  The issue of why computational resolution in Navier-Stokes turbulence is so
hard to achieve is addressed. It is shown that Navier-Stokes solutions can
potentially behave differently in two distinct regions of space-time
$\mathbb{R}^{\pm}$ where $\mathbb{R}^{-}$ is comprised of a union of disjoint
space-time `anomalies'. Large values of $|\nabla\bom|$ dominate
$\mathbb{R}^{-}$, which is consistent with the formation of vortex sheets or
tightly-coiled filaments. The local number of degrees of freedom
$\mathcal{N}^{\pm}$ needed to resolve the regions in $\mathbb{R}^{\pm}$
satisfies $$\mathcal{N}^{\pm}(\bx, t)\lessgtr c_{\pm}\mathcal{R}_{u}^{3}$$
where $\mathcal{R}_{u} = uL/\nu$ is a Reynolds number dependent on the local
velocity field $u(\bx, t)$.
