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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 163689, 16 pages
Research Article

Potential Symmetry Studies on a Rotating Fluid System

1Department of Physics, Ningbo University, Ningbo 315211, China
2Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China
3School of Mathematics, Fudan University, Shanghai 200433, China
4Physical Oceanography Laboratory, Ocean University of China, Qingdao 266003, China

Received 13 July 2011; Revised 26 September 2011; Accepted 26 October 2011

Academic Editor: Marc de Montigny

Copyright © 2012 S. Y. Lou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A rotational fluid model which can be used to describe broad vortical flows ranging from large scale to the atmospheric mesoscale and the oceanic submesoscale is studied by the symmetry group theory. After introducing one scalar-, two vector-, and two tensor potentials, we find that the Lie symmetries of the extended system include many arbitrary functions of z and {z,t}. The obtained Lie symmetries are used to find some types of exact solutions. One of exact solutions can be used to qualitatively describe the three-dimensional structure of hurricanes.