Symmetry Analysis of Barotropic Potential Vorticity Equation

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理论物理通讯 ›› 2009, Vol. 52 ›› Issue (04) : 697-700.

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Symmetry Analysis of Barotropic Potential Vorticity Equation

Alexander Bihlo¹ and Roman O. Popovych^1,2

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Abstract

Recently F. Huang [Commun. Theor. Phys. 42 (2004) 903] and X. Tang and P.K. Shukla [Commun. Theor. Phys. 49 (2008) 229] investigated symmetry properties of the barotropic potential vorticity equation without forcing and
dissipation on the beta-plane. This equation is governed by two dimensionless parameters, F and β, representing the ratio of the characteristic length scale to the Rossby radius of deformation and the variation of earth' angular rotation, respectively. In the present paper it is shown that in the case F≠ 0 there exists a well-defined point transformation to set β= 0. The
classification of one- and two-dimensional Lie subalgebras of the Lie symmetry algebra of the potential vorticity equation is given for the parameter combination F≠0 and β = 0. Based upon this classification, distinct classes of group-invariant solutions are obtained and extended to the case β≠ 0.

导出引用

Alexander Bihlo and Roman O. Popovych,. Symmetry Analysis of Barotropic Potential Vorticity Equation[J]. 理论物理通讯, 2009, 52(04): 697-700

Alexander Bihlo and Roman O. Popovych,. Symmetry Analysis of Barotropic Potential Vorticity Equation[J]. Communications in Theoretical Physics, 2009, 52(04): 697-700

中图分类号： 47.35.-i 47.32.-y 02.20.Sv