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Volume 2 Issue 4

Oct.  1985

Article Contents

SOME CATASTROPHE PROPERTIES OF TWO-LAYER SHEAR FLOW


doi: 10.1007/BF02678748

  • In this paper a simple current system which consists of two stratified incompressible layers is examined. For the basic equations of the motion of fluid a lower order spectrum model is established by means of Galerkin method. Adopting the difference of wind velocity between the upper and lower layers, As =as a control parameter, the bifurcation and stability of the solution of the dynamical systemare discussed. It is found that the flow states in the lower layer will have a catastrophe, when where Cg is the phase velocity of the internal inertio-gravitational wave in a geostrophic current.These results may give a reasonable explanation for the mechanism of the catastrophe phenomena, including the "pressure-jump" in the atmosphere.
  • [1] ZHANG Ming, ZHAO Yanling, HUANG Hong, LIANG Danqing, 2007: The Generalized Energy Equation and Instability in the Two-layer Barotropic Vortex, ADVANCES IN ATMOSPHERIC SCIENCES, 24, 147-151.  doi: 10.1007/s00376-007-0147-1
    [2] Li Yang, Mu Mu, 1996: Baroclinic Instability in the Generalized Phillips’ Model Part I: Two-layer Model, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 33-42.  doi: 10.1007/BF02657026
    [3] Zhao Qiang, Fu Zuntao, Liu Shikuo, 2001: Equatorial Envelope Rossby Solitons in a Shear Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 418-428.  doi: 10.1007/BF02919321
    [4] Shen Xinyong, Ni Yunqi, Ding Yihui, 2002: On Problem of Nonlinear Symmetric Instability in Zonal Shear Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 350-364.  doi: 10.1007/s00376-002-0027-7
    [5] He Jianzhong, 1993: Topography and the Non-linear Rossby Wave in the Zonal Shear Basic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 10, 233-242.  doi: 10.1007/BF02919146
    [6] Li Maicun, 1987: EQUATORIAL SOLITARY WAVES OF TROPICAL ATMOSPHERIC MOTION IN SHEAR FLOW, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 125-136.  doi: 10.1007/BF02677059
    [7] Qi GAO, Qingqing LI, Yufan DAI, 2020: Characteristics of the Outer Rainband Stratiform Sector in Numerically Simulated Tropical Cyclones: Lower-Layer Shear versus Upper-Layer Shear, ADVANCES IN ATMOSPHERIC SCIENCES, 37, 399-419.  doi: 10.1007/s00376-020-9202-y
    [8] Ren Shuzhan, 1991: Nonlinear Stability of Plane Rotating Shear Flow under Three-Dimensional Nondivergence Disturbances, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 129-136.  doi: 10.1007/BF02658089
    [9] Qiu Jinhuan, 1995: Two-wavelength Lidar Measurement of Cloud-aerosol Optical Properties, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 177-186.  doi: 10.1007/BF02656830
    [10] LIU Ximing, CHENG Xueling, WU Qiong, FU Minning, ZENG Qingcun, 2013: Some Characteristics of the Surface Boundary Layer of a Strong Cold Air Process over Southern China, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 210-218.  doi: 10.1007/s00376-012-1223-8
    [11] Zheng Xingyu, Zeng Qingcun, Huang Ronghui, 1992: The Propagation of Inertia-Gravity Waves and Their Influence on Zonal Mean Flow Part Two: Wave Breaking and Critical Levels, ADVANCES IN ATMOSPHERIC SCIENCES, 9, 29-36.  doi: 10.1007/BF02656927
    [12] Liu Yongming, Mu Mu, 1992: A Problem Related to Nonlinear Stability Criteria for Multi-layer Quasi-geostrophic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 9, 337-345.  doi: 10.1007/BF02656943
    [13] Wu Rongsheng, 1985: THE INFLUENCES OF OROGRAPHY UPON THE FLOW WITHIN EKMAN BOUNDARY LAYER UNDER THE APPROXIMATION OF GEOSTROPHIC MOMENTUM, ADVANCES IN ATMOSPHERIC SCIENCES, 2, 1-7.  doi: 10.1007/BF03179731
    [14] Hu Yinqiao, Su Congxian, Ge Zhengmo, 1988: A TWO-DIMENSIONAL AND STEADY-STATE NUMERICAL MODEL OF THE PLANETARY BOUNDARY LAYER, ADVANCES IN ATMOSPHERIC SCIENCES, 5, 523-534.  doi: 10.1007/BF02656796
    [15] 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
    [16] Gao Shouting, 2000: The Instability of the Vortex Sheet along the Shear Line, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 525-537.  doi: 10.1007/s00376-000-0016-7
    [17] Duan Tingyang, Elmar R. Reiter, 1990: Some Characteristics of Cumulus Convection over the Tibetan Plateau, ADVANCES IN ATMOSPHERIC SCIENCES, 7, 87-97.  doi: 10.1007/BF02919171
    [18] Ji Zhongzhen, Wang Bin, 1995: Some Splitting Methods for Equations of Geophysical Fluid Dynamics, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 109-113.  doi: 10.1007/BF02661293
    [19] Wu Rongsheng, Fang Juan, 2001: Mechanism of Balanced Flow and Frontogenesis, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 323-334.  doi: 10.1007/BF02919313
    [20] Tan Zhemin, Wu Rongsheng, 1994: Helicity Dynamics of Atmospheric Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 175-188.  doi: 10.1007/BF02666544

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Manuscript History

Manuscript received: 10 October 1985
Manuscript revised: 10 October 1985
通讯作者: 陈斌, bchen63@163.com
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SOME CATASTROPHE PROPERTIES OF TWO-LAYER SHEAR FLOW

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

Abstract: In this paper a simple current system which consists of two stratified incompressible layers is examined. For the basic equations of the motion of fluid a lower order spectrum model is established by means of Galerkin method. Adopting the difference of wind velocity between the upper and lower layers, As =as a control parameter, the bifurcation and stability of the solution of the dynamical systemare discussed. It is found that the flow states in the lower layer will have a catastrophe, when where Cg is the phase velocity of the internal inertio-gravitational wave in a geostrophic current.These results may give a reasonable explanation for the mechanism of the catastrophe phenomena, including the "pressure-jump" in the atmosphere.

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