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 and . 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.