THE EFFECT OF ASPECT RATIO ON THE BIFURCATION PROPERTIES OF A DOUBLE PARALLEL-CONNECTION LORENZ SYSTEM

Zou Chengzhi; Yang Peicai; Zhou Xiuji

doi:10.1007/BF02657931

Impact Factor: 5.8

Volume 3 Issue 4

Oct. 1986

Article Contents

Article > ADVANCES IN ATMOSPHERIC SCIENCES > 1986 > 3(4): 406-423

THE EFFECT OF ASPECT RATIO ON THE BIFURCATION PROPERTIES OF A DOUBLE PARALLEL-CONNECTION LORENZ SYSTEM

1.
Institute of Atmospheric Physics, Acadeinia Sinica, Beijing,Institute of Atmospheric Physics, Acadeinia Sinica, Beijing,Institute of Meteorological Science, State Meteorological Administration, Beijing

doi: 10.1007/BF02657931

Abstract
References
Related papers
PDF

Abstract:
A double parallel-connection (DPC) Lorenz system is developed by performing spectrum truncation of the Galerkin series expansion of the two-dimensional Rayleigh-Benard convection equation. Analyses of the equilibrium states indicate that a convective roll stems from a flow with a given wavenumber first losing its stability for a particular aspect ratio β after a stable laminar flow gets unstable; when β has the value βc able to deprive synchronously two flows with different wavenumbers of stability, occurrences of convective rolls with different wavenumbers depend entirely on the initial conditions, in good agreement with the relevant experimental results. The calculations of the unstablized rolls show that, with a smaller β (as compared with βc), the DPC Lorenz system has the same bifurcation properties as the ordinary Lorenz system; for a moderate β, the system has very complicated periodic, quasi-periodic and phase-locking motions; for a larger β, it results in intermittent chaos and causes mean flows with different numbers of vortices to occur alternately with time. All these indicate that β has substantial effect on the two Lorenz systems coupled through parallel connection in their interaction and the results.
References

[1]	Ying ZHANG, Kayo IDE, Eugenia KALNAY, 2015: Bred Vectors of the Lorenz63 System, ADVANCES IN ATMOSPHERIC SCIENCES, 32, 1533-1538. doi: 10.1007/s00376-015-4275-8
[2]	Zhong Wenyi, Yang Peicai, 1986: THE TRANSITION OF A MULTI-DIMENSIONAL LORENZ SYSTEM, ADVANCES IN ATMOSPHERIC SCIENCES, 3, 289-301. doi: 10.1007/BF02678650
[3]	REN Hongli, CHOU Jifan, HUANG Jianping, ZHANG Peiqun, 2009: Theoretical Basis and Application of an Analogue- Dynamical Model in the Lorenz System, ADVANCES IN ATMOSPHERIC SCIENCES, 26, 67-77. doi: 10.1007/s00376-009-0067-3
[4]	Wan Jun, Yang Fanglin, 1990: The Phenomena of Bifurcation and Catastrophe of Large-Scale Horizontal Motion in the Atmosphere under the Effect of Rossby Parameter, ADVANCES IN ATMOSPHERIC SCIENCES, 7, 409-422. doi: 10.1007/BF03008871
[5]	Zhang Fuqing, Lin Zhenshan, Jiang Quanrong, 1994: The Fractal Dimension Distribution of the Short-Term Climate System in China and It’s Connection with the Monsoon Climate, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 459-462. doi: 10.1007/BF02658166
[6]	Dai Honghua, 1988: SEVERAL PROPERTIES OF METEOROLOGICAL KNOWLEDGE USED FOR EXPERT SYSTEM, ADVANCES IN ATMOSPHERIC SCIENCES, 5, 515-521. doi: 10.1007/BF02656795
[7]	LIU Shikuo, LIU Shida, FU Zuntao, XIN Guojun, LIANG Fuming, 2004: The Structure and Bifurcation of Atmospheric Motions, ADVANCES IN ATMOSPHERIC SCIENCES, 21, 557-561. doi: 10.1007/BF02915723
[8]	Junlin AN, Huan LV, Min XUE, Zefeng ZHANG, Bo HU, Junxiu WANG, Bin ZHU, 2021: Analysis of the Effect of Optical Properties of Black Carbon on Ozone in an Urban Environment at the Yangtze River Delta, China, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 1153-1164. doi: 10.1007/s00376-021-0367-9
[9]	GUO Zhun, ZHOU Tianjun, 2015: Seasonal Variation and Physical Properties of the Cloud System over Southeastern China Derived from CloudSat Products, ADVANCES IN ATMOSPHERIC SCIENCES, 32, 659-670. doi: 10.1007/s00376-014-4070-y
[10]	Zou Chengzhi, Zhou Xiuji, Yang Peicai, 1985: THE STATISTICAL STRUCTURE OF LORENZ STRANGE ATTRACTORS, ADVANCES IN ATMOSPHERIC SCIENCES, 2, 215-224. doi: 10.1007/BF03179753
[11]	Ye Zhuojia, Roger A. Pielke, 1995: A Parameterization of Bowen Ratio with Respect to Soil Moisture Availability, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 449-474. doi: 10.1007/BF02657005
[12]	Li Shuyong, Wang Bin, Zhang Xin, 2001: The Parallel Computing of GPS Ray-shooting Model, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 1185-1191. doi: 10.1007/s00376-001-0032-2
[13]	Ji-Hyun HA, Dong-Kyou LEE, 2012: Effect of Length Scale Tuning of Background Error in WRF-3DVAR System on Assimilation of High-Resolution Surface Data for Heavy Rainfall Simulation, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 1142-1158. doi: 10.1007/s00376-012-1183-z
[14]	Zhao Yanzeng, Hu Yuliang, Zhao Hongjie, 1984: INTEGRATION METHOD AND RATIO METHOD FOR RETRIEVING EXTINCTION COEFFICIENT FROM LIDAR SIGNALS, ADVANCES IN ATMOSPHERIC SCIENCES, 1, 53-75. doi: 10.1007/BF03187616
[15]	Bo HAN, Shihua LÜ, Ruiqing LI, Xin WANG, Lin ZHAO, Cailing ZHAO, Danyun WANG, Xianhong MENG, 2017: Global Land Surface Climate Analysis Based on the Calculation of a Modified Bowen Ratio, ADVANCES IN ATMOSPHERIC SCIENCES, 34, 663-678. doi: 10.1007/s00376-016-6175-y
[16]	Zhou Xiuji, Qiu Jinhuan, 1984: CHARACTERISTICS OF ATMOSPHERIC EXTINCTION-TO-BACKSCATTERING RATIO IN RUBY LIDAR MEASUREMENTS, ADVANCES IN ATMOSPHERIC SCIENCES, 1, 179-198. doi: 10.1007/BF02678130
[17]	Wang Yuan, Wu Rongsheng, 2001: Theoretical Aspect of Suitable Spatial Boundary Condition Specified for Adjoint Model on Limited Area, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 1081-1089. doi: 10.1007/s00376-001-0024-2
[18]	ZHOU Botao, WANG Huijun, 2008: Interdecadal Change in the Connection Between Hadley Circulation and Winter Temperature in East Asia, ADVANCES IN ATMOSPHERIC SCIENCES, 25, 24-30. doi: 10.1007/s00376-008-0024-6
[19]	ZHANG Jinqiang, XUAN Yuejian, YAN Xiaolu, LIU Mingyuan, TIAN Hongmin, XIA Xiang'ao, PANG Li, and ZHENG Xiangdong, 2014: Development and Preliminary Evaluation of a Double-cell Ozonesonde, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 938-947. doi: 10.1007/s00376-013-3104-1
[20]	DING Ruiqiang, LI Jianping, 2012: Relationships between the Limit of Predictability and Initial Error in the Uncoupled and Coupled Lorenz Models, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 1078-1088. doi: 10.1007/s00376-012-1207-8

PDF

Get Citation+

Export:

Article Metrics

Article Views: 1354 Times

PDF downloads: 1126 Times

Cited by: Times

Proportional views

Manuscript History

Manuscript received: 10 October 1986

Manuscript revised: 10 October 1986

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

THE EFFECT OF ASPECT RATIO ON THE BIFURCATION PROPERTIES OF A DOUBLE PARALLEL-CONNECTION LORENZ SYSTEM

1. Institute of Atmospheric Physics, Acadeinia Sinica, Beijing,Institute of Atmospheric Physics, Acadeinia Sinica, Beijing,Institute of Meteorological Science, State Meteorological Administration, Beijing

Manuscript received: 1986-10-10
Manuscript revised: 1986-10-10

Abstract: A double parallel-connection (DPC) Lorenz system is developed by performing spectrum truncation of the Galerkin series expansion of the two-dimensional Rayleigh-Benard convection equation. Analyses of the equilibrium states indicate that a convective roll stems from a flow with a given wavenumber first losing its stability for a particular aspect ratio β after a stable laminar flow gets unstable; when β has the value βc able to deprive synchronously two flows with different wavenumbers of stability, occurrences of convective rolls with different wavenumbers depend entirely on the initial conditions, in good agreement with the relevant experimental results. The calculations of the unstablized rolls show that, with a smaller β (as compared with βc), the DPC Lorenz system has the same bifurcation properties as the ordinary Lorenz system; for a moderate β, the system has very complicated periodic, quasi-periodic and phase-locking motions; for a larger β, it results in intermittent chaos and causes mean flows with different numbers of vortices to occur alternately with time. All these indicate that β has substantial effect on the two Lorenz systems coupled through parallel connection in their interaction and the results.