A note on similarity reductions of barotropic and quasi-geostrophic potential vorticity equation. (English) Zbl 1392.35018
Summary: Applying the classical Lie symmetry approach to the barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a \(\beta\)-plane channel, we find a new symmetry, which is not presented in a previous work [F. Huang, Commun. Theor. Phys. 42, No. 6, 903–908 (2004; Zbl 1167.76358)]. A general finite transformation group is obtained based on the full Lie point symmetry. Furthermore, two new types of similarity reduction solutions are obtained.
MSC:
35B06 | Symmetries, invariants, etc. in context of PDEs |
35Q86 | PDEs in connection with geophysics |
35C05 | Solutions to PDEs in closed form |