Symmetry analysis and explicit solutions of the (3+1)-dimensional baroclinic potential vorticity equation

doi:10.1088/1674-1056/19/8/080203

中国物理B ›› 2010, Vol. 19 ›› Issue (8): 80203-080203.doi: 10.1088/1674-1056/19/8/080203

Symmetry analysis and explicit solutions of the (3+1)-dimensional baroclinic potential vorticity equation

黄菲¹, 胡晓瑞², 陈勇³

(1)Department of Marine Meteorology, Ocean University of China, Qingdao 266003, China; (2)Institute of Theoretical Computing, East China Normal University, Shanghai 200062, China; (3)Institute of Theoretical Computing, East China Normal University, Shanghai 200062, China;Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China

收稿日期:2009-12-21 修回日期:2010-01-22 出版日期:2010-08-15 发布日期:2010-08-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10735030, 90718041 and 40975038), Shanghai Leading Academic Discipline Project (Grant No. B412), Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT0734).

Symmetry analysis and explicit solutions of the (3+1)-dimensional baroclinic potential vorticity equation

Hu Xiao-Rui(胡晓瑞)^a), Chen Yong(陈勇)^{a) b)†ger}, and Huang Fei(黄菲)^c)

^a Institute of Theoretical Computing, East China Normal University, Shanghai 200062, China ; ^b Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China; ^c Department of Marine Meteorology, Ocean University of China, Qingdao 266003, China

Received:2009-12-21 Revised:2010-01-22 Online:2010-08-15 Published:2010-08-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10735030, 90718041 and 40975038), Shanghai Leading Academic Discipline Project (Grant No. B412), Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT0734).

摘要/Abstract

摘要： This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-(3+1)-dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmetry algebra, symmetry group and group-invariant solutions are analysed. Otherwise, some exact explicit solutions are obtained from the corresponding (2+1)-dimensional equation, the inviscid barotropic nondivergent vorticy equation. To show the properties and characters of these solutions, some plots as well as their possible physical meanings of the atmospheric circulation are given.

Abstract: This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-(3+1)-dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmetry algebra, symmetry group and group-invariant solutions are analysed. Otherwise, some exact explicit solutions are obtained from the corresponding (2+1)-dimensional equation, the inviscid barotropic nondivergent vorticy equation. To show the properties and characters of these solutions, some plots as well as their possible physical meanings of the atmospheric circulation are given.

Key words: (3+1)-dimensional nonlinear baroclinic potential vorticity equation, symmetry group, group-invariant solution, explicit solution

中图分类号: (General circulation)

92.60.Bh

92.10.ab (General circulation)

胡晓瑞, 陈勇, 黄菲. Symmetry analysis and explicit solutions of the (3+1)-dimensional baroclinic potential vorticity equation[J]. 中国物理B, 2010, 19(8): 80203-080203.

Hu Xiao-Rui(胡晓瑞), Chen Yong(陈勇), and Huang Fei(黄菲). Symmetry analysis and explicit solutions of the (3+1)-dimensional baroclinic potential vorticity equation[J]. Chin. Phys. B, 2010, 19(8): 80203-080203.

参考文献 27

[1]	Lie S 1891 textit Arch. Math. 6 328
[2]	Ovsiannikov L V 1892 Group Analysis of Differential Equations (New York: Academic)
[3]	Olver P J 1993 Applications of Lie Groups to Differential Equations (Verlag: Springer)
[4]	Bluman G W and Anco S C 2002 Symmetry and Integration Methods for Differential Equations (New York: Springer)
[5]	Chen Y and Fan E G 2007 Chin. Phys. 16 6
[6]	Yao R X, Jiao X Y and Lou S Y 2009 Chin. Phys. B 18 1821
[7]	Li J H and Lou S Y 2008 Chin. Phys. B 17 747
[8]	Zhang S L, Lou S Y and Qu C Z 2006 Chin. Phys. 15 2765
[9]	Yang P, Chen Y and Li Z B 2008 Chin. Phys. B 17 3953
[10]	Zhang S Q, Xu G Q and Li Z B 2002 Chin. Phys. 11 933
[11]	Xia T C, Zhang H Q and Yan Z Y 2001 Chin. Phys. 10 694
[12]	Zha Q L and Li Z B 2008 Chin. Phys. B 17 2333
[13]	Wang J and Li B 2009 Chin. Phys. B 18 2213
[14]	Zhang H P, Chen Y and Li B 2009 Acta Phys. Sin. 58 7393 (in Chinese)
[15]	Sundkvist D, Krasnoselskikh V, Shukla P K, Vaivads A, Andr'e M, Buchert S and R`eme H 2005 Nature bf436 825
[16]	Pedrizzetti G 2005 Phys. Rev. Lett. 94 194502
[17]	Yurov A V and Yurova A A 2006 Theor. Math. Phys. 147 501
[18]	Huang F and Lou S Y 2004 Phys. Lett. A 320 428
[19]	Tang X Y, Huang F and Lou S Y 2006 Chin. Phys. Lett. 24 887
[20]	Huang F, Tang X Y, Lou S Y and Lu C H 2007 J. Atmos. Sci. 64 52
[21]	Lou S Y, Jia M, Huang F and Tang X Y 2007 Int. J. Theor. Phys. 46 2082
[22]	Lou S Y, Jia M, Tang X Y and Huang F 2007 Phys. Rev. E bf75 056318
[23]	Huang F and Lou S Y 2007 Commun. Theor. Phys. 48 895
[24]	Hu X R, Dong Z Z, Huang F and Chen Y 2009 Z. Naturforsch (accepted)
[25]	Pedlosky J 1979 Geophisical Fluid Dynamics (New York: Springer)
[26]	Zhang H P, Li B, Chen Y and Hang F Chin. Phys. B 19 060302
[27]	Luo D 1996 Wave Motion bf24 315

Symmetry analysis and explicit solutions of the (3+1)-dimensional baroclinic potential vorticity equation

Symmetry analysis and explicit solutions of the (3+1)-dimensional baroclinic potential vorticity equation

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