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Volume 9 Issue 3

Jul.  1992

Article Contents
Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 1992 >  9(3): 337-345

A Problem Related to Nonlinear Stability Criteria for Multi-layer Quasi-geostrophic Flow

  • 1.

    Institute of Mathematics, Anhui University, Hefei 230939,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100080


doi: 10.1007/BF02656943

  • The second author studied the nonlinear stability of N-layer quasi－geostrophic flow subject to perturbations of parameters and initial data, and established the stability criteria for the flow in question, which involve finding out the lowest eigenvalue of an elliptic boundary value problem.In this paper when the domain is a periodic zonal channel, a formula of the lowest eigenvalue is established, which is useful for further studies and practical applications.
  • [1] 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
    [2] 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
    [3] 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
    [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] 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
    [6] Zhao Ming, 1991: The Effect of Topography on Quasi-Geostrophic Frontogenesis, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 23-40.  doi: 10.1007/BF02657362
    [7] 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
    [8] Liu Shikuo, He Anguo, 1991: A Simple Quasi-Geostrophic Coupled Ocean-Atmosphere Model, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 257-271.  doi: 10.1007/BF02919608
    [9] Zeng Xinmin, Zhao Ming, Su Bingkai, Wang Hanjie, 1999: Study on a Boundary-layer Numerical Model with Inclusion of Heterogeneous Multi-layer Vegetation, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 431-442.  doi: 10.1007/s00376-999-0021-4
    [10] 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
    [11] 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
    [12] 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
    [13] 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
    [14] Wu Rongsheng, 1985: THE INFLUENCES OF OROGRAPHY UPON THE FLOW WITHIN EKMAN BOUNDARY LAYER UNDER THE APPROXIMATION OF GEOSTROPHIC MOMENTUM, ADVANCES IN ATMOSPHERIC SCIENCES, 2, 1-7.  doi: 10.1007/BF03179731
    [15] Fang Juan, Wu Rongsheng, 2002: Energetics of Geostrophic Adjustment in Rotating Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 845-854.  doi: 10.1007/s00376-002-0049-1
    [16] Xie Zhenghui, Dai Yongjiu, Zeng Qingcun, 1999: An Unsaturated Soil Water Flow Problem and Its Numerical Simulation, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 183-196.  doi: 10.1007/BF02973081
    [17] He Jianzhong, 1994: Nonlinear Ultra-Long Wave and Its Stability, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 91-100.  doi: 10.1007/BF02656998
    [18] Ren Shuzhan, 1994: Note on the Symmetric Stability of Quasi-Homogeneous and Incompressible Rotating Ocean, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 74-78.  doi: 10.1007/BF02656996
    [19] 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
    [20] Lin Wantao, Ji Zhongzhen, Wang Bin, 2001: Computational Stability of the Explicit Difference Schemes of the Forced Dissipative Nonlinear Evolution Equations, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 413-417.  doi: 10.1007/BF02919320
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    • Manuscript History

    Manuscript received: 10 July 1992
    Manuscript revised: 10 July 1992
    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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    A Problem Related to Nonlinear Stability Criteria for Multi-layer Quasi-geostrophic Flow

    • 1. Institute of Mathematics, Anhui University, Hefei 230939,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100080
    • Manuscript received: 1992-07-10
    • Manuscript revised: 1992-07-10

    Abstract: The second author studied the nonlinear stability of N-layer quasi－geostrophic flow subject to perturbations of parameters and initial data, and established the stability criteria for the flow in question, which involve finding out the lowest eigenvalue of an elliptic boundary value problem.In this paper when the domain is a periodic zonal channel, a formula of the lowest eigenvalue is established, which is useful for further studies and practical applications.

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