Estimating intermittency in three-dimensional Navier–Stokes turbulence

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 R± where R− is comprised of a union of disjoint space-time ‘anomalies’. Large values of |∇ω| dominate R−, 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 R± satisfies N±(x, t) ≶ c±Ru where Ru = uL/ν is a Reynolds number dependent on the local velocity field u(x, t).