Direct numerical and large-eddy simulation of trefoil knotted vortices

This paper investigates pre- and post-reconnection dynamics of an unperturbed trefoil knotted vortex for circulation-based Reynolds numbers and 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, , 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, , and the vortex-tube-integrated helicity 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.

Automated summary

This paper investigates the pre- and post-reconnection dynamics of a trefoil knotted vortex, finding that the self-advection velocity before reconnection scales with inviscid parameters and reconnection occurs earlier and more rapidly at higher Reynolds numbers. The vortex propagation velocities after reconnection are affected by viscous effects, with the larger vortex ring carrying most of the helicity and enstrophy. The total helicity dissipation rate agrees reasonably well between large-eddy simulations and direct numerical simulations, with vortex centerline helicity and vortex-tube-integrated helicity being less sensitive to the reconnection process.