Relative equilibria of point vortices on the sphere

PHYSICA D-NONLINEAR PHENOMENA

卷:148

Article

Lim, C ; Montaldi, J ; Roberts, M

关键词: point vortices;    symmetry;    first integrals;    flow on a sphere;   

DOI  :  10.1016/S0167-2789(00)00167-6

来源: Elsevier

【 摘 要 】

We prove the existence of many different symmetry types of relative equilibria for systems of identical point vortices on a non-rotating sphere. The proofs use the rotational symmetry group SO(3) and the resulting conservation laws, the time-reversing reflectional symmetries in O(3), and the finite symmetry group of permutations of identical vortices. Results include both global existence theorems and local results on bifurcations from equilibria. A more detailed study is made of relative equilibria which consist of two parallel rings with n vortices in each rotating about a common axis. The paper ends with discussions of the bifurcation diagrams for systems of 3-6 identical vortices. (C) 2001 Elsevier Science B.V. All rights reserved.

【 授权许可】

Free