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Volume 16 Issue 4

Oct.  1999

Article Contents
Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 1999 >  16(4): 569-580

Nonlinear Stability Analysis of the Zonal Flows at Middle and High Latitudes

  • 1.

    LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029


doi: 10.1007/s00376-999-0032-1

  • An attempt has been made to apply Arnol’d type nonlinear stability criteria to the diagnostic study of the persistence (stability) or breakdown (instability) of the atmospheric flows. In the case of the blocking high, the cut-off low and the zonal flow, the relationships of the geostrophic stream function versus the po-tential vorticity of the observed atmosphere are analyzed, which indicates that Arnol'd second type nonlinear stability theorem is more relevant to the observed atmosphere than the first one. For both the sta-ble and unstable zonal flows, Arnol’d second type nonlinear stability criteria are applied to the diagnosis. The primary results show that our analyses correspond well to the evolution of the atmospheric motions. The synoptically stable zonal flows satisfy Arnol'd second type nonlinear stability criteria; while the synoptically unstable ones violate the nonlinear stability criteria.
  • [1] LIU Yongming, CAI Jingjing, 2006: On Nonlinear Stability Theorems of 3D Quasi-geostrophic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 809-814.  doi: 10.1007/s00376-006-0809-4
    [2] Liu Yongming, 1999: Nonlinear Stability of Zonally Symmetric Quasi-geostrophic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 107-118.  doi: 10.1007/s00376-999-0007-2
    [3] Jie SONG, 2024: The Persistence and Zonal Scale of Atmospheric Dipolar Modes, ADVANCES IN ATMOSPHERIC SCIENCES, 41, 478-492.  doi: 10.1007/s00376-023-3023-8
    [4] Liu Yongming, Mu Mu, 1994: Arnol’d’s Second Nonlinear Stability Theorem for General Multilayer Quasi-geostrophic Model, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 36-42.  doi: 10.1007/BF02656991
    [5] Li Yang, Mu Mu, Wu Yonghui, 2000: A Study on the Nonlinear Stability of Fronts in the Ocean on a Sloping Continental Shelf, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 275-284.  doi: 10.1007/s00376-000-0009-6
    [6] Li Yang, Mu Mu, 1996: On the Nonlinear Stability of Three-Dimensional Quasigeostrophic Motions in Spherical Geometry, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 203-216.  doi: 10.1007/BF02656863
    [7] Liu Yongming, Mu Mu, 1992: A Problem Related to Nonlinear Stability Criteria for Multi-layer Quasi-geostrophic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 9, 337-345.  doi: 10.1007/BF02656943
    [8] Yang Hongwei, Wang Bin, Ji Zhongzhen, 2002: Application of the Artificial Compression Method to the Simulation of Two-Dimensional Frontogenesis, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 863-869.  doi: 10.1007/s00376-002-0051-7
    [9] Mu Mu, Zeng Qingcun, 1991: Criteria for the Nonlinear Stability of Three-Dimensional Quasi-Geostrophic Motions, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 1-10.  doi: 10.1007/BF02657360
    [10] Li Yang, 2000: Baroclinic Instability in the Generalized Phillips’ Model Part II: Three-layer Model, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 413-432.  doi: 10.1007/s00376-000-0033-6
    [11] Shenming FU, Jie CAO, Xingwen JIANG, Jianhua SUN, 2017: On the Variation of Divergent Flow: An Eddy-flux Form Equation Based on the Quasi-geostrophic Balance and Its Application, ADVANCES IN ATMOSPHERIC SCIENCES, 34, 599-612.  doi: 10.1007/s00376-016-6212-x
    [12] Shen Xinyong, Ni Yunqi, Ding Yihui, 2002: On Problem of Nonlinear Symmetric Instability in Zonal Shear Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 350-364.  doi: 10.1007/s00376-002-0027-7
    [13] Zhao Ping, 1991: The Effects of Zonal Flow on Nonlinear Rossby Waves, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 299-306.  doi: 10.1007/BF02919612
    [14] Zhao Ming, 1991: The Effect of Topography on Quasi-Geostrophic Frontogenesis, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 23-40.  doi: 10.1007/BF02657362
    [15] Ren Shuzhan, 1991: Nonlinear Stability of Plane Rotating Shear Flow under Three-Dimensional Nondivergence Disturbances, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 129-136.  doi: 10.1007/BF02658089
    [16] Liu Shikuo, He Anguo, 1991: A Simple Quasi-Geostrophic Coupled Ocean-Atmosphere Model, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 257-271.  doi: 10.1007/BF02919608
    [17] Li Liming, Huang Feng, Chi Dongyan, Liu Shikuo, Wang Zhanggui, 2002: Thermal Effects of the Tibetan Plateau on Rossby Waves from the Diabatic Quasi-Geostrophic Equations of Motion, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 901-913.  doi: 10.1007/s00376-002-0054-4
    [18] Chen Jiong, Liu Shikuo, 1998: The Solitary Waves of the Barotropic Quasi-Geostrophic Model with the Large-scale Orography, ADVANCES IN ATMOSPHERIC SCIENCES, 15, 404-411.  doi: 10.1007/s00376-998-0010-z
    [19] Zhang Minghua, Zeng Qingcun, 1999: Discrete Spectra and Continuous Spectrum of the Barotropic Quasi-Geostrophic Model-A Calculation of Meteorological Data, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 487-506.  doi: 10.1007/s00376-999-0026-z
    [20] He Jianzhong, 1994: Nonlinear Ultra-Long Wave and Its Stability, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 91-100.  doi: 10.1007/BF02656998
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    • Manuscript History

    Manuscript received: 10 October 1999
    Manuscript revised: 10 October 1999
    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

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    Nonlinear Stability Analysis of the Zonal Flows at Middle and High Latitudes

    • 1. LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
    • Manuscript received: 1999-10-10
    • Manuscript revised: 1999-10-10

    Abstract: An attempt has been made to apply Arnol’d type nonlinear stability criteria to the diagnostic study of the persistence (stability) or breakdown (instability) of the atmospheric flows. In the case of the blocking high, the cut-off low and the zonal flow, the relationships of the geostrophic stream function versus the po-tential vorticity of the observed atmosphere are analyzed, which indicates that Arnol'd second type nonlinear stability theorem is more relevant to the observed atmosphere than the first one. For both the sta-ble and unstable zonal flows, Arnol’d second type nonlinear stability criteria are applied to the diagnosis. The primary results show that our analyses correspond well to the evolution of the atmospheric motions. The synoptically stable zonal flows satisfy Arnol'd second type nonlinear stability criteria; while the synoptically unstable ones violate the nonlinear stability criteria.

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