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Motion of two vortex rings

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Abstract

It is well-known [1] that two coaxial rings which are moving in the same direction pass through each other alternately. In the case of thin vortex rings this phenomenon was first considered qualitatively in [2]. The assumption that the vortex rings are thin means that when their interaction is considered they can be assumed to be annular vortex filaments. In the present paper, on the basis of the approach suggested in [2], certain new properties are determined for a system of two coaxial vortex rings of the same intensity.

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Literature cited

  1. H. Lamb, Hydrodynamics, Cambridge (1932).

  2. W. M. Hicks, “On the mutual threading of vortex rings,” Proc. R. Soc. London Ser. A102, 111 (1923).

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  3. G. K. Batchelor, Introduction to Fluid Dynamics, Cambridge University Press (1967).

  4. N. E. Kochin, I. A. Kibel', and N. V. Roze, Theoretical Hydrodynamics, New York (1964).

  5. A. A. Andronov, A. A. Vitt, and S. E. Khaikin, Theory of Oscillations, Pergamon Press, Oxford (1966).

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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 176–177, September–October, 1985.

The authors express their sincere thanks to A. A. Aleksandrov for his interest in their work.

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Boyarintsev, V.I., Levchenko, E.S. & Savin, A.S. Motion of two vortex rings. Fluid Dyn 20, 818–819 (1985). https://doi.org/10.1007/BF01050100

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  • DOI: https://doi.org/10.1007/BF01050100

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