TY - JOUR
T1 - Topological transition and helicity conversion of vortex knots and links
AU - Shen, Weiyu
AU - Yao, Jie
AU - Hussain, Fazle
AU - Yang, Yue
N1 - Publisher Copyright:
©
PY - 2022/7/25
Y1 - 2022/7/25
N2 - Topological transition and helicity conversion of vortex torus knots and links are studied using direct numerical simulations of the incompressible Navier-Stokes equations. We find three topological transitional routes (viz. merging, reconnection and transition to turbulence) in the evolution of vortex knots and links over a range of torus aspect ratios and winding numbers. The topological transition depends not only on the initial topology but also on the initial geometry of knots/links. For small torus aspect ratios, the initially knotted or linked vortex tube rapidly merges into a vortex ring with a complete helicity conversion from the writhe and link components to the twist. For large torus aspect ratios, the vortex knot or link is untied into upper and lower coiled loops via the first vortex reconnection, with a helicity fluctuation including loss of writhe and link, and generation of twist. Then, the relatively unstable lower loop can undergo a secondary reconnection to split into multiple small vortices with a similar helicity fluctuation. Surprisingly, for moderate torus aspect ratios, the incomplete reconnection of tangled vortex loops together with strong vortex interactions triggers transition to turbulence, in which the topological helicity decomposition fails due to the breakdown of vortex core lines.
AB - Topological transition and helicity conversion of vortex torus knots and links are studied using direct numerical simulations of the incompressible Navier-Stokes equations. We find three topological transitional routes (viz. merging, reconnection and transition to turbulence) in the evolution of vortex knots and links over a range of torus aspect ratios and winding numbers. The topological transition depends not only on the initial topology but also on the initial geometry of knots/links. For small torus aspect ratios, the initially knotted or linked vortex tube rapidly merges into a vortex ring with a complete helicity conversion from the writhe and link components to the twist. For large torus aspect ratios, the vortex knot or link is untied into upper and lower coiled loops via the first vortex reconnection, with a helicity fluctuation including loss of writhe and link, and generation of twist. Then, the relatively unstable lower loop can undergo a secondary reconnection to split into multiple small vortices with a similar helicity fluctuation. Surprisingly, for moderate torus aspect ratios, the incomplete reconnection of tangled vortex loops together with strong vortex interactions triggers transition to turbulence, in which the topological helicity decomposition fails due to the breakdown of vortex core lines.
KW - topological fluid dynamics
KW - vortex dynamics
UR - http://www.scopus.com/inward/record.url?scp=85132737357&partnerID=8YFLogxK
U2 - 10.1017/jfm.2022.464
DO - 10.1017/jfm.2022.464
M3 - Article
AN - SCOPUS:85132737357
SN - 0022-1120
VL - 943
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
M1 - A41
ER -