Bull. Korean Math. Soc. 2010; 47(1): 73-79
Printed January 1, 2010
https://doi.org/10.4134/BKMS.2010.47.1.73
Copyright © The Korean Mathematical Society.
Sun-Chul Kim
Chung-Ang University
A pair of point vortices of the same strength but opposite sign is called a vortex dipole. We consider the limiting case where two vortices approach infinitely close while the ratio of the strength to the distance kept constant. The motion of such point vortex dipole on the ellipsoid of revolution is investigated geometrically to conclude that the trajectory draws a geodesic up to the leading order of perturbation, whose direction is determined by the initial orientation of the dipole. Related issues are also remarked.
Keywords: point vortex, ellipsoid of revolution, perturbation expansion, geodesic, vortex dipole
MSC numbers: Primary 76B47, 76M45, 53A17
1998; 35(1): 189-193
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