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 [3]. In the present paper, 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. Prom the viewpoint of the configuration of three vortices, we classify the motion with assistance of the numerical computation.
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References
H. Aref, Three vortex motion with zero total circulation: Addendum. J. Appl. Math. Phys. (ZAMP),40 (1989), 495–500.
H. Aref and N. Pompherey, Integrable and chaotic motions of four vortices I: The case of identical vortices. Proc. R. Soc. Lond.,A380 (1982), 359–387.
V.A. Bogomolov, Dynamics of vorticity at a sphere. Izv. Acad. Sci. USSR Atoms. Oceanic Phys.,15 (1979), 863–870.
B. Eckhardt, Integrable four vortex motion. Phys. Fluids,31 (1988), 2796–2801.
Y. Kimura, Similarity solution of two-dimensional point vortices. J. Phys. Soc. Japan,56 (1987), 2024–2030.
H. Okamoto, Nonlinear Dynamics (in Japanese). Chapter 4.
N. Rott, Three vortex motion with zero total circulation. J. Appl. Math. Phys. (ZAMP),40 (1989), 473–494.
J.L. Synge, On the motion of three vortices. Canadian J. Math.,1 (1949), 257–270.
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Sakajo, T. The motion of three point vortices on a sphere. Japan J. Indust. Appl. Math. 16, 321–347 (1999). https://doi.org/10.1007/BF03167361
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DOI: https://doi.org/10.1007/BF03167361