What trefoil reconnection says about Navier-Stokes regularity

Abstract eng:
Scheeler et al. [1] have recently demonstrated that one can experimentally investigate helicity by imprinting high Reynolds number helical vortex knots into a fluid by yanking 3D-printed aerofoils covered with hydrogen bubbles out of a water tank. Some surprising claims were made based upon the evolution of the resulting vortex filaments. This contribution will address those claims by simulating the evolution and self-reconnection of a similarly perturbed trefoil vortex knot over a range of Reynolds numbers and core diameters. The surprisingly long time it takes for reconnection to begin is confirmed. However, the simulations suggest that the significance of the trefoil is not just in the initial preservation of helicity, but in how it is dissipated in a finite time once reconnection begins. This result implies that the trefoil’s vortex dynamics is controlled primarily by the helicity, and not the energy, enstrophy or peak vorticity.

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