The motion of three point vortices on a sphere

Abstract:

We consider the incompressible and inviscid flow on a sphere. The vorticity distributes as a point vortex. The governing equation for point vortices on a sphere is given by Bogomolov. In the present study, we study the motion of three point vortices. We prove that the motion is integrable Hamiltonian system and its solution never blows up in finite time. From the viewpoint of the configuration of three vortices, we classify the motion with assistance of the numerical computation.

Conclusion:

We focus on the spherical triangle which is formed by three vortices. As a result, the motion of three point vortices is qualitatively classified in terms of some parameters. (The first invariant and the strength of point vortices. ) The fact that the summation of the three vortices' strength vanishes is substantially important to the problem.

Reference:

T. Sakajo, The motion of three point vortices on a sphere, Japan Jounal of Industrial and Applied Mathematics, (1999) Vol.16 No.3 pp.321-347.
(This paper is awarded by JSIAM as the paper of the year,2000.)

Back