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Volume 14 Issue 3

Jul.  1997

Article Contents
Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 1997 >  14(3): 355-368

A Finite-Mode Model of Ideal Fluid Dynamics on the 2-Sphere

  • 1.

    CRC for Southern Hemisphere Meteorology CSIRO Division or Atmospheric Research PMB I. Aspendale, Vic. 3195, Australia


doi: 10.1007/s00376-997-0056-3

  • We develop the finite-mode model for a two-dimensional Euler system on the sphere based on Hopped’s discovery in group theory. This model strives to keep as many invariants of the original Euler equation as possible. Theoretically, the number of invariants in this model is limited only by computing power. At present, almost all the popular numerical models in weather and climate researches such as numerical weather prediction models and general circulation models (GCMs) use spectral method. However all these spectrally truncated models do not keep all the invariants except for the energy and the enstrophy. By using this model one is able to study the influence from some other lost invariants. The result from this model is expected to be closer to that of the original Euler equations than from ordinary spectrally truncated models. The relevant fundamental equations and important formulas for this model are given explicitly.
  • [1] Mozheng Wei, 1996: A Low-order Model of Two-dimensional Fluid Dynamics on the Surface of a Sphere, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 67-90.  doi: 10.1007/BF02657029
    [2] Zhangcai QIN, Xi DENG, Bronson GRISCOM, Yao HUANG, Tingting LI, Pete SMITH, Wenping YUAN, Wen ZHANG, 2021: Natural Climate Solutions for China: The Last Mile to Carbon Neutrality, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 889-895.  doi: 10.1007/s00376-021-1031-0
    [3] Yong. L. McHall, 1990: Generalized Available Potential Energy, ADVANCES IN ATMOSPHERIC SCIENCES, 7, 395-408.  doi: 10.1007/BF03008870
    [4] ZHANG Ming, ZHAO Yanling, HUANG Hong, LIANG Danqing, 2007: The Generalized Energy Equation and Instability in the Two-layer Barotropic Vortex, ADVANCES IN ATMOSPHERIC SCIENCES, 24, 147-151.  doi: 10.1007/s00376-007-0147-1
    [5] Ji Zhongzhen, Wang Bin, Zhao Ying, Yang Hongwei, 2002: Total Energy Conservation and the Symplectic Algorithm, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 459-467.  doi: 10.1007/s00376-002-0079-8
    [6] Li Hongji, Xu Hong, Wang Ronghua, 1988: A HIGH-RESOLUTION ANALYSIS METHOD OF INSTABILITY ENERGY, ADVANCES IN ATMOSPHERIC SCIENCES, 5, 75-86.  doi: 10.1007/BF02657348
    [7] Shou Shaowen, Li Shenshen, 1991: Diagnosis of Kinetic Energy Balance of a Decaying Onland Typhoon, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 479-488.  doi: 10.1007/BF02919270
    [8] Runkua Yang, J. Shukla, P.J. Sellers, 1994: The Influence of Changes in Vegetation Type on the Surface Energy Budget, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 139-161.  doi: 10.1007/BF02666542
    [9] Yuan Zhuojian, Jian Maoqiu, 2001: Diagnostic Equations for the Walker Circulation, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 166-178.  doi: 10.1007/s00376-001-0011-7
    [10] Baofeng JIAO, Lingkun RAN, Na LI, Ren CAI, Tao QU, Yushu ZHOU, 2023: Comparative Analysis of the Generalized Omega Equation and Generalized Vertical Motion Equation, ADVANCES IN ATMOSPHERIC SCIENCES, 40, 856-873.  doi: 10.1007/s00376-022-1435-5
    [11] Yaokun LI, Jiping CHAO, Yanyan KANG, 2021: Variations in Wave Energy and Amplitudes along the Energy Dispersion Paths of Nonstationary Barotropic Rossby Waves, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 49-64.  doi: 10.1007/s00376-020-0084-9
    [12] Yaokun LI, Jiping CHAO, Yanyan KANG, 2022: Variations in Amplitudes and Wave Energy along the Energy Dispersion Paths for Rossby Waves in the Quasigeostrophic Barotropic Model, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 876-888.  doi: 10.1007/s00376-021-1244-2
    [13] Qiu Yongyan, 1993: On the Seasonal Transition and the Interannual Variability in Global Kinetic Energy at 500 hPa, Accompanied with Anomalies of Energy during the 1982 / 83 ENSO, ADVANCES IN ATMOSPHERIC SCIENCES, 10, 248-256.  doi: 10.1007/BF02919148
    [14] GAO Shouting, XU Pengcheng, LI Na, 2012: On the Generalized Ertel--Rossby Invariant, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 690-694.  doi: 10.1007/s00376-012-1145-5
    [15] YANG Shuai, GAO Shouting, LU Chungu, 2014: A Generalized Frontogenesis Function and Its Application, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 1065-1078.  doi: 10.1007/s00376-014-3228-y
    [16] LU Weisong, SHAO Haiyan, 2003: Generalized Nonlinear Subcritical Symmetric Instability, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 623-630.  doi: 10.1007/BF02915505
    [17] Liu Yangang, 1995: On the Generalized Theory of Atmospheric Particle Systems, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 419-438.  doi: 10.1007/BF02657003
    [18] Xinping XU, Shengping HE, Huijun WANG, 2020: Relationship between Solar Wind−Magnetosphere Energy and Eurasian Winter Cold Events, ADVANCES IN ATMOSPHERIC SCIENCES, 37, 652-661.  doi: 10.1007/s00376-020-9153-3
    [19] Xiang Jie, Sun Litan, 2002: Nonlinear Saturation of Baroclinic Instability in the Phillips Model: The Case of Energy, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 1079-1090.  doi: 10.1007/s00376-002-0066-0
    [20] ZUO Qunjie, GAO Shouting, and LÜ Daren, 2014: Eddy Kinetic Energy Study of the Snowstorm over Southern China in January 2008, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 972-984.  doi: 10.1007/s00376-013-3122-z
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    • Manuscript History

    Manuscript received: 10 July 1997
    Manuscript revised: 10 July 1997
    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 Finite-Mode Model of Ideal Fluid Dynamics on the 2-Sphere

    • 1. CRC for Southern Hemisphere Meteorology CSIRO Division or Atmospheric Research PMB I. Aspendale, Vic. 3195, Australia
    • Manuscript received: 1997-07-10
    • Manuscript revised: 1997-07-10

    Abstract: We develop the finite-mode model for a two-dimensional Euler system on the sphere based on Hopped’s discovery in group theory. This model strives to keep as many invariants of the original Euler equation as possible. Theoretically, the number of invariants in this model is limited only by computing power. At present, almost all the popular numerical models in weather and climate researches such as numerical weather prediction models and general circulation models (GCMs) use spectral method. However all these spectrally truncated models do not keep all the invariants except for the energy and the enstrophy. By using this model one is able to study the influence from some other lost invariants. The result from this model is expected to be closer to that of the original Euler equations than from ordinary spectrally truncated models. The relevant fundamental equations and important formulas for this model are given explicitly.

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