Re-visiting the Taylor-Green vortex up to and after t ∼ 4.5

The evolution of the classic Taylor-Green vortex, under both Euler and Navier-Stokes, is re-visited using recent numerical analysis developed for vortex reconnection. For ν ≡ 0 Euler doubly-exponential, non-singular growth of ∥ω(t)∥_∞ is shown, supported using nonlinear inequalities of vorticity moments, all of which point away from singular growth. For Navier-Stokes, for a short period around t ∼ 4.5 when the interior vortices cross, the higher-order vorticity moments Ω_m can be scaled using the viscosity as ν^1/4 in a process that sheds negative helicity vorticity sheets. Including finite- time ν-independent convergence of √νZ(t)=(V^1/2ν^1/4Ω₁)² and ν^1/4∥ω(t)∥_∞ during the phase leading to reconnection. The origin of the ν^1/4 scaling comes from how the sheets expand to compensate for the ν^1/2 scaled compression around those crossings. However, the type of post-reconnection acceleration of enstrophy growth that could lead to a viscosity-independent energy dissipation rate does not occur due to the restrictions imposed by the (2π)³ periodic domain.