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Volume 3 Issue 4

Oct.  1986

Article Contents

A STUDY ON THE EXCITATION, ESTABLISHMENT AND TRANSITION OF MULTIPLE EQUILIBRIUM STATES PRODUCED BY NEARLY RESONANT THERMAL FORCING-PART II: THEORETICAL ANALYSIS OF THE MECHANISM OF MULTIPLE EQUILIBRIUM STATES


doi: 10.1007/BF02657930

  • Based on the results acquired in Part I of this paper, analysis is made of the theoretical mechanism of thermal forcing multiple equilibrium states (MES) and their stability. The results are as follows: 1) non-linear effect and external forcing are determinative factors for MES formation; 2) under proper “environ-mental conditions” the forcing can excite stable MES, particularly three types of solutions, two of which, with larger amplitude of resonance, are not sensitive to the change in the forcing intensity; while the other, i. e. the one of small amplitude, dependent significantly on it; 3) in general, the domain of parameter values for the MES existence increases, but the stability decreases, with increasing thermal forcing; 4) steady thermal forced waves are always unstable for the most part; 5) thermal driving and orographic effect act equally as dynamical triggers; 6) friction has significant influence upon the behavior of MES solutions.Analysis shows that the changes in the “environmental parameters”, such as the alteration of the shear of a basic current and intensity of the forcing, induce the transition between different equilibria.
  • [1] Qin Jianchun, Zhu Baozhen, 1986: A STUDY ON THE EXCITATION, ESTABLISHMENT AND TRANSITION OF MULTIPLE EQUILIBRIUM STATES PRODUCED BY NEARLY RESONANT THERMAL FORCING---- PART I: ASYMPTOTIC SOLUTIONS OF MULTIPLE EQUILIBRIUM STATES, ADVANCES IN ATMOSPHERIC SCIENCES, 3, 277-288.  doi: 10.1007/BF02678649
    [2] SUN Guodong, MU Mu, 2012: Inducing Unstable Grassland Equilibrium States Due to Nonlinear Optimal Patterns of Initial and Parameter Perturbations: Theoretical Models, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 79-90.  doi: 10.1007/s00376-011-0226-1
    [3] 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
    [4] 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
    [5] Li Tianming, Zhu Yongti, 1989: On the Multiple Equilibrium of the Development of Tropical Cyclone in Nonlinear CISK Model, ADVANCES IN ATMOSPHERIC SCIENCES, 6, 447-456.  doi: 10.1007/BF02659078
    [6] ZUO Ruiting, WANG Liqiong, ZENG Qingcun, ZHANG Ming, 2005: Equilibrium Mechanism Analysis on the Physical Processes of IAP3.0, ADVANCES IN ATMOSPHERIC SCIENCES, 22, 525-533.  doi: 10.1007/BF02918485
    [7] LI Fang, ZENG Xiaodong, SONG Xiang, TIAN Dongxiao, SHAO Pu, ZHANG Dongling, 2011: Impact of Spin-up Forcing on Vegetation States Simulated by a Dynamic Global Vegetation Model Coupled with a Land Surface Model, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 775-788.  doi: 10.1007/s00376-010-0009-0
    [8] Chenyu MA, Wei YUAN, Ji NIE, 2020: Responses of Mean and Extreme Precipitation to Different Climate Forcing Under Radiative-Convective Equilibrium, ADVANCES IN ATMOSPHERIC SCIENCES, 37, 377-386.  doi: 10.1007/s00376-020-9236-1
    [9] 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
    [10] Zhao Ping, Chen Longxun, 2000: Calculation of Solar Albedo and Radiation Equilibrium over the Qinghai-Xizang Plateau and Analysis of Their Climatic Features, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 140-156.  doi: 10.1007/s00376-000-0050-5
    [11] Yong. L. McHall, 1991: Planetary Stationary Waves in the Atmosphere Part II: Thermal Stationary Waves, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 225-236.  doi: 10.1007/BF02658096
    [12] Zhuojian Yuan, Donald R. Johnson, 1998: The Role of Diabatic Heating, Torques and Stabilities in Forcing the Radial-Vertical Circulation within Cyclones Part II: Case Study of Extratropical and Tropical Cyclones, ADVANCES IN ATMOSPHERIC SCIENCES, 15, 447-488.  doi: 10.1007/s00376-998-0026-4
    [13] Yang Guoxiang, Lu Hancheng, He Qiqiang, 1987: A MESO-α-SCALE STUDY OF MEIYU FRONT HEAVY RAIN-PART II: THE DYNAMICAL ANALYSIS OF RAIN-BAND DISTURBANCE, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 485-495.  doi: 10.1007/BF02656747
    [14] XU Wenhui, NI Yunqi, WANG Xiaokang, QIU Xuexing, BAO Xinghua, JIN Wenyan, 2011: A Study of Structure and Mechanism of a Meso-beta-scale Convective Vortex and Associated Heavy Rainfall in the Dabie Mountain Area Part I: Diagnostic Analysis of the Structure, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 1159-1176.  doi: 10.1007/s00376-010-0170-5
    [15] WANG Pengfei, HUANG Gang, WANG Zaizhi, 2006: Analysis and Application of Multiple-Precision Computation and Round-off Error for Nonlinear Dynamical Systems, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 758-766.  doi: 10.1007/s00376-006-0758-y
    [16] LI Zhen, YAN Zhongwei, 2010: Application of Multiple Analysis of Series for Homogenization to Beijing Daily Temperature Series (1960--2006), ADVANCES IN ATMOSPHERIC SCIENCES, 27, 777-787.  doi: 10.1007/s00376-009-9052-0
    [17] Li'an Xie, Leonard J.Pietrafesa, Kejian Wu, 2002: Interannual and Decadal Variability of Landfalling Tropical Cyclones in the Southeast Coastal States of the United States, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 677-686.  doi: 10.1007/s00376-002-0007-y
    [18] JIANG Zhihong, DING Yuguo, ZHENG Chunyu, CHEN Weilin, 2011: An Improved, Downscaled, Fine Model for Simulation of Daily Weather States, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 1357-1366.  doi: 10.1007/s00376-011-0086-8
    [19] Shouhong WANG, MA Tian, 2011: El Nino Southern Oscillation as Sporadic Oscillations between Metastable States, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 612-622.  doi: 10.1007/s00376-010-9089-0
    [20] Zhou Yushu, Deng Guo, Gao Shouting, Xu Xiangde, 2002: The Wave Train Characteristics of Teleconnection Caused by the Thermal Anomaly of the Underlying Surface of the Tibetan Plateau. Part Ⅰ: Data Analysis, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 583-593.  doi: 10.1007/s00376-002-0002-3

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Manuscript History

Manuscript received: 10 October 1986
Manuscript revised: 10 October 1986
通讯作者: 陈斌, bchen63@163.com
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    沈阳化工大学材料科学与工程学院 沈阳 110142

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A STUDY ON THE EXCITATION, ESTABLISHMENT AND TRANSITION OF MULTIPLE EQUILIBRIUM STATES PRODUCED BY NEARLY RESONANT THERMAL FORCING-PART II: THEORETICAL ANALYSIS OF THE MECHANISM OF MULTIPLE EQUILIBRIUM STATES

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

Abstract: Based on the results acquired in Part I of this paper, analysis is made of the theoretical mechanism of thermal forcing multiple equilibrium states (MES) and their stability. The results are as follows: 1) non-linear effect and external forcing are determinative factors for MES formation; 2) under proper “environ-mental conditions” the forcing can excite stable MES, particularly three types of solutions, two of which, with larger amplitude of resonance, are not sensitive to the change in the forcing intensity; while the other, i. e. the one of small amplitude, dependent significantly on it; 3) in general, the domain of parameter values for the MES existence increases, but the stability decreases, with increasing thermal forcing; 4) steady thermal forced waves are always unstable for the most part; 5) thermal driving and orographic effect act equally as dynamical triggers; 6) friction has significant influence upon the behavior of MES solutions.Analysis shows that the changes in the “environmental parameters”, such as the alteration of the shear of a basic current and intensity of the forcing, induce the transition between different equilibria.

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