Quantized Vortex Rings and Loop Solitons
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Quantized Vortex Rings and Loop Solitons P. J. Green1 · M. J. Grant1 · J. W. Nevin1 · P. M. Walmsley1 · A. I. Golov1 Received: 15 July 2019 / Accepted: 8 August 2020 © The Author(s) 2020
Abstract The vortex filament model is used to investigate the interaction of a quantized vortex ring with a straight vortex line and also the interaction of two solitons traveling in opposite directions along a vortex. When a ring reconnects with a line, we find that a likely outcome is the formation of a loop soliton. When they collide, loop solitons reconnect as they overlap each other producing either one or two vortex rings. These simulations are relevant for experiments on quantum turbulence in the zero temperature limit where small vortex rings are expected to be numerous. It seems that loop solitons might also commonly occur on vortex lines as they act as transient states between the absorption of a vortex ring before another ring is emitted when the soliton is involved in a reconnection. Keywords Quantized vortices · Solitons · Vortex rings · Quantum turbulence
1 Introduction The dynamics of quantized vortices in the limit of zero temperature are interesting due to the broad range of length scales and the rich variety of physics involved [1, 2]. The dissipation of turbulent vortex tangles is thought to be due to the emission of phonons from short-wavelength Kelvin waves and also the release of small vortex rings that can travel to the walls of the container unimpeded. The vast majority of theoretical and computational research on quantum turbulence has focused only on these two types of vortex structure: linear helical deformations (Kelvin waves) [3–5] and vortex rings [6, 7]. However, other types of nonlinear deformations are possible (e.g., such as breathers [8]), and in this paper, we investigate whether one particular type of nonlinear deformation, loop solitons * P. M. Walmsley [email protected] A. I. Golov [email protected] 1
Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
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Journal of Low Temperature Physics
[9], may have a role to play in the dynamics of quantum turbulence. Solitons are solitary waves that can travel large distances without any change of shape or dissipation and can be found in a wide range of physical systems including fluids, optics, atomic and condensed matter physics [10]. In this work, we start by investigating the interaction between a vortex ring and a straight vortex line. Previous research has only considered the special case where the ring is initially travelling perpendicular to the line [11–15]. It was found that when the ring reconnects with the line it is either absorbed, with the energy transferred to packets of Kelvin waves, or a smaller secondary ring is emitted. In this work, we consider a more general case where the initial angle between the direction of the ring’s motion and the line is varied. Our motivation is that as new experiments are currently being developed to
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