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Over a wide range of viscosities, a perturbed trefoil vortex knot generatesReynolds number independent finite-time energy dissipation $\Delta E_\epsilon$(1) with evidence for a transient Kolmogorov spectra at the highest Reynoldsnumber. Satisfying one definition for a dissipation anomaly. To cover therequired range of Reynolds numbers, factors of $\nu^{1/4}$ must be consideredfor both the largest scale $L$, the size of the periodic domain, whichincreases as $L\sim\nu^{-1/4}$, and vorticity moments at the the earliesttimes, which converge when scaled as $\nu^{1/4}\Omega_m$, including$m=9,\infty$ at times $t_\infty<\dots<t_m\dots t_1=t_x$. The $\nu^{1/4}$scaling ends at $t=t_x$ with convergence of $\sqrt{\nu}Z(t)$, $Z=L^3\Omega_1^2$being the volume-integrated enstrophy, after which the growth of $Z(t)$accelerates until there is approximate convergence of the dissipation rates$\epsilon=\nu Z$ at $t\sim t_\epsilon\sim2t_x$. This continues long enough togenerate a dissipation anomaly with finite $\Delta E_\epsilon$ (1). To achievethe convergence of $\sqrt{\nu}Z(t)$ at $t_x$, $L$ is increased from $4\pi$ to$12\pi$, meaning that the following restriction must be addressed: That$\nu\ne0$ Navier-Stokes solutions in $(2\pi)^3$ periodic domains are bounded bytheir $\nu\equiv0$ Euler solutions as $\nu\to0$ for $\nu<\nu_s$, with thebounding critical viscosities $\nu_s$ determined using Sobolev space analysis.By rescaling the original Sobolev space result in $(2\pi)^3$ into larger$(2\ell\pi)^3$ domains, a reduction in the bounding critical viscosities$\nu_s$ can be shown which allows growth of $Z(t)$ in those domains.

Navier-Stokes bounds and scaling for compact trefoils in $(2\ell\pi)^3$ domains