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Coaxial interactions of two vortex rings or of a ring with a body. (English) Zbl 0854.76022

The authors consider the coaxial interactions of two vortex rings, including head-on collisions and leapfrogging motions, as well as interactions of vortex rings with a solid boundary in an ideal fluid. Interactions of vortex rings with solid bodies are investigated by combining the contour dynamics technique with a boundary integral equation method. Numerical results show that a clean, successful passage motion is possible for two vortex rings with sufficiently thin cores. In both cases of head-on collisions and leapfrogging motion, very large core deformations are observed when two vortex rings get close to each other. A head-tail structure is formed in the latter stage of a head-on collision of two fat vortices. It is also shown numerically that a vortex ring will stretch and slowly flow down when it moves towards a solid boundary, will shrink and speed up when it moves away from a solid boundary, and will either translate steadily or approach an oscillating asymptotic state when it is far away from any boundaries.

MSC:

76B47 Vortex flows for incompressible inviscid fluids
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