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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.9

ISSN Imprimir: 2152-5102
ISSN On-line: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v30.i2.40
18 pages

Two Approaches to the Analysis of the Coaxial Interaction of Vortex Rings

V. V. Meleshko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
G. J. F. van Heijst
Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands

RESUMO

Two models for describing vortex rings: the Dyson's model with a continuous vorticity distribution and the vorton model with discrete vorticity distribution, which both can be used to describe the coaxial interaction of two identical vortex rings, are compared. The presentation of motion equations of both models in a similar formulation makes possible an extended analysis of both the analogies and differences between the models: comparing trajectories, impulses and energies of the vortex rings system in both cases for periodical interaction of two identical vortex rings in an unbounded fluid. The slightly different trajectories can be entirely explained theoretically from the respective equations of motion for vortex rings and vorton rings. The analysis of matching and comparison of the initial parameters of two different models, which both describe the same interaction, is presented in this article. A possible criterion, which can be used for description of a non-coaxial interaction of vortex rings by means of discrete vorton model, was obtained.


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