大气运动的慢流形概论

doi:10.11867/j.issn.1001-8166.2007.04.0331

地球科学进展 ›› 2007, Vol. 22 ›› Issue (4): 331 -340. doi: 10.11867/j.issn.1001-8166.2007.04.0331

研究论文下一篇

大气运动的慢流形概论

赵南 ¹, 沈新勇 ², 丁一汇 ³

1.中国气象科学研究院灾害天气国家重点实验室,北京 100081; 2.南京信息工程大学,江苏省气象灾害重点实验室,江苏南京 210044；3.国家气候中心,北京 100081

收稿日期:2006-11-20 修回日期:2007-02-25 出版日期:2007-04-10
通讯作者: 赵南(1963-), 男,陕西洛南人，研究员, 主要从事气候动力学与大气中非线性过程方面研究.E-mail: zhaon@cams.cma.gov.cn E-mail:zhaon@cams.cma.gov.cn
基金资助:
国家重点基础研究发展计划项目“我国南方致洪暴雨监测和预测的理论和方法研究”(编号：2004CB418301)；国家科技部攀登A计划项目“南海季风试验（SCSMEX）”共同资助.

Review on the Slow Manifold of Atmosphere Motion

ZHAO Nan ¹, SHEN Xin-yong ², DING Yi-hui ³

1.LaSW,Chinese Academy of Meteorological Sciences,Beijing 100081,China;2.Nanjing University of Information Science and Technology,Nanjing 210044,China; 3.National Climate Center, Beijing 100081, China

Received:2006-11-20 Revised:2007-02-25 Online:2007-04-10 Published:2007-04-10

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从动力学系统的慢流形（slow manifold）的一般概念及数学描述出发，系统地论述了大气运动的慢流形的存在性和一般性质。文中侧重于讨论与大气运动的慢流形密切相关的一些重要问题，包括平衡运动或平衡流的性质以及它对惯性重力波的自发辐射（spontaneous emission）、PV反演理论和应用、与数值模式初始化问题的联系等，并对上述研究领域的研究历史和现状也进行了较为全面的综述，旨在为国内气象界相关方向的研究者提供了解该领域概貌并较快切入具体研究问题的线索。

关键词: 慢流形, 平衡流, 惯性重力波自发辐射, PV反演, 数值模式初始化

Based on the general concept of slow manifold of dynamical system and its mathematical description, the authors discuss systematically the existence and some general properties of slow manifold in atmospheric dynamics. The discussion emphasizes particularly on some important issues closely related to the slow manifold of the atmospheric motion such as properties of the balance dynamics, the spontaneous emission of inertia gravity wave from balance flow, theory and application of PV inversion and the relation to initialization issue of numerical model. Moreover, an overview of the history and the state of the art of researches in this field are given to provide domestic researchers of relevant topics a clue for the understanding of general picture of this field and entering into specific research issues.

Key words: Slow manifold, Balance flow, Spontaneous emission, PV inversion, Initialization.

中图分类号:

P433

[1]Anosov D V, Arnold V I. Dynamical Systems I[M]. Beijing：Springer-Verlag, World Publishing Corp,1990.
[2]Leith C E. Nonlinear normal mode initialization and quasi-geostrophic theory[J].Journal of the Atmospheric Sciences,1980, 37:958-968.
[3]Lorenz E N. Attractor sets and quasi-geostrophic equilibrium[J]. Journal of the Atmospheric Sciences,1980, 37：1 685-1 699. 
[4]Lorenz E N. On the existence of a slow manifold[J]. Journal of the Atmospheric Sciences,1986, 43：1 547-1 557.
[5]Lorenz E N,Krishnamurthy V.On the nonexistence of a slow manifold[J]. Journal of the Atmospheric Sciences,1987,44：2 940-2 950.
[6]Warn T,Menard R. Nonlinear balance and gravity-inertial wave saturation in a simple atmospheric model [J]. Tellus, 1986, 38：285-294.
[7]Vautard R, Legras B. Invariant manifolds, quasi-geostrophy and initialization [J]. Journal of the Atmospheric Sciences,1986, 43：565-584. 
[8]Jacobs S J. On the existence of a slow manifold in a model system of equations [J]. Journal of the Atmospheric Sciences,1991, 48：793-801.
[9]Lorenz E N. The slow manifold-What is it?[J].Journal of the Atmospheric Sciences,1992,49:2 449-2 451.
[10]Ford R, McIntyre M E, Norton W A. Balance and the slow quasimanifold: Some explicit results[J].Journal of the Atmospheric Sciences,2000, 57：1 236-1 254.
[11]Warn T. Nonlinear balance and quasi-geostrophic sets[J].Atmosphere Ocean,1997,35：135-145.
[12]Bokhove O, Shepherd T G. On Hamiltonian balanced dynamics and the slowest invariant manifold[J]. Journal of the Atmospheric Sciences,1996, 53：276-297.
[13]McIntyre M E. Balance, potential-vorticity inversion, Lighhill radiation and the slow quasimanifold[C]∥Hodnett P F, ed. Proceeding of IUTAM/IUGG/Royal Irish Academy Symposium on Advanced in Mathematical Modelling of Atmosphere and Ocean. University of Limerick, Ireland, 2-7 July 2000:45-68.
[14]Guckenheimer J, Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields [M]. Tokyo: Springer-Verlag,1993.
[15]Ford R. The instability of an axisymmetric vortex with monotonic potential vorticity in rotating shallow water[J]. Journal of Fluid Mechanics, 1994, 280：303-334.
[16]Kushner P J, McIntyre M E, Shepherd T G. Coupled Kelvin wave and mirage-wave instabilities in semigeostrophic dynamics[J]. Journal of Physical Oceanography, 1998, 28：737-762.
[17]Yavneh I, McWilliams J C, Molemaker M J. Non-axisymmetric instability of centrifugally-stable stratified Taylor Couette flow[J]. Journal of Fluid Mechanics,2001，448：1-21. 
[18]Molemaker M J, McWilliams J C, Yavneh I. Instability and equilibration of centrifugally-stable stratified Taylor-Couette flow[J]. Physics Review Letter,2001, 86:5 270-5 273.
[19]Gelfreich V, Lerman L. Almost invariant elliptic manifold in a singularly perturbed Hamiltonian system[J]. Nonlinearity,2002, 15：447-457.
[20]Vanneste J,Yavneh I. Exponentially small inertia gravity waves and the breakdown of quasigeostrophic balance[J].Journal of the Atmospheric Sciences,2004,61（2）：211-223.
[21]Saujani S, Shepherd T G. Comments on Balance and the slow quasimanifold: Some explicit results[J]. Journal of the Atmospheric Sciences,2002, 59：2 874-2 877. 
[22]Ford R, McIntyre M E, Norton W A. Reply[J].Journal of the Atmospheric Sciences,2002, 59：2 878-2 882.
[23]Whitaker J S.A comparison of primitive and balance equation simulations of baroclinic waves[J]. Journal of the Atmospheric Sciences,1993,50：1 519-1 530.
[24]Medvedev S B. The slow manifold for the shallow water equation on the f plane [J].Journal of the Atmospheric Sciences,1999, 56：1 050-1 054.
[25]Lighthill M J. On sound generated aerodynamically I. General theory[J].Proceedings of the Royal Society of London, 1952,211:564-587.
[26]Salmon R. Halmiltonian fluid mechanics [J]. Annual Review of Fluid Mechanics,1988, 20：225-256.
[27]Hoskins B J, McIntyre M E, Robertson A. On the use and significance of isentropic potential vorticity maps [J].Quarterly Journal of the Royal Meteorological Society,1985, 111：887-946.
[28]Warn T, Bokhove O, Shepherd T G, et al. Rossby number expansions, slaving principles, and balance dynamics[J].Quarterly Journal of the Royal Meteorological Society,1995,121：723-739.
[29]Vallis G K. Potential vorticity and balanced equation of motion for rotating and stratified flows[J].Quarterly Journal of the Royal Meteorological Society,1996, 122：291-322.
[30]Bishop C H, Thorpe A J. Potential vorticity and the electrostatics analogy: Quasi-geostrophic theory[J]. Quarterly Journal of the Royal Meteorological Society,1994, 120：713-731.
[31]Robinson W A. Analysis of LIMS data by potential vorticity inversion [J]. Journal of the Atmospheric Sciences,1988,45：2 319-2 342.
[32]Davis C A, Emanuel K A. Potential vorticity diagnostics of cyclogenesis[J]. Monthly Weather Review, 1991, 119：1 925-1 953.
[33]Davis C A. Piecewise potential vorticity inversion [J]. Journal of the Atmospheric Sciences,1992, 49：1 397-1 411.
[34]Hartley D E, Villarin J T, Black R X, et al. A new perspective on the dynamical link between the stratosphere and troposphere[J]. Nature,1998, 391:471-74.
[35]McIntyre M E,Norton W A. Potential vorticity inversion on a Hemisphere [J]. Journal of the Atmospheric Sciences,2000, 57：1 214-1 235.
[36]Wu C C, Huang T S,Chou K H. Potential vorticity diagnosis of the key factors affecting the motion of typhoon Sinlaku (2002)[J]. Monthly Weather Review, 2002,132：2 084-2 093.
[37]Ambaum M H P, Hoskins B J. The NAO troposphere-stratosphere connection[J]. Journal of Climate,2002,15:1 969-1 978.
[38]Black R X. Stratospheric forcing of surface climate in the Arctic Oscillation[J]. Journal of Climate,2002, 15:268-77.
[39]Davis C A. Potential vorticity inversion and MM5[EB/OL].http://www.mmm.ucar.edu/mm5/workshop,2003.

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