Nonlinear Saturation of Baroclinic Instability in the Generalized Phillips Model(Ⅱ)-The Lower Bound on the Disturbance Energy and Potential Enstrophy to the Nonlinearly Unstable Basic Flow

ZHANG Gui; XIANG Jie

Volume 23 Issue 11

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Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(11): 1195-1202

ZHANG Gui, XIANG Jie. Nonlinear Saturation of Baroclinic Instability in the Generalized Phillips Model(Ⅱ)-The Lower Bound on the Disturbance Energy and Potential Enstrophy to the Nonlinearly Unstable Basic Flow[J]. Applied Mathematics and Mechanics, 2002, 23(11): 1195-1202.

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Nonlinear Saturation of Baroclinic Instability in the Generalized Phillips Model(Ⅱ)-The Lower Bound on the Disturbance Energy and Potential Enstrophy to the Nonlinearly Unstable Basic Flow

ZHANG Gui¹,
XIANG Jie²

1.
Department of Mathematics and Physics, Institute of Science, University of Science and Technology, P L A, Nanjing 211101, P R China;
2.
Department of Meteorology, P O Box 003, Nanjing 211101, P R China

Received Date: 2001-11-29
Rev Recd Date: 2002-05-25
Publish Date: 2002-11-15

Abstract

Abstract

On the basis of the nonlinear stability theorem in the context of Arnol'd's second theorem for the generalized Phillips model,nonlinear saturation of baroclinic instability in the generalized Phillips model is investigated.The lower bound on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model is presented,which indicates that there may exist an allocation between a nonlinearly unstable basic flow and a growing disturbance.
- nonlinear saturation,
- baroclinic instability,
- generalized Phillips model,
- basic flow

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References(11)

References

[1]	张瑰.广义Phillips模式的非线性稳定性判据[J].空军气象学院学报,1999,20(2):133-143.
[2]	张瑰,项杰,李东辉.广义Phillips模式非线性不稳定的饱和问题(Ⅰ)——基流不稳定时扰动演变的上界估计[J].应用数学和力学,2002,23(1):73-81.
[3]	Shepherd T G. Nonlinear saturation of baroclinic instability,Part-one:the two-layer model[J].Journal of the Atmospheric Sciences,1998,45(14):2014-2025.
[4]	Shepherd T G. Nonlinear saturation of baroclinic instability,Part-two:Continuously-statified fluid[J].Journal of the Atmospheric Sciences,1989,46(7):888-907.
[5]	Shepherd T G. Nonlinear saturation of baroclinic instability,part-three:bounds on the energy[J].Journal of the Atmospheric Sciences,1993,50(16):2697-2709.
[6]	MU Mu.Nonlinear stability theorem of two-dimensional quasi-geostrophic motions,geophys, Astrophy[J].Fluid Dynamics,1992,65(1):57-76.
[7]	Paret J,Vanneste J.Nonlinear saturation of baroclinic instability in a three-layer model[J].Journal of the Atmospheric Sciences,1996,53(20):2905-2917.
[8]	Cho H R, Shepherd T G, Vladimirov V A. Application of the direct Liapunov method to the problem of symmetric stability in the atmosphere[J].Journal of the Atmospheric Sciences,1993,50(6):822-834
[9]	MU Mu,Shepherd T G, Swanson K. On nonlinear symmetric stability and the nonlinear saturation of symmetric instability[J].Journal of the Atmospheric Sciences,1996,53(20):2918-2923.
[10]	ZENG Qing-cun. Variational Principle of instability of atmosphic motions[J].Adv Atmos Sci,1989,6(2):137-172.
[11]	XIANG Jie,MU Mu.Lower bound of disturbances for the nonlinearly unstable basic flow in the phillips model[A].In:CHINE Wei-zang, Ed.Proceeding of the Third International Conference on Nonlinear Mechanics[C].Shanghai,1998:548-553.

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