• Corpus ID: 119383102

Trefoil knot structure during reconnection

@article{Kerr2017TrefoilKS,
  title={Trefoil knot structure during reconnection},
  author={Robert McDougall Kerr},
  journal={arXiv: Fluid Dynamics},
  year={2017}
}

• Robert McDougall Kerr
• Published 5 March 2017
• Physics
• arXiv: Fluid Dynamics

By comparing vortex structures at multiple times from the numerical evolution and reconnection of a perturbed trefoil vortex knot, the $t=t_x$ end of a scaling regime where $\sqrt{\nu}Z(t_x)$ is independent of $\nu$ is identified as when the last snippet of the original trefoil vortex is cut by viscous reconnection. During this phase there is good correspondence with the experimental trefoil reconnection of Kleckner and Irvine (2013) when a camber correction is added to the nonlinear timescales formed by the circulation $\Gamma$ and the radius rf of the trefoils. Maintaining the $\sqrt{\nu}Z(t_x)$ scaling as $\nu\to0$ requires increasing the domain size without an upper bound and generating negative helicity away from the reconnection. Furthermore, the helicity is preserved during, and a bit after, this phase. Confirming the experimentally observed preservation of helicity over an equivalent timespan (Scheeler et al. 2014). The mechanism for preserving the helicity through the reconnection is that after the trefoil loops become anti-parallel, oppositely-signed sheets of helicity dissipation of equal magnitude form within the reconnection zone (Laing et al. 2015).