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


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.
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    [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
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    [10] 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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    [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
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    [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
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    [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
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Manuscript History

Manuscript received: 10 April 1996
Manuscript revised: 10 April 1996
通讯作者: 陈斌, bchen63@163.com
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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

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.

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