ATTRACTOR SETS AND MULTIPLE EQUILIBRIA IN THE RESONANCE OF TOPOGRAPHICALLY FORCED WAVES

Li Xianlang

doi:10.1007/BF02656746

Impact Factor: 5.8

Volume 4 Issue 4

Oct. 1987

Article Contents

Article > ADVANCES IN ATMOSPHERIC SCIENCES > 1987 > 4(4): 471-484

ATTRACTOR SETS AND MULTIPLE EQUILIBRIA IN THE RESONANCE OF TOPOGRAPHICALLY FORCED WAVES

Li Xianlang

1.
Center for Meteorology and Physical Oceanography, Massachusetts Institute of Technology

Li Xianlang

doi: 10.1007/BF02656746

Abstract
References
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Abstract:
The resonance of topographically forced waves is studied using a quasi-geostrophic spectral model on the rotating sphere. The use of complete spectral expansions without truncation leads to the exact solutions of the nonlinear coupling equations by means of the random phase approximation and the projection operator techniques under the dissipation-vanishing limit. The energy transfer process between topographically forced wave ensemble and zonal mean flow is described.It is shown that the dynamical system loses stability and further bifurcation takes place when the to-pographic force has occurred. There are two sorts of equilibrium point in the resonance system. The unstable equilibrium is an isolated equilibrium point and, therefore, is hardly observed to occur. The stable equilibrium is an attractor set which is related to the phenomenon of blocking.
References

[1]	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
[2]	Zhu Baozhen, Zhao Jingxia, 1987: MULTIPLE FLOW EQUILIBRIA IN THE TROPICAL CIRCULA-TION AND MONSOON, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 375-384. doi: 10.1007/BF02656738
[3]	SUN Guodong, MU Mu, 2009: Nonlinear Feature of the Abrupt Transitions between Multiple Equilibria States of an Ecosystem Model, ADVANCES IN ATMOSPHERIC SCIENCES, 26, 293-304. doi: 10.1007/s00376-009-0293-8
[4]	Zhao Jingxia, Zhu Baozhen, 1989: Sensitivity of the Multiple Equilibria to Gorverning System, Mode Chosen and Parameter, ADVANCES IN ATMOSPHERIC SCIENCES, 6, 33-43. doi: 10.1007/BF02656916
[5]	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
[6]	Zhu Zhengxin, 1985: EQUILIBRIUM STATES OF PLANETARY WAVES FORCED BY TOPOGRAPHY AND PERTURBATION HEATING AND BLOCKING SITUATION, ADVANCES IN ATMOSPHERIC SCIENCES, 2, 359-367. doi: 10.1007/BF02677252
[7]	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
[8]	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
[9]	Li Xianlang, 1988: NONLINEAR RESONANCE INTERACTIONS AND INDEX CYCLES IN THE ATMOSPHERE, ADVANCES IN ATMOSPHERIC SCIENCES, 5, 253-264. doi: 10.1007/BF02656750
[10]	Cao Hongxing, 1987: A TECHNIQUE FOR VERIFICATION OF WEATHER FORECAST AND CLIMATE SIMULATION WITH FUZZY SETS, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 363-374. doi: 10.1007/BF02663606
[11]	Jie FENG, Jianping LI, Jing ZHANG, Deqiang LIU, Ruiqiang DING, 2019: The Relationship between Deterministic and Ensemble Mean Forecast Errors Revealed by Global and Local Attractor Radii, ADVANCES IN ATMOSPHERIC SCIENCES, 36, 271-278. doi: 10.1007/s00376-018-8123-5
[12]	LI Mingxing, MA Zhuguo, 2010: Comparisons of Simulations of Soil Moisture Variations in the Yellow River Basin Driven by Various Atmospheric Forcing Data Sets, ADVANCES IN ATMOSPHERIC SCIENCES, 27, 1289-1302. doi: 10.1007/s00376-010-9155-7
[13]	Yan Shaojin, Peng Yongqing, Wang Jianzhong, 1991: Determination of Kolmogorov Entropy of Chaotic Attractor Included in One-Dimensional Time Series of Meteorological Data, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 243-250. doi: 10.1007/BF02658098
[14]	Zipeng YUAN, Xiaoyong ZHUGE, Yuan WANG, 2020: The Forced Secondary Circulation of the Mei-yu Front, ADVANCES IN ATMOSPHERIC SCIENCES, 37, 766-780. doi: 10.1007/s00376-020-9177-8
[15]	Qiwei WANG, Ming XUE, Zhemin TAN, 2016: Convective Initiation by Topographically Induced Convergence Forcing over the Dabie Mountains on 24 June 2010, ADVANCES IN ATMOSPHERIC SCIENCES, 33, 1120-1136. doi: 10.1007/s00376-016-6024-z
[16]	Fu Yunfei, Han Zhaoyuan, Gong Minwei, 1995: Condensation Induced by Rarefaction Waves and Reflected Rarefaction Waves, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 507-512. doi: 10.1007/BF02657008
[17]	Zhang Xuehong, Zeng Qingcun, Bao Ning, 1986: NONLINEAR BAROCLINIC HAURWITZ WAVES, ADVANCES IN ATMOSPHERIC SCIENCES, 3, 330-340. doi: 10.1007/BF02678653
[18]	Liu Shida, Liu Shikuo, 1985: NONLINEAR WAVES IN BAROTROPIC MODEL, ADVANCES IN ATMOSPHERIC SCIENCES, 2, 147-157. doi: 10.1007/BF03179747
[19]	Xiaofan Li, Han-Ru Cho, 1997: Development and Propagation of Equatorial Waves, ADVANCES IN ATMOSPHERIC SCIENCES, 14, 323-338. doi: 10.1007/s00376-997-0053-6
[20]	KE Zongjian, DONG Wenjie, ZHANG Peiqun, WANG Jin, ZHAO Tianbao, 2009: An Analysis of the Difference between the Multiple Linear Regression Approach and the Multimodel Ensemble Mean, ADVANCES IN ATMOSPHERIC SCIENCES, 26, 1157-1168. doi: 10.1007/s00376-009-8024-8

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Manuscript History

Manuscript received: 10 October 1987

Manuscript revised: 10 October 1987

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

ATTRACTOR SETS AND MULTIPLE EQUILIBRIA IN THE RESONANCE OF TOPOGRAPHICALLY FORCED WAVES

Li Xianlang

1. Center for Meteorology and Physical Oceanography, Massachusetts Institute of Technology

Manuscript received: 1987-10-10
Manuscript revised: 1987-10-10

Abstract: The resonance of topographically forced waves is studied using a quasi-geostrophic spectral model on the rotating sphere. The use of complete spectral expansions without truncation leads to the exact solutions of the nonlinear coupling equations by means of the random phase approximation and the projection operator techniques under the dissipation-vanishing limit. The energy transfer process between topographically forced wave ensemble and zonal mean flow is described.It is shown that the dynamical system loses stability and further bifurcation takes place when the to-pographic force has occurred. There are two sorts of equilibrium point in the resonance system. The unstable equilibrium is an isolated equilibrium point and, therefore, is hardly observed to occur. The stable equilibrium is an attractor set which is related to the phenomenon of blocking.