Sensitivity of trefoil vortex knot reconnection to the initial vorticity profile

Five sets of Navier-Stokes trefoil vortex knots in (27t )3 domains show how the shape of their initial profiles, Gaussian/Lamb-Oseen or algebraic, and their widths influence their evolution, as defined by their enstrophy Z(t), helicity ?-L(t), and changes in their dissipation-scale structures. Significant differences develop even when all have the same three-fold symmetric trajectory, the same initial circulation and the same range of the viscosities v. The focus is upon how the dynamics of helicity density h = u & BULL; & omega; affects reconnection and the evolution of enstrophy. h & LE; 0 patches on the vorticity isosurfaces show where and how reconnection forms. For the Lamb-Oseen profile, the tightest and most linearly unstable, there is only a brief spurt of enstrophy growth as thin braids form at these positions; before being dissipated as the post-reconnection helicity ?-L grows significantly. For the algebraic cases: as h < 0 vortex sheets form prior to reconnection, there is v-independent convergence of ,/vZ(t) at a common tx. For those with the broadest wings, enstrophy growth accelerates after reconnection, leading to approximately convergent dissipation rates e = vZ(t). Maps of terms from the budget equations onto centerlines illustrate the divergent behavior. Lamb-Oseen briefly forms six locations of centerline convergence with local negative dips in the helicity dissipation eh and vortical-helicity flux hf . These are the source of the following positive increase in the global ?-L and suppression of enstrophy production. For the algebraic profiles there are only three locations of centerline convergence, each with spans of less localized eh < 0 that could be the seeds for the h < 0 vortex sheets and whose interactions can explain the later accelerated growth of the enstrophy, approximate v-independent convergence of the energy dissipation rates e, and evidence for finite-time energy dissipation 4Ee, despite the initial symmetries.