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

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

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.

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

Received: 21 December 2009
Revised: 22 January 2010
Accepted manuscript online:

PACS:	92.60.Bh	(General circulation)
	92.10.ab	(General circulation)

Fund: 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).

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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 2010 Chin. Phys. B 19 080203

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

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