Lie reduction and exact solutions of vorticity equation on rotating sphere

Following our paper [A. Bihlo, R.O. Popovych, J. Math. Phys. 50 (2009) 123102 (12 pp.), arXiv:0902.4099], we systematically carry out Lie symmetry analysis for the barotropic vorticity equation on the rotating sphere. All finite-dimensional subalgebras of the corresponding maximal Lie invariance algebra, which is infinite-dimensional, are classified. Appropriate subalgebras are then used to exhaustively determine Lie reductions of the equation under consideration. The relevance of the constructed exact solutions for the description of real-world physical processes is discussed. It is shown that the results of the above paper are directly related to the results of the recent Letter [N.H. Ibragimov, R.N. Ibragimov, Phys. Lett. A 375 (2011) 3858] in which Lie symmetries and some exact solutions of the nonlinear Euler equations for an atmospheric layer in spherical geometry were determined.

► Finite-dimensional subalgebras of an infinite-dimensional Lie algebra are classified.
► Lie reductions of the vorticity equation on the sphere are carried out.
► Exact solutions of the vorticity equation on the sphere are found.