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Volume 10 Issue 4

Oct.  1993

Article Contents
Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 1993 >  10(4): 435-446

Study on Atmospheric Travelling Wave Solutions and Review of Its Present Developments

  • 1.

    Laboratory of Numerical Modelling for Atmospheric Sciences and Geophysical Fluid Dynamics, Chinese Academy of Sciences, Beijing 100080,Laboratory of Numerical Modelling for Atmospheric Sciences and Geophysical Fluid Dynamics, Chinese Academy of Sciences, Beijing 100080


doi: 10.1007/BF02656968

  • The scientific achievements of travelling waves in a barotropic atmosphere are introduced, including i) the exist-ence conditions of periodic solutions (wavetrain solutions) and solitary wave solutions (pulse solutions), together with the solution finding methods and a series of related problems, ii) seeking solutions of monotonous wave (wave front) and of nonmonotonous travelling wave (oscillatory wave) by using phase plane shooting technique and iii) progress in the study of travelling wave solution at home and abroad. The investigation of travelling wave solutions in recent years has been found in mathematics, physics, chemistry, biology and other sciences. Over the past decade the prob-lem has been the subject of much interest and become an important area of research. So it is no doubt of great signifi-cance to investigate the travelling wave solutions and thereby explain phenomena of weather.
  • [1] Xu Xihua, 1989: The Solitary Wave of Barotropic Atmosphere on a Sphere, ADVANCES IN ATMOSPHERIC SCIENCES, 6, 457-466.  doi: 10.1007/BF02659079
    [2] 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
    [3] Lu Peisheng, 1992: The Structure and Propagation of Stationary Planetary Wave Packet in the Barotropic Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 9, 157-166.  doi: 10.1007/BF02657506
    [4] 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
    [5] S. Panchev, 1990: An Exact Solution for Two-Dimensional Frictionless Motion in the Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 7, 137-141.  doi: 10.1007/BF02919151
    [6] Luo Dehai, Ji Liren, 1988: ALGEBRAIC ROSSBY SOLITARY WAVE AND BLOCKING IN THE ATMOSPHERE, ADVANCES IN ATMOSPHERIC SCIENCES, 5, 445-454.  doi: 10.1007/BF02656790
    [7] 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
    [8] Lu WANG, Wei QIANG, Haiyun XIA, Tianwen WEI, Jinlong YUAN, Pu JIANG, 2021: Robust Solution for Boundary Layer Height Detections with Coherent Doppler Wind Lidar, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 1920-1928.  doi: 10.1007/s00376-021-1068-0
    [9] Qiu Jinhuan, 1988: SENSITIVITY OF LIDAR EQUATION SOLUTION TO BOUNDA-RY VALUES AND DETERMINATION OF THE VALUES, ADVANCES IN ATMOSPHERIC SCIENCES, 5, 229-241.  doi: 10.1007/BF02656784
    [10] D. R. Chakraborty, P.S. Salvekar, 1989: An Efficient Accurate Direct Solution of Poisson’s Equation for Computation of Meteorological Parameters, ADVANCES IN ATMOSPHERIC SCIENCES, 6, 501-508.  doi: 10.1007/BF02659084
    [11] ZHANG Lifeng, WANG Xingbao, ZHANG Ming, 2003: Spatial and Time Structure of a Gravity Wave in Horizontal Atmosphere of Heterogeneous Stratification, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 29-36.  doi: 10.1007/BF03342047
    [12] Li Guoping, Lu Jinghua, 1996: Some Possible Solutions of Nonlinear Internal Inertial Gravity Wave Equations in the Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 244-252.  doi: 10.1007/BF02656866
    [13] WEN Yuanqiao, HUANG Liwen, DENG Jian, ZHANG Jinfeng, WANG Sisi, WANG Lijun, 2006: Framework of Distributed Coupled Atmosphere-Ocean-Wave Modeling System, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 442-448.  doi: 10.1007/s00376-006-0442-2
    [14] 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
    [15] Luo Dehai, 1990: Topographically Forced Rossby Wave Instability and the Development of Blocking in the Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 7, 433-440.  doi: 10.1007/BF03008873
    [16] 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
    [17] 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
    [18] Huan WU, Xiaomeng LI, Guy J.-P. SCHUMANN, Lorenzo ALFIERI, Yun CHEN, Hui XU, Zhifang WU, Hong LU, Yamin HU, Qiang ZHU, Zhijun HUANG, Weitian CHEN, Ying HU, 2021: From China’s Heavy Precipitation in 2020 to a “Glocal” Hydrometeorological Solution for Flood Risk Prediction, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 1-7.  doi: 10.1007/s00376-020-0260-y
    [19] HU Shujuan, CHOU Jifan, 2004: Uncertainty of the Numerical Solution of a Nonlinear System's Long-term Behavior and Global Convergence of the Numerical Pattern, ADVANCES IN ATMOSPHERIC SCIENCES, 21, 767-774.  doi: 10.1007/BF02916373
    [20] Chen Jiabin, Wang Jun, 1996: Studies on Non-interpolating Semi-Lagrangian Scheme and Numerical Solution to KdV Equation, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 265-268.  doi: 10.1007/BF02656869
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    • Manuscript History

    Manuscript received: 10 October 1993
    Manuscript revised: 10 October 1993
    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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    Study on Atmospheric Travelling Wave Solutions and Review of Its Present Developments

    • 1. Laboratory of Numerical Modelling for Atmospheric Sciences and Geophysical Fluid Dynamics, Chinese Academy of Sciences, Beijing 100080,Laboratory of Numerical Modelling for Atmospheric Sciences and Geophysical Fluid Dynamics, Chinese Academy of Sciences, Beijing 100080
    • Manuscript received: 1993-10-10
    • Manuscript revised: 1993-10-10

    Abstract: The scientific achievements of travelling waves in a barotropic atmosphere are introduced, including i) the exist-ence conditions of periodic solutions (wavetrain solutions) and solitary wave solutions (pulse solutions), together with the solution finding methods and a series of related problems, ii) seeking solutions of monotonous wave (wave front) and of nonmonotonous travelling wave (oscillatory wave) by using phase plane shooting technique and iii) progress in the study of travelling wave solution at home and abroad. The investigation of travelling wave solutions in recent years has been found in mathematics, physics, chemistry, biology and other sciences. Over the past decade the prob-lem has been the subject of much interest and become an important area of research. So it is no doubt of great signifi-cance to investigate the travelling wave solutions and thereby explain phenomena of weather.

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