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Volume 8 Issue 2

Mar.  1991

Article Contents

Nonlinear Stability of Plane Rotating Shear Flow under Three-Dimensional Nondivergence Disturbances


doi: 10.1007/BF02658089

  • Nonlinear stability criterion for plane rotating shear flow under three-dimensional nondivergence disturbances was obtained by using both variational principle and convexity estimate introduced by Arnold (1965) and Holm et al. (1985). The results obtained in this paper show that the effect of Coriolis force plays an important role in the nonlinear stability criterion, and the nonlinear stability property of the basic flow depends on both the distribution of basic states and the way the external disturbance acts on the states. The upper bound of the gradient of the mass density displacement from the equilibrium k2 = is determined by the basic states and one example was given to show the exact upper value of k. The remarks on Blumen's paper were also given at Section 4 of this paper.
  • [1] Li Yang, Mu Mu, 1996: On the Nonlinear Stability of Three-Dimensional Quasigeostrophic Motions in Spherical Geometry, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 203-216.  doi: 10.1007/BF02656863
    [2] Mu Mu, Zeng Qingcun, 1991: Criteria for the Nonlinear Stability of Three-Dimensional Quasi-Geostrophic Motions, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 1-10.  doi: 10.1007/BF02657360
    [3] Jae-Jin KIM, Jong-Jin BAIK, 2010: Effects of Street-Bottom and Building-Roof Heating on Flow in Three-Dimensional Street Canyons, ADVANCES IN ATMOSPHERIC SCIENCES, 27, 513-527.  doi: 10.1007/s00376-009-9095-2
    [4] H.L. Kuo, 1995: Three-dimensional Global Scale Permanent-wave Solutions of the Nonlinear Quasigeostrophic Potential Vorticity Equation and Energy Dispersion, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 387-404.  doi: 10.1007/BF02657001
    [5] 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
    [6] Zeng Qingcun, Lu Peisheng, Li Rongfeng, Yuan Chongguang, 1986: EVOLUTION OF LARGE SCALE DISTURBANCES AND THEIR INTERACTION WITH MEAN FLOW IN A ROTATING BAROTROPIC ATMOSPHERE —PART I, ADVANCES IN ATMOSPHERIC SCIENCES, 3, 39-58.  doi: 10.1007/BF02682551
    [7] Zeng Qingcun, Lu Peisheng, Li Rongfeng, Yuan Chongguang, 1986: EVOLUTION OF LARGE SCALE DISTURBANCES AND THEIR INTERACTION WITH MEAN FLOW IN A ROTATING BAROTROPIC ATMOSPHERE PART II, ADVANCES IN ATMOSPHERIC SCIENCES, 3, 172-188.  doi: 10.1007/BF02680044
    [8] SHI Ning, and BUEH Cholaw, 2013: Three-dimensional dynamic features of two Arctic oscillation types, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 1039-1052.  doi: 10.1007/s00376-012-2077-9
    [9] ZHANG Lei, QIU Chongjian, HUANG Jianping, 2008: A Three-Dimensional Satellite Retrieval Method for Atmospheric Temperature and Moisture Profiles, ADVANCES IN ATMOSPHERIC SCIENCES, 25, 897-904.  doi: 10.1007/s00376-008-0897-4
    [10] Yu Xing, Dai Jin, Jiang Weimei, Fan Peng, 2000: A Three-Dimensional Model of Transport and Diffusion of Seeding Agents within Stratus, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 617-635.  doi: 10.1007/s00376-000-0024-7
    [11] LIU Yongming, CAI Jingjing, 2006: On Nonlinear Stability Theorems of 3D Quasi-geostrophic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 809-814.  doi: 10.1007/s00376-006-0809-4
    [12] 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
    [13] Zhu Xun, 1987: ON GRAVITY WAVE-MEAN FLOW INTERACTIONS IN A THREE DIMENSIONAL STRATIFIED ATMOSPHERE, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 287-299.  doi: 10.1007/BF02663599
    [14] LIU Ye, YAN Changxiang, 2010: Application of a Recursive Filter to a Three-Dimensional Variational Ocean Data Assimilation System, ADVANCES IN ATMOSPHERIC SCIENCES, 27, 293-302.  doi: 10.1007/s00376-009-8112-9
    [15] ZENG Zhihua, DUAN Yihong, LIANG Xudong, MA Leiming, Johnny Chung-leung CHAN, 2005: The Effect of Three-Dimensional Variational Data Assimilation of QuikSCAT Data on the Numerical Simulation of Typhoon Track and Intensity, ADVANCES IN ATMOSPHERIC SCIENCES, 22, 534-544.  doi: 10.1007/BF02918486
    [16] ZHANG Chengwei, YU Fan, WANG Chenxi, YANG Jianyu, 2011: Three-dimensional Extension of the Unit-Feature Spatial Classification Method for Cloud Type, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 601-611.  doi: 10.1007/s00376-010-9056-9
    [17] LI Yan, ZHU Jiang, WANG Hui, 2013: The Impact of Different Vertical Diffusion Schemes in a Three-Dimensional Oil Spill Model in the Bohai Sea, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 1569-1586.  doi: 10.1007/s00376-012-2201-x
    [18] Leilei KOU, Zhuihui WANG, Fen XU, 2018: Three-dimensional Fusion of Spaceborne and Ground Radar Reflectivity Data Using a Neural Network-Based Approach, ADVANCES IN ATMOSPHERIC SCIENCES, 35, 346-359.  doi: 10.1007/s00376-017-6334-9
    [19] Lu LIU, Lingkun RAN, Shouting GAO, 2019: A Three-dimensional Wave Activity Flux of Inertia-Gravity Waves and Its Application to a Rainstorm Event, ADVANCES IN ATMOSPHERIC SCIENCES, 36, 206-218.  doi: 10.1007/s00376-018-8018-5
    [20] Kong Fanyou, Huang Meiyuan, Xu Huaying, 1993: Three-Dimensional Numerical Simulations of the Effects of a Cold Water Surface on the Evolution and Propagation of Thunderstorms, ADVANCES IN ATMOSPHERIC SCIENCES, 10, 261-272.  doi: 10.1007/BF02658132

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Manuscript History

Manuscript received: 10 March 1991
Manuscript revised: 10 March 1991
通讯作者: 陈斌, bchen63@163.com
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Nonlinear Stability of Plane Rotating Shear Flow under Three-Dimensional Nondivergence Disturbances

  • 1. Institute of Atmospheric physics, Academia Sinica, Beijing 100080, China

Abstract: Nonlinear stability criterion for plane rotating shear flow under three-dimensional nondivergence disturbances was obtained by using both variational principle and convexity estimate introduced by Arnold (1965) and Holm et al. (1985). The results obtained in this paper show that the effect of Coriolis force plays an important role in the nonlinear stability criterion, and the nonlinear stability property of the basic flow depends on both the distribution of basic states and the way the external disturbance acts on the states. The upper bound of the gradient of the mass density displacement from the equilibrium k2 = is determined by the basic states and one example was given to show the exact upper value of k. The remarks on Blumen's paper were also given at Section 4 of this paper.

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