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Volume 11 Issue 1

Jan.  1994

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Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 1994 >  11(1): 74-78

Note on the Symmetric Stability of Quasi-Homogeneous and Incompressible Rotating Ocean

  • 1.

    LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100080


doi: 10.1007/BF02656996

  • The general property of zonally symmetric stability of quasi-homogeneous and incompressible rotating ocean can be determined by a nondimensional parameter Rs which is similar to the Richardson number in Howard’s paper. The results indicate that the rotating effect leads to stabilize the basic flows and the horizontal shear effect leads to destabilize the basic flows. In addition, the most unstable growth rate is obtained and the semicircle and semiellipse theorem about the distributions of the unstable phase velocity are given in this paper.
  • [1] Ren Shuzhan, 1994: Symmetric Stability of Rotation and Boussinesq Fluid in Bounded Domain by Using Normal Mode Method, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 291-295.  doi: 10.1007/BF02658148
    [2] LU Weisong, SHAO Haiyan, 2003: Generalized Nonlinear Subcritical Symmetric Instability, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 623-630.  doi: 10.1007/BF02915505
    [3] 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
    [4] Liu Yongming, 1999: Nonlinear Stability of Zonally Symmetric Quasi-geostrophic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 107-118.  doi: 10.1007/s00376-999-0007-2
    [5] 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
    [6] Liu Yongming, Mu Mu, 1994: Arnol’d’s Second Nonlinear Stability Theorem for General Multilayer Quasi-geostrophic Model, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 36-42.  doi: 10.1007/BF02656991
    [7] Yang Fanglin, 1991: The Stability of Large-Scale Horizontal Air Motion in the Non-linear Basic Zephyr Flow under the Effect of Rossby Parameter, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 149-164.  doi: 10.1007/BF02658091
    [8] 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
    [9] 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
    [10] Zhou Weican, Chen Jiukang, Zhou Shunwu, 1997: Symmetric Development of Meso Perturbation in Zonally Curved Basic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 14, 527-534.  doi: 10.1007/s00376-997-0070-5
    [11] Zheng Yi, 2000: Study on Horizontal Relative Diffusion in the Troposphere and Lower Stratosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 93-102.  doi: 10.1007/s00376-000-0046-1
    [12] LIU Yudi, WANG Bin, JI Zhongzhen, 2003: Research on Atmospheric Motion in Horizontal Discrete Grids, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 139-148.  doi: 10.1007/BF03342058
    [13] Huang Runheng, Kuo-Nan Liou, 1985: EFFECTS OF HORIZONTAL ORIENTATION ON THE RADIATIVE PROPERTIES OF ICE CLOUDS, ADVANCES IN ATMOSPHERIC SCIENCES, 2, 20-27.  doi: 10.1007/BF03179733
    [14] He Jianzhong, 1994: Nonlinear Ultra-Long Wave and Its Stability, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 91-100.  doi: 10.1007/BF02656998
    [15] Lei Xiaoen, 1985: EFFECT OF WIND VERTICAL SHEAR ON DIFFUSION CHARACTERISTICS IN THE MESOSCALE RANGE, ADVANCES IN ATMOSPHERIC SCIENCES, 2, 225-233.  doi: 10.1007/BF03179754
    [16] Yang Peicai, 1985: SOME CATASTROPHE PROPERTIES OF TWO-LAYER SHEAR FLOW, ADVANCES IN ATMOSPHERIC SCIENCES, 2, 498-507.  doi: 10.1007/BF02678748
    [17] Yi Zengxin, T. Warn, 1987: A NUMERICAL METHOD FOR SOLVING THE EVOLUTION EQUATION OF SOLITARY ROSSBY WAVES ON A WEAK SHEAR, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 43-54.  doi: 10.1007/BF02656660
    [18] Li Maicun, 1987: EQUATORIAL SOLITARY WAVES OF TROPICAL ATMOSPHERIC MOTION IN SHEAR FLOW, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 125-136.  doi: 10.1007/BF02677059
    [19] 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
    [20] Wen Jingsong, Wang Yongguang, 1995: The Effect of Weak Shear-induced Motion on Brownian Coagulation of Aerosol Particles, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 187-194.  doi: 10.1007/BF02656831
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    • Manuscript History

    Manuscript received: 10 January 1994
    Manuscript revised: 10 January 1994
    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

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    Note on the Symmetric Stability of Quasi-Homogeneous and Incompressible Rotating Ocean

    • 1. LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100080
    • Manuscript received: 1994-01-10
    • Manuscript revised: 1994-01-10

    Abstract: The general property of zonally symmetric stability of quasi-homogeneous and incompressible rotating ocean can be determined by a nondimensional parameter Rs which is similar to the Richardson number in Howard’s paper. The results indicate that the rotating effect leads to stabilize the basic flows and the horizontal shear effect leads to destabilize the basic flows. In addition, the most unstable growth rate is obtained and the semicircle and semiellipse theorem about the distributions of the unstable phase velocity are given in this paper.

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