Abstract
We have used the vortex filament method to numerically investigate the interactions between pairs of quantized vortex rings that are initially traveling in the same direction but with their axes offset by a variable impact parameter. The interaction of two circular rings of comparable radii produce outcomes that can be categorized into four regimes, dependent only on the impact parameter; the two rings can either miss each other on the inside or outside, or they can reconnect leading to final states consisting of either one or two deformed rings. The fraction of of energy went into ring deformations and the transverse component of velocity of the rings are analyzed for each regime. We find that rings of very similar radius only reconnect for a very narrow range of the impact parameter, much smaller than would be expected from geometrical cross-section alone. In contrast, when the radii of the rings are very different, the range of impact parameters producing a reconnection is close to the geometrical value. A second type of interaction considered is the collision of circular rings with a highly deformed ring. This type of interaction appears to be a productive mechanism for creating small vortex rings. The simulations are discussed in the context of experiments on colliding vortex rings and quantum turbulence in superfluid helium in the zero temperature limit.
Highlights
Vortex rings [1,2] are a common feature of many different fluid systems and can occur on a huge variety of length scales ranging from nanometers to interstellar plasmas
The local induction approximation (LIA) does not capture the long-range interactions that can occur between vortex rings nor is it sufficient for accurately describing the effect of large-amplitude Kelvin wave excitations on a ring and we use the full Biot-Savart approach (5) for all of the simulations presented in this paper
We have used the vortex filament model to investigate the interactions between pairs of unidirectional vortex rings with a variable impact parameter
Summary
Vortex rings [1,2] are a common feature of many different fluid systems and can occur on a huge variety of length scales ranging from nanometers to interstellar plasmas. The scenario where two rings are initially traveling in the same direction has not been studied in as much detail [9,10] and this paper seeks to address this issue In this case, the relative velocity of the rings is much lower, which allows a much longer time for nonlocal effects to act, resulting in several novel outcomes. The motion of the rings could be controlled and detected by tagging each ring with a trapped ion and the application of an electric field allowed R0 to be tuned to particular values These equations have been used to extract values for superfluid 4He of κ and a0 in the limit of zero temperature and pressure from measurements of the time of flight (and velocity) as a function of the energy imparted to a beam of rings [33,34]. VI we discuss the implications of these results for experiments in superfluid 4He
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