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Volume 8 Issue 2

Mar.  1991

Article Contents

A-B Hybrid Equation Method of Nonlinear Bifurcation in Wave-Flow Interaction


doi: 10.1007/BF02658092

  • In this paper, A-B hybrid equation method is given. This method is different not only from high truncated spec-tral method, but also from amplitude evolution method. Dynamic problem in the baroclinic atmosphere may be transferred into complex Lorenz system by means of the method. Therefore, this method is an effective tool for stud-ying nonlinear bifurcation in wave-flow interaction. Meanwhile, it is of advantage to use this method, because it can overcome a lot of difficulties existing in high truncated spectral method and amplitude evolution method.
  • [1] Gao Shouting, Liu Kunru, 1990: Introduction of the Direct Method by Illustrating Schr?dinger Equation and Its Application to Wave-Wave Striking Interaction, ADVANCES IN ATMOSPHERIC SCIENCES, 7, 186-191.  doi: 10.1007/BF02919156
    [2] 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
    [3] Zeng Qingcun, Zhang Minghua, 2000: Wave-Mean Flow Interaction: the Role of Continuous-Spectrum Disturbances, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 1-17.  doi: 10.1007/s00376-000-0039-0
    [4] Luo Dehai, 1999: Bifurcation of Nonlinear Kelvin Wave-CISK with Conditional Heating in a Truncated Spectral Model: A Possible Mechanism of 30-60-Day Osculation at the Equator, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 279-296.  doi: 10.1007/BF02973088
    [5] 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
    [6] Xu Youfeng, 1986: THE NONLINEAR INTERACTION BETWEEN DIFFERENT WAVE COMPONENTS AND THE PROCESS OF INDEX CYCLE OF GENERAL CIRCULATION, ADVANCES IN ATMOSPHERIC SCIENCES, 3, 478-488.  doi: 10.1007/BF02657937
    [7] Ji Zhongzhen, Wang Bin, 1997: Multispectrum Method and the Computation of Vapor Equation, ADVANCES IN ATMOSPHERIC SCIENCES, 14, 563-568.  doi: 10.1007/s00376-997-0074-1
    [8] Luo Dehai, Li Jianping, 2001: Interaction between a Slowly Moving Planetary-Scale Dipole Envelope Rossby Soliton and a Wavenumber-Two Topography in a Forced Higher Order Nonlinear Schr dinger Equation, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 239-256.  doi: 10.1007/s00376-001-0017-1
    [9] Yong. L. McHall, 1992: Nonlinear Planetary Wave Instability and Blocking, ADVANCES IN ATMOSPHERIC SCIENCES, 9, 173-190.  doi: 10.1007/BF02657508
    [10] He Jianzhong, 1994: Nonlinear Ultra-Long Wave and Its Stability, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 91-100.  doi: 10.1007/BF02656998
    [11] 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
    [12] R. Dhar, C. Guha-Roy, D. K. Sinha, 1991: On a Class of Solitary Wave Solutions of Atmospheric Nonlinear Equations, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 357-362.  doi: 10.1007/BF02919618
    [13] Zhao Ping, 1991: The Effects of Zonal Flow on Nonlinear Rossby Waves, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 299-306.  doi: 10.1007/BF02919612
    [14] 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
    [15] Peng Yongqing, Yan Shaojin, Wang Tongmei, 1995: A Nonlinear Time-lag Differential Equation Model for Predicting Monthly Precipitation, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 319-324.  doi: 10.1007/BF02656980
    [16] Yi Zengxin, T. Warn, 1987: A NUMERICAL METHOD FOR SOLVING THE EVOLUTION EQUATION OF SOLITARY ROSSBY WAVES ON A WEAK SHEAR, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 43-54.  doi: 10.1007/BF02656660
    [17] Xiangjun TIAN, Xiaobing FENG, 2019: An Adjoint-Free CNOP-4DVar Hybrid Method for Identifying Sensitive Areas in Targeted Observations: Method Formulation and Preliminary Evaluation, ADVANCES IN ATMOSPHERIC SCIENCES, , 721-732.  doi: 10.1007/s00376-019-9001-5
    [18] He Jianzhong, 1993: Topography and the Non-linear Rossby Wave in the Zonal Shear Basic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 10, 233-242.  doi: 10.1007/BF02919146
    [19] Zhu Xun, 1987: ON GRAVITY WAVE-MEAN FLOW INTERACTIONS IN A THREE DIMENSIONAL STRATIFIED ATMOSPHERE, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 287-299.  doi: 10.1007/BF02663599
    [20] Li Chongyin, Liao Qinghai, 1996: Behaviour of Coupled Modes in a Simple Nonlinear Air-Sea Interaction Model, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 183-195.  doi: 10.1007/BF02656861

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Manuscript History

Manuscript received: 10 March 1991
Manuscript revised: 10 March 1991
通讯作者: 陈斌, bchen63@163.com
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A-B Hybrid Equation Method of Nonlinear Bifurcation in Wave-Flow Interaction

  • 1. Institute of Atmospheric Physics, Academia Sinica, Beijing 100029, China

Abstract: In this paper, A-B hybrid equation method is given. This method is different not only from high truncated spec-tral method, but also from amplitude evolution method. Dynamic problem in the baroclinic atmosphere may be transferred into complex Lorenz system by means of the method. Therefore, this method is an effective tool for stud-ying nonlinear bifurcation in wave-flow interaction. Meanwhile, it is of advantage to use this method, because it can overcome a lot of difficulties existing in high truncated spectral method and amplitude evolution method.

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