Estimating intermittency in three-dimensional Navier-Stokes turbulence

The Issue of why computational resolution in Navier-Stokes turbulence is hard to achieve is addressed. Under the assumption that the three-dimensional Navier-Stokes equations have a global attractor it is nevertheless shown that Solutions can potentially behave differently in two distinct regions of space-time S+/- where S- is comprised of a union of disjoint space-time 'anomalies'. If S- is non-empty it is dominated by large values of vertical bar del omega vertical bar, which is consistent with the formation of vortex sheets or tightly coiled filaments. The local number of degrees of freedom N+/- needed to resolve the regions in S+/- satisfies N+/-(x, t) greater than or less than 3 root 2 R-u(3), where R-u = uL/v is a Reynolds number dependent oil the local velocity field u(x, t).