2023/04/16 by Kerr, Robert M.
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
paper · doi:10.48550/arxiv.2304.07697
Six sets of Navier-Stokes trefoil vortex knots in (2π)3 domains show how the shape of the initialprofile influences the evolution of the enstrophy Z, helicity \cal H and dissipation-scale. Significant differences develop even when all have the same three-fold symmetric trajectory, the same initial circulation and the same range of the viscosities ν. Maps of the helicity density h=u⋅ω onto vorticity isosurfaces patches show where h\lesssim0 sheets form during reconnection. For the Gaussian/Lamb-Oseen profile helicity \cal H grows significantly, with only a brief spurt of enstrophy growth as thin braids form then decay during reconnection. The remaining profiles are algebraic. For the untruncated algebraic cases,h<0 vortex sheets form in tandem with ν-independent convergence of √νZ(t) at a common tx. For those with the broadest wings, enstrophy growth accelerates during reconnection, leading to approximately ν-independent convergent finite-time dissipation rates ε=νZ. By mapping terms from the budget equations onto centerlines, the origins of the divergent behavior are illustrated. Lamb-Oseen has six locations of centerline convergence form with local negative helicity dissipation, εh<0, and small, but positive h. Later, the sum of these localized patches of εh<0 leads to a positive increase in the global \cal H and suppression of enstrophy production. For the algebraic profiles: There are only three locations of centerline convergence, each with spans of less localized εh<0 and some h<0. Spans that could be the seeds for the h<0 vortex sheets that form in the lower half of the trefoil as the √νZ(t) phase begins and can explain accelerated growth of the enstrophy and evidence for finite-time energy dissipation ΔEε. Despite the initial symmetries.