  Six sets of Navier-Stokes trefoil vortex knots in $(2\pi)^3$ 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 $\nu$. Maps of the helicity
density $h=u\cdot\omega$ 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 $\nu$-independent convergence of
$\sqrt{\nu}Z(t)$ at a common $t_x$. For those with the broadest wings,
enstrophy growth accelerates during reconnection, leading to approximately
$\nu$-independent convergent finite-time dissipation rates $\epsilon=\nu Z$. 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, $\epsilon_h<0$, and
small, but positive $h$. Later, the sum of these localized patches of
$\epsilon_h<0$ 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
$\epsilon_h<0$ 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
$\sqrt{\nu}Z(t)$ phase begins and can explain accelerated growth of the
enstrophy and evidence for finite-time energy dissipation $\Delta E_\epsilon$.
Despite the initial symmetries.
