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Effects of twist on the evolution of knotted magnetic flux tubes

Published online by Cambridge University Press:  22 May 2020

Shiying Xiong Open the ORCID record for Shiying Xiong [Opens in a new window]  and
Yue Yang Open the ORCID record for Yue Yang [Opens in a new window]
Shiying Xiong
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, 100871Beijing, PR China
Yue Yang*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, 100871Beijing, PR China CAPT and BIC-ESAT, Peking University, 100871Beijing, PR China
*
†Email address for correspondence: yyg@pku.edu.cn
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Abstract

We develop a general method for constructing knotted flux tubes with finite thickness, arbitrary shape and tunable twist. The central axis of the knotted tube is specified by a smooth and non-degenerate parametric equation. The helicity of the corresponding solenoidal knotted field can be explicitly decomposed into writhe, normalized total torsion and intrinsic twist. We construct several knotted magnetic flux tubes with various twisting degrees, and investigate the effect of twist on their evolution in resistive magnetohydrodynamic flows using direct numerical simulation. For large twist, the magnetic knot gradually shrinks to a tight stable state, similar to the relaxation process in ideal magnetohydrodynamic flows. For small twist, the knotted flux tube splits at early times, accompanied by a rising magnetic dissipation rate. We elucidate the mechanism of the tube splitting using the phase portrait of the Lorentz force projected onto divergence-free space. For finite twist, the Hopf bifurcation from an unstable spiral point to a limit cycle occurs on the phase plane. In the evolution, field lines inside the limit cycle form invariant tori, whereas they become chaotic outside the limit cycle.

JFM classification

Mathematical Foundations: Topological fluid dynamics MHD and Electrohydrodynamics: Plasmas Vortex Flows: Vortex dynamics

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 895 , 25 July 2020 , A28
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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