphere-Land Interactions in an LES from the Perspective of Heterogeneity Propagation, ADVANCES IN ATMOSPHERIC SCIENCES, 33, 571-578.  doi: 10.1007/s00376-015-5212-6
    [4] Zhu Xun, 1987: ON GRAVITY WAVE-MEAN FLOW INTERACTIONS IN A THREE DIMENSIONAL STRATIFIED ATMOSPHERE, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 287-299.  doi: 10.1007/BF02663599
    [5] Zhang Xuehong, 1985: THE SECOND ORDER APPROXIMATION TO THE NONLINEAR WAVE IN BAROTROPIC ATMOSPHERE, ADVANCES IN ATMOSPHERIC SCIENCES, 2, 167-177.  doi: 10.1007/BF03179749
    [6] Xu Youfeng, 1986: THE NONLINEAR INTERACTION BETWEEN DIFFERENT WAVE COMPONENTS AND THE PROCESS OF INDEX CYCLE OF GENERAL CIRCULATION, ADVANCES IN ATMOSPHERIC SCIENCES, 3, 478-488.  doi: 10.1007/BF02657937
    [7] Wang Zhiren, Wu Dexing, Chen Dake, Wu Huiding, Song Xuejia, Zhang Zhanhai, 2002: Critical Time Span and Nonlinear Action Structure of Climatic Atmosphere and Ocean, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 741-756.  doi: 10.1007/s00376-002-0013-0
    [8] Li Guoping, Lu Jinghua, 1996: Some Possible Solutions of Nonlinear Internal Inertial Gravity Wave Equations in the Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 244-252.  doi: 10.1007/BF02656866
    [9] JIANG Zhina, 2006: Applications of Conditional Nonlinear Optimal Perturbation to the Study of the Stability and Sensitivity of the Jovian Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 775-783.  doi: 10.1007/s00376-006-0775-x
    [10] Li Xianlang, 1987: ATTRACTOR SETS AND MULTIPLE EQUILIBRIA IN THE RESONANCE OF TOPOGRAPHICALLY FORCED WAVES, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 471-484.  doi: 10.1007/BF02656746
    [11] Zhong Qing, Ji Liren, 1992: A Further Study on an Extended Nonlinear Ocean-Atmosphere Coupled Hydrodynamic Characteristic System and the Abrupt Feature of ENSO Events, ADVANCES IN ATMOSPHERIC SCIENCES, 9, 131-146.  doi: 10.1007/BF02657504
    [12] Koji DAIRAKU, Seita EMORI, Toru NOZAWA, 2008: Impacts of Global Warming on Hydrological Cycles in the Asian Monsoon Region, ADVANCES IN ATMOSPHERIC SCIENCES, 25, 960-973.  doi: 10.1007/s00376-008-0960-1
    [13] YUAN Weihua, YU Rucong, LI Jian, 2013: Changes in the Diurnal Cycles of Precipitation over Eastern China in the Past 40 Years, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 461-467.  doi: 10.1007/s00376-012-2092-x
    [14] Xiquan DONG, 2018: Preface to the Special Issue: Aerosols, Clouds, Radiation, Precipitation, and Their Interactions, ADVANCES IN ATMOSPHERIC SCIENCES, 35, 133-134.
    [15] LI Jianping, Julian X.L.WANG, 2003: A New North Atlantic Oscillation Index and Its Variability, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 661-676.  doi: 10.1007/BF02915394
    [16] LI Jianping, ZENG Qingcun, 2003: A New Monsoon Index and the Geographical Distribution of the Global Monsoons, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 299-302.  doi: 10.1007/s00376-003-0016-5
    [17] Yao Dirong, 1988: THE NONLINEAR DISCRIMINANT AND STEPWISE NONLINEAR DISCRIMINANT ANALYSES, ADVANCES IN ATMOSPHERIC SCIENCES, 5, 27-34.  doi: 10.1007/BF02657343
    [18] Luo Dehai, Li Jianping, 2000: Barotropic Interaction between Planetary- and Synoptic-Scale Waves during the Life Cycles of Blockings, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 649-670.  doi: 10.1007/s00376-000-0026-5
    [19] XU Yongfu, HUANG Yao, LI Yangchun, 2012: Summary of Recent Climate Change Studies on the Carbon and Nitrogen Cycles in the Terrestrial Ecosystem and Ocean in China, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 1027-1047.  doi: 10.1007/s00376-012-1206-9
    [20] Luo Dehai, Li Jianping, Huang Fei, 2002: Life Cycles of Blocking Flows Associated with Synoptic-Scale Eddies: Observed Results and Numerical Experiments, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 594-618.  doi: 10.1007/s00376-002-0003-2

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Manuscript History

Manuscript received: 10 July 1988
Manuscript revised: 10 July 1988
通讯作者: 陈斌, bchen63@163.com
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NONLINEAR RESONANCE INTERACTIONS AND INDEX CYCLES IN THE ATMOSPHERE

  • 1. Center for Meteorology and Physical Oceanography, Massachusetts Institute of Technology, U.S.A.

Abstract: A barotropic spectral model is used to study the planetary-scale motions of an atmosphere whose wave ensemble modes are externally driven. Pertubations are induced by a barotropic analogue of thermal driving and by Ekman friction, bottom topography, and the vanished internal dissipation. The use of complete spectral expansions without truncation leads to that the nonlinear coupling equations between the low-index mode and the high-index mode are obtained by means of the random phase approximation and the projec-tion operator techniques. The nonlinear coupling equations are entirely equivalent to the Volterra systems in ecology.In the phase-plane, the orbits of the nonlinear coupling equations are the family of closed curves, indicat-ing a bound, and periodic motion. The qualitative behaviors of low-index and high-index modes as functions of time picture the motion of atmospheric flows, with exchanges of energy between the low-index mode and the high-index mode by nonlinear resonance interaction. It is suggested that the phenomenon of blocking be exponentially grown of the low-index mode, the atmospheric motion then evolved to the high-index mode due to relaxation process. The results therefore lead to a plausible hypothesis concerning index cycles in the atmosphere discussed by Lorenz’s early works.

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