Advanced Search
Article Contents

Nonlinear Three-Wave Interaction among Barotropic Rossby Waves in a Large-scale Forced Barotropic Flow


doi: 10.1007/s00376-999-0023-2

  • In this paper, the coupling equations describing nonlinear three-wave interaction among Rossby waves including the forcing of an external vorticity source are obtained. Under certain conditions, the coupling equations with a constant amplitude forcing, the stability analysis indi-cates that when the amplitude of the external forcing increases to a certain extent, a pitchfork bifurcation occurs. Also, it is shown from numerical results that the bifurcation can lead to chaotic behavior of “strange” attractor. For the obtained three-variable equation, when the amplitude of modulated external forcing gradually increases, a period-doubling bifurcation is found to lead to chaotic behavior. Thus, in a nonlinear three-wave coupling model in the large-scale forced barotropic atmospheric flow, chaotic behavior can be observed. This chaotic behavior can explain in part 30-60-day low-frequency oscillations observed in mid-high latitudes.
  • [1] 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
    [2] Yashu WU, Jianhua LU, 2023: A Quantitative Method of Detecting Transient Rossby Wave Phase Speed: No Evidence of Slowing Down with Global Warming, ADVANCES IN ATMOSPHERIC SCIENCES, 40, 251-261.  doi: 10.1007/s00376-022-2164-5
    [3] Brian HOSKINS, 2015: Potential Vorticity and the PV Perspective, ADVANCES IN ATMOSPHERIC SCIENCES, 32, 2-9.  doi: 10.1007/s00376-014-0007-8
    [4] MENG Xiangfeng, WU Dexing, LIN Xiaopei, LAN Jian, 2006: A Further Investigation of the Decadal Variation of ENSO Characteristics with Instability Analysis, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 156-164.  doi: 10.1007/s00376-006-0016-3
    [5] Liao Qinghai, Li Chongyin, 1995: CISK-rossby wave and the 30-60 Day Oscillation in the Tropics, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 1-12.  doi: 10.1007/BF02661282
    [6] 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
    [7] 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
    [8] Chen Longxun, Zhu Congwen, Wang Wen, Zhang Peiqun, 2001: Analysis of the Characteristics of 30-60 Day Low-Frequency Oscillation over Asia during 1998 SCSMEX, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 623-638.  doi: 10.1007/s00376-001-0050-0
    [9] Lu Keli, Zhu Yongchun, 1994: Seasonal Variation of Stationary and Low-Frequency Rossby Wave Rays, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 427-435.  doi: 10.1007/BF02658163
    [10] 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
    [11] Zhang Ren, Yu Zhihao, 2000: Low-Frequency CISK-Rossby Wave and Stratospheric QBO in the Tropical Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 311-321.  doi: 10.1007/s00376-000-0012-y
    [12] Chen Zhongming, Liu Fuming, Li Xiaoping, Tao Jie, 1994: Oscillatory Rossby Solitary Waves in the Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 65-73.  doi: 10.1007/BF02656995
    [13] LU Riyu*, DONG Huilin, SU Qin, and Hui DING, 2014: The 30-60-day Intraseasonal Oscillations over the Subtropical Western North Pacific during the Summer of 1998, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 1-7.  doi: 10.1007/s00376-013-3019-x
    [14] Jiangyu MAO, Ming WANG, 2018: The 30-60-day Intraseasonal Variability of Sea Surface Temperature in the South China Sea during May-September, ADVANCES IN ATMOSPHERIC SCIENCES, 35, 550-566.  doi: 10.1007/s00376-017-7127-x
    [15] Li Chongyin, 1993: A Further Inquiry on the Mechanism of 30-60 Day Oscillation in the Tropical Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 10, 41-53.  doi: 10.1007/BF02656952
    [16] Song Yi, Chen Longxun, 1992: The Characteristics of 30-60 Day Oscillation and Its Relations to the Interannual Oscillations, ADVANCES IN ATMOSPHERIC SCIENCES, 9, 323-336.  doi: 10.1007/BF02656942
    [17] Tianju WANG, Zhong ZHONG, Ju WANG, 2018: Vortex Rossby Waves in Asymmetric Basic Flow of Typhoons, ADVANCES IN ATMOSPHERIC SCIENCES, 35, 531-539.  doi: 10.1007/s00376-017-7126-y
    [18] Jiang Guorong, 1996: CISK-related Rossby Waves in the Tropical Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 115-123.  doi: 10.1007/BF02657032
    [19] Zhao Ping, 1991: The Effects of Zonal Flow on Nonlinear Rossby Waves, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 299-306.  doi: 10.1007/BF02919612
    [20] REN Baohua, HUANG Ronghui, 2003: 30-60-day Oscillations of Convection and Circulation Associated with the Thermal State of the Western Pacific Warm Pool during Boreal Summer, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 781-793.  doi: 10.1007/BF02915403

Get Citation+

Export:  

Share Article

Manuscript History

Manuscript received: 10 July 1999
Manuscript revised: 10 July 1999
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

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Nonlinear Three-Wave Interaction among Barotropic Rossby Waves in a Large-scale Forced Barotropic Flow

  • 1. Department of Atmospheric and Oceanic Sciences. Ocean University of Qingdao, Qingdao 266003

Abstract: In this paper, the coupling equations describing nonlinear three-wave interaction among Rossby waves including the forcing of an external vorticity source are obtained. Under certain conditions, the coupling equations with a constant amplitude forcing, the stability analysis indi-cates that when the amplitude of the external forcing increases to a certain extent, a pitchfork bifurcation occurs. Also, it is shown from numerical results that the bifurcation can lead to chaotic behavior of “strange” attractor. For the obtained three-variable equation, when the amplitude of modulated external forcing gradually increases, a period-doubling bifurcation is found to lead to chaotic behavior. Thus, in a nonlinear three-wave coupling model in the large-scale forced barotropic atmospheric flow, chaotic behavior can be observed. This chaotic behavior can explain in part 30-60-day low-frequency oscillations observed in mid-high latitudes.

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return