Two approaches to the analysis of the coaxial interaction of vortex rings (Q2784935)

Two models for describing vortex rings: Dyson model with a continuous vorticity distribution and 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 unbounded fluid. The slightly different trajectories could be entirely explained theoretically from the respective equation of motion for vortex rings and vorton rings. The analysis of matching and comprising 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 an application to non-coaxial interaction of vortex rings by means of discrete vorton model, was obtained.