  Three-dimensional images of evolving numerical trefoil vortex knots are used
to study the growth and decay of the enstrophy and helicity. Negative helicity
density ($h<0$) plays several roles. First, sheets of oppositely-signed
helicity dissipation of equal magnitude on either side of the maximum of the
enstrophy dissipation allow the global helicity ${\cal H}$ to be preserved
through the first reconnection, as suggested theoretically (Laing et al 2015)
and observed experimentally (Scheeler et al. 2014). Next, to maintain the
growth of the enstrophy and positive helicity within the trefoil while ${\cal
H}$ is preserved, $h<0$ forms in the outer parts of the trefoil so long as the
periodic boundaries do not interfere. To prevent that, the domain size $\ell$
is increased as the viscosity $\nu\to0$. Combined, this allows two sets of
trefoils to form a new scaling regime with linearly decreasing
$(\sqrt{\nu}Z(t))^{-1/2}$ up to common $\nu$-independent times $t_x$ that the
graphics show is when the first reconnection ends. During this phase there is
good correspondence between the evolution of the simulated vortices and the
reconnecting experimental trefoil of Kleckner and Irvine (2013) when time is
scaled by their respective nonlinear timescales $t_f$. The timescales $t_f$ are
based upon by the radii $r_f$ of the trefoils and their circulations $\Gamma$,
so long as the strong camber of the experimental hydrofoil models is used to
correct the published experimental circulations $\Gamma$ that use only the
flat-plate approximation.
