Direct numerical and large-eddy simulation of trefoil knotted vortices. (15th January 2021)

• Record Type: Journal Article
• Authors: Zhao, Xinran; Yu, Zongxin; Chapelier, Jean-Baptiste; Scalo, Carlo
• Is Part Of: Journal of fluid mechanics. Volume 910(2021)
• Publication Date: 2021-01-15
• Subjects: vortex dynamics, -- turbulence simulation, -- vortex interactions; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.943
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: Abstract : This paper investigates pre- and post-reconnection dynamics of an unperturbed trefoil knotted vortex for circulation-based Reynolds numbers $Re_\varGamma = 2\times 10^3$ and $6\times 10^3$ by means of direct numerical simulations based on an adaptive mesh refinement framework. Companion coherent-vorticity preserving large-eddy simulations are also carried out on a uniform Cartesian grid. The complete vortex structure and flow evolution are simulated, including reconnection and subsequent separation into a smaller and a larger vortex ring, and the resulting helicity dynamics. The self-advection velocity before reconnection is found to scale with inviscid parameters. The reconnection process, however, occurs earlier (and more rapidly) in the higher Reynolds number case due to higher induced velocities associated with a thinner vortex core. The vortex propagation velocities after reconnection and separation are also affected by viscous effects, more prominently for the smaller vortex ring; the larger one is shown to carry the bulk of the helicity and enstrophy after reconnection. The domain integrated, or total helicity, $H(t)$, does not significantly change up until reconnection, at which point it varies abruptly due to the rapid dissipation of helicity caused by super-helicity hotspots localized at the reconnection sites. The total helicity dissipation rate predicted by the large-eddy simulation agrees reasonably well with the direct numerical simulation results, with a significant contribution from the modelled subgrid-scale stresses. On the other hand, variations in the vortex centreline helicity, $H_C(t)$, and the vortex-tube-integrated helicity $H_V(t)$ are less sensitive to the reconnection process. Periodic vortex bursting events are also observed and are shown to be due to converging axial flow velocities in the detached vortex rings at later stages of evolution.