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Volume 2 Issue 2

Apr.  1985

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NONLINEAR WAVES IN BAROTROPIC MODEL


doi: 10.1007/BF03179747

  • In this paper, from the system of equation describing a barotropic atmosphere using the method of Taylor expansion for the nonlinear terms, the periodic solutions of the nonlinear inertio-surface gravity waves and Rossby waves have been obtained.The finite-amplitude nonlinear inertio-surface gravity waves and Rossby waves with horizontal divergence satisfy all the KdV equation. The solutions are all the cnoidal function, i, e, the cnoidal waves which in-clude the linear waves and form the solitary waves under certain conditions. For the finite-amplitude Rossby waves with horizontal divergence, we find the new dispersive relation including both the wave number and the amplitude parameter. In case of small amplitude it is reduced to the Yeh formula. It is shown that the larger the amplitude and width, the faster the finite-amplitude inertio-surface gravity waves and the slower the finite-amplitude Rossby waves with horizontal divergence propagate. The blocking or cut-off system in which the amplitude and width are large may be considered as Rossby solitary waves.
  • [1] Luo Dehai, 1999: Nonlinear Three-Wave Interaction among Barotropic Rossby Waves in a Large-scale Forced Barotropic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 451-466.  doi: 10.1007/s00376-999-0023-2
    [2] 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
    [3] 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
    [4] Fu Zuntao, Liu Shikuo, Fu Caixia, 1998: Low-Frequency Waves Forced by Large-scale Topography in the Barotropic Model, ADVANCES IN ATMOSPHERIC SCIENCES, 15, 312-320.  doi: 10.1007/s00376-998-0003-y
    [5] Jie FENG, Ruiqiang DING, Jianping LI, Deqiang LIU, 2016: Comparison of Nonlinear Local Lyapunov Vectors with Bred Vectors, Random Perturbations and Ensemble Transform Kalman Filter Strategies in a Barotropic Model, ADVANCES IN ATMOSPHERIC SCIENCES, 33, 1036-1046.  doi: 10.1007/s00376-016-6003-4
    [6] Zhang Xuehong, Zeng Qingcun, Bao Ning, 1986: NONLINEAR BAROCLINIC HAURWITZ WAVES, ADVANCES IN ATMOSPHERIC SCIENCES, 3, 330-340.  doi: 10.1007/BF02678653
    [7] Liu Shida, Liu Shikuo, 1990: Advances in Studies on Nonlinear Atmospheric Waves, ADVANCES IN ATMOSPHERIC SCIENCES, 7, 227-244.  doi: 10.1007/BF02919161
    [8] Zhang Xuehong, 1985: THE SECOND ORDER APPROXIMATION TO THE NONLINEAR WAVE IN BAROTROPIC ATMOSPHERE, ADVANCES IN ATMOSPHERIC SCIENCES, 2, 167-177.  doi: 10.1007/BF03179749
    [9] ZHONG Wei, LU Han-Cheng, Da-Lin ZHANG, 2010: Mesoscale Barotropic Instability of Vortex Rossby Waves in Tropical Cyclones, ADVANCES IN ATMOSPHERIC SCIENCES, 27, 243-252.  doi: 10.1007/s00376-009-8183-7
    [10] Qin XU, Wei GU, GAO Shouting, 2005: Nonlinear Oscillations of Semigeostrophic Eady Waves in the Presence of Diffusivity, ADVANCES IN ATMOSPHERIC SCIENCES, 22, 49-57.  doi: 10.1007/BF02930869
    [11] Zhao Ping, 1991: The Effects of Zonal Flow on Nonlinear Rossby Waves, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 299-306.  doi: 10.1007/BF02919612
    [12] HUANG Feng, LIU Shikuo, 2004: Physical Mechanism and Model of Turbulent Cascades in a Barotropic Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 21, 34-40.  doi: 10.1007/BF02915678
    [13] Luo Dehai, Li Jianping, 2000: Barotropic Interaction between Planetary- and Synoptic-Scale Waves during the Life Cycles of Blockings, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 649-670.  doi: 10.1007/s00376-000-0026-5
    [14] 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
    [15] He Jianzhong, He Jinhai, 1993: Nondispersive Periodic Solution of a Barotropic Semi-Geostrophic Model, ADVANCES IN ATMOSPHERIC SCIENCES, 10, 465-474.  doi: 10.1007/BF02656971
    [16] Luo Dehai, 1998: Topographically Forced Three-Wave Quasi-Resonant and Non-Resonant Interactions among Barotropic Rossby Waves on an Infinite Beta-Plane, ADVANCES IN ATMOSPHERIC SCIENCES, 15, 83-98.  doi: 10.1007/s00376-998-0020-x
    [17] LIU Shikuo, LIU Shida, FU Zuntao, SUN Lan, 2005: A Nonlinear Coupled Soil Moisture-Vegetation Model, ADVANCES IN ATMOSPHERIC SCIENCES, 22, 337-342.  doi: 10.1007/BF02918747
    [18] A. Bandyopadhyay, 1992: Split-Explicit Integration of Primitive Equation Barotropic Model for the Prediction of Movement of Monsoon Depression, ADVANCES IN ATMOSPHERIC SCIENCES, 9, 83-92.  doi: 10.1007/BF02656933
    [19] M. Y. Totagi, D. R. Talwalkar, S. Rajamani, S. S. Singh, 1992: Analysis-Prediction Experiments over Indian Region Using Primitive Equation Barotropic Model, ADVANCES IN ATMOSPHERIC SCIENCES, 9, 477-482.  doi: 10.1007/BF02677080
    [20] N. R. Parija, S. K. Dash, 1995: Some Aspects of the Characteristics of Monsoon Disturbances Using a Combined Barotropic-Baroclinic Model, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 487-506.  doi: 10.1007/BF02657007

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Manuscript History

Manuscript received: 10 April 1985
Manuscript revised: 10 April 1985
通讯作者: 陈斌, bchen63@163.com
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NONLINEAR WAVES IN BAROTROPIC MODEL

  • 1. Department of Geophysics, Peking University, Beijing,Department of Geophysics, Peking University, Beijing

Abstract: In this paper, from the system of equation describing a barotropic atmosphere using the method of Taylor expansion for the nonlinear terms, the periodic solutions of the nonlinear inertio-surface gravity waves and Rossby waves have been obtained.The finite-amplitude nonlinear inertio-surface gravity waves and Rossby waves with horizontal divergence satisfy all the KdV equation. The solutions are all the cnoidal function, i, e, the cnoidal waves which in-clude the linear waves and form the solitary waves under certain conditions. For the finite-amplitude Rossby waves with horizontal divergence, we find the new dispersive relation including both the wave number and the amplitude parameter. In case of small amplitude it is reduced to the Yeh formula. It is shown that the larger the amplitude and width, the faster the finite-amplitude inertio-surface gravity waves and the slower the finite-amplitude Rossby waves with horizontal divergence propagate. The blocking or cut-off system in which the amplitude and width are large may be considered as Rossby solitary waves.

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