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.
Similar content being viewed by others
Literature cited
H. Lamb, Hydrodynamics, Cambridge (1932).
W. M. Hicks, “On the mutual threading of vortex rings,” Proc. R. Soc. London Ser. A102, 111 (1923).
G. K. Batchelor, Introduction to Fluid Dynamics, Cambridge University Press (1967).
N. E. Kochin, I. A. Kibel', and N. V. Roze, Theoretical Hydrodynamics, New York (1964).
A. A. Andronov, A. A. Vitt, and S. E. Khaikin, Theory of Oscillations, Pergamon Press, Oxford (1966).
Author information
Authors and Affiliations
Additional information
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.
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01050100