Helicity conservation under quantum reconnection of vortex rings

Abstract

Here we show that under quantum reconnection, simulated by using the three-dimensional Gross- Pitaevskii equation, self-helicity of a system of two interacting vortex rings remains conserved. By resolving the fine structure of the vortex cores, we demonstrate that total length of the vortex system reaches a maximum at the reconnection time, while both writhe helicity and twist helicity remain separately unchanged throughout the process. Self-helicity is computed by two independent methods, and topological information is based on the extraction and analysis of geometric quantities such as writhe, total torsion and intrinsic twist of the reconnecting vortex rings.

References in corpus (6)

• Introduction to quantum turbulence
• Quantum vortex reconnections
• Helicity conservation by flow across scales in reconnecting vortex links and knots
• Pade approximations of solitary wave solutions of the Gross-Pitaevskii equation
• Reconnection Dynamics for Quantized Vortices
• Reconnections of quantized vortex rings in superfluid ${}^4$He at very low temperatures

Cited by in corpus (10)

• (Non)-universality of vortex reconnections in superfluids
• Crossover from interaction to driven regimes in quantum vortex reconnections
• A Vortex Filament Tracking Method for the Gross-Pitaevskii Model of a Superfluid
• Dual cascade and dissipation mechanisms in helical quantum turbulence
• Helicity, Topology and Kelvin Waves in reconnecting quantum knots
• Helicity Conservation, and Twisted Seifert Surfaces for Superfluid Vortices
• Kolmogorov and Kelvin wave cascades in a generalized model for quantum turbulence
• A matching theory to characterize sound emission during vortex reconnection in quantum fluids
• Finite temperature effects in helical quantum turbulence
• INFFTM: Fast evaluation of 3d Fourier series in MATLAB with an application to quantum vortex reconnections