Helical and compact Navier-Stokes solutions with finite dissipation

For several Navier-Stokes solutions with initial helicity, two types of vorticity moment convergence are observed. First is a sequence of ν-independent times t_m that correspond with a set of scaled, volume-integrated vorticity moments ν^1/4O_Vm, with this hierarchy t_∞ ≤... ≤t_m...t₁ = t_x and O_Vm = ∫_Vl|ω|^2mdV)^1/2m. For the volume-integrated enstrophy Z(t), convergence of √νZ(t) = (ν^1/4O_V1(t))² at t_x = t₁ marks the end of reconnection scaling. These temporal convergences form as localized knots shed double vortex sheets for these configurations: trefoil vortex knots, nested rings, orthogonal vortices and even initially smooth Taylor-Green. The second convergence develops for t>t_x as reconnection and the growth of enstrophy Z accelerates towards approximate finite-time ν-independent convergence of the energy dissipation rate ϵ(t) = νZ(t) at t_e ∼1.5−2t_x. Most strongly if the initial condition is compact and the computational domain can grow as the viscosity decreases. For perturbed trefoil vortex knots this is sustained over a finite temporal span ∆T_ε giving Reynolds number independent finite-time, temporally integrated dissipation, ∆E_ε = ∫_∆Tε ϵdt, thus satisfying one definition for a dissipation anomaly with enstrophy spectra that are consistent. A critical factor in achieving these temporal convergences is how the computational domain V_l = (2ℓπ)³ is increased as ℓ∼ν^1/4, for ℓ= 2 to 12, as ν decreases. Compatibility with (2π)³ mathematics is shown where ν≡0 Euler bounds small ν Navier-Stokes.