Helicity dynamics in reconnection events of topologically complex vortex flows

In this paper, we address the question of whether total helicity is conserved through viscous reconnection events in topologically complex vortex flows. To answer this question, we performed direct numerical simulations (DNS) focused on two complex vortex flow problems: (1) a trefoil knot and (2) a two-ring link, both simulated for various vortex core radii. The DNS framework relies on a block-structured adaptive mesh refinement (AMR) technique. A third simulation of a colliding pair of unlinked vortex rings, which exhibit no total helicity change, is also performed to serve as a reference case. The results show that a well-defined total helicity jump occurs during the unknotting/unlinking events of cases (1) and (2), which arises from the annihilation of the local helicity density content in the reconnection regions. Changes in total helicity become steeper as thinner core radii are considered for both cases (1) and (2). Finally, an analytical derivation based on the reconnection of two infinitesimal anti-parallel vortex filaments is provided that quantitatively links helicity annihilation and viscous circulation transfer processes, which unveils the fundamental hydrodynamic mechanisms responsible for production/destruction of total helicity during reconnection events.

Automated summary

In this study, the conservation of total helicity through viscous reconnection events in topologically complex vortex flows was investigated using direct numerical simulations. The results demonstrated a clear correlation between helicity annihilation and viscous circulation transfer processes, revealing fundamental hydrodynamic mechanisms responsible for the production/destruction of total helicity during reconnection events.