
arXiv: 0801.2408
A simple - yet plausible - model for B-type vortex breakdown flows is postulated; one that is based on the immersion of a pair of slender coaxial vortex rings in a swirling flow of an ideal fluid rotating around the axis of symmetry of the rings. It is shown that this model exhibits in the advection of passive fluid particles (kinematics) just about all of the characteristics that have been observed in what is now a substantial body of published research on the phenomenon of vortex breakdown. Moreover, it is demonstrated how the very nature of the fluid dynamics in axisymmetric breakdown flows can be predicted and controlled by the choice of the initial ring configurations and their vortex strengths. The dynamic intricacies produced by the two ring + swirl model are illustrated with several numerical experiments.
40 pages, 9 figures, submitted to Physica D
Melnikov function, advection, FOS: Physical sciences, General theory of rotating fluids, Shilnikov chaos, Dynamical Systems (math.DS), Mathematical Physics (math-ph), Vortex flows for incompressible inviscid fluids, swirl, 37J20, Dynamical systems in fluid mechanics, oceanography and meteorology, 37J20; 37J25, 37J25, FOS: Mathematics, Mathematics - Dynamical Systems, Poincaré map, Mathematical Physics
Melnikov function, advection, FOS: Physical sciences, General theory of rotating fluids, Shilnikov chaos, Dynamical Systems (math.DS), Mathematical Physics (math-ph), Vortex flows for incompressible inviscid fluids, swirl, 37J20, Dynamical systems in fluid mechanics, oceanography and meteorology, 37J20; 37J25, 37J25, FOS: Mathematics, Mathematics - Dynamical Systems, Poincaré map, Mathematical Physics
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 5 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
