The motion of point vortex dipole on the ellipsoid of revolution
Bull. Korean Math. Soc. 2010 Vol. 47, No. 1, 73-79
https://doi.org/10.4134/BKMS.2010.47.1.73
Printed January 1, 2010
Sun-Chul Kim
Chung-Ang University
Abstract : 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
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