Advanced Search
Impact Factor: 5.8

Volume 13 Issue 2

Apr.  1996

Article Contents
Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 1996 >  13(2): 203-216

On the Nonlinear Stability of Three-Dimensional Quasigeostrophic Motions in Spherical Geometry

  • 1.

    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/BF02656863

  • Nonlinear Mobility criteria for the motions geoverned by three-dimensional quasigeostrophic model in spherical geometry are obtained by using Arnol’d’s variational principle and a priori estimate method. The results gained in this paper are parallel to Arnol’d’s second theorem and better than the known results. Especially, under the approxima-tion of vertically integrated nondivergency, criteria corresponding to Arnol’d’s second theorem are first established by a detailed analysis.
  • [1] Mu Mu, Wu Yonghui, Tang Mozhi, Liu Haiyan, 1999: Nonlinear Stability Analysis of the Zonal Flows at Middle and High Latitudes, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 569-580.  doi: 10.1007/s00376-999-0032-1
    [2] 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
    [3] 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
    [4] 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
    [5] 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
    [6] LI Xingliang, CHEN Dehui, PENG Xindong, XIAO Feng, CHEN Xiongshan, 2006: Implementation of the Semi-Lagrangian Advection Scheme on a Quasi-Uniform Overset Grid on a Sphere, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 792-801.  doi: 10.1007/s00376-006-0792-9
    [7] 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
    [8] He Jianzhong, 1994: Nonlinear Ultra-Long Wave and Its Stability, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 91-100.  doi: 10.1007/BF02656998
    [9] H.L. Kuo, 1995: Three-dimensional Global Scale Permanent-wave Solutions of the Nonlinear Quasigeostrophic Potential Vorticity Equation and Energy Dispersion, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 387-404.  doi: 10.1007/BF02657001
    [10] Mu Mu, Guo Huan, Wang Jiafeng, LiYong, 2000: The Impact of Nonlinear Stability and Instability on the Validity of the Tangent Linear Model, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 375-390.  doi: 10.1007/s00376-000-0030-9
    [11] 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
    [12] 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
    [13] 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
    [14] Yang Fanglin, 1991: The Stability of Large-Scale Horizontal Air Motion in the Non-linear Basic Zephyr Flow under the Effect of Rossby Parameter, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 149-164.  doi: 10.1007/BF02658091
    [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 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
    [17] Mu Mu, Xiang Jie, 1998: On the Evolution of Finite-amplitude Disturbance to the Barotropic and Baroclinic Quasigeostrophic Flows, ADVANCES IN ATMOSPHERIC SCIENCES, 15, 113-123.  doi: 10.1007/s00376-998-0023-7
    [18] Yi ZHANG, Rucong YU, Jian LI, 2017: Implementation of a Conservative Two-step Shape-Preserving Advection Scheme on a Spherical Icosahedral Hexagonal Geodesic Grid, ADVANCES IN ATMOSPHERIC SCIENCES, 34, 411-427.  doi: 10.1007/s00376-016-6097-8
    [19] Jinhe YU, Lei BI, Wei HAN, Xiaoye ZHANG, 2022: Application of a Neural Network to Store and Compute the Optical Properties of Non-Spherical Particles, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 2024-2039.  doi: 10.1007/s00376-021-1375-5
    [20] Xiao Qingnong, Wu Rongsheng, 1995: A Study on Frontal Motion over Orography, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 325-334.  doi: 10.1007/BF02656981
PDF

Get Citation+

shu
Export:  

Share Article

Article Metrics

Article Views: 1221 Times

PDF downloads: 909 Times

Cited by: Times
  • 加载中

    • Manuscript History

    Manuscript received: 10 April 1996
    Manuscript revised: 10 April 1996
    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

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    On the Nonlinear Stability of Three-Dimensional Quasigeostrophic Motions in Spherical Geometry

    • 1. LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
    • Manuscript received: 1996-04-10
    • Manuscript revised: 1996-04-10

    Abstract: Nonlinear Mobility criteria for the motions geoverned by three-dimensional quasigeostrophic model in spherical geometry are obtained by using Arnol’d’s variational principle and a priori estimate method. The results gained in this paper are parallel to Arnol’d’s second theorem and better than the known results. Especially, under the approxima-tion of vertically integrated nondivergency, criteria corresponding to Arnol’d’s second theorem are first established by a detailed analysis.

      HTML

    Catalog

      Publish with AAS

      Contact us

      Links

      Copyright © 2018-2028 ADVANCES IN ATMOSPHERIC SCIENCES 京ICP备14024088号-7

      Supported by: Beijing Renhe Information Technology Co. Ltd  support: info@rhhz.net  

      /

      DownLoad:  Full-Size Img  PowerPoint
      Return
      Return