> 1$ would mean that the solution in view is entering the diffusion regime (as depicted in the $Z_\alpha$ framework) and is, in fact, contained in the regularity class $Z_\frac{1}{2}$.

Indeed, data analysis of the time-interval of interest-sourced from a spatially highly-resolved (${1024}^3$) simulation–revealed a very strong evidence of a power-law scaling; moreover, the scaling exponent $\alpha$ crystalized at 1.098(9) (cf. Figure 3). This was very exciting to see, and the complementary rigorous analysis in the $Z_\alpha$ framework is currently underway.

A rigorous explanation of the Boratav-Pelz computational results
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Boratav and Pelz considered the Kida vortex flows as–among other things–a laboratory for the computational study of the possible singularity formation in solutions to the 3D NSE and Euler flows. In particular, they discovered a time-interval of extreme intermittency (preceding the peak of the vorticity maximum) in which the local pointwise and integrated quantities increase sharply, noting that “The increase is so sudden and sharp that questions arise as to whether some of these quantities would diverge in finite time or not” [@BP94].

They performed a singularity analysis revealing that the vorticity maximum–in a time-interval leading to its peak–scales closely to the self-similar, critical scaling of $\frac{1}{t-T^*}$. This could, in 