while the last subsection contains a brief description of the simulation, data collection and analysis.

Towards closing of the scaling gap
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Recall that in the $Z_\alpha$ framework, the rigorous regularity and *a priori*-bound classes are $Z_\frac{1}{2}$ and $Z_\frac{2}{5}$, respectively [@BrFaGr18]. In order to test whether there may be an obstruction to advancing the $Z_\alpha$ *a priori* bounds even further–with the ultimate goal of *closing* the scaling gap–we considered a Kida-vortex initialized flow, a flow with the highly symmetric initial condition exhibiting a sharp increase (a ‘burst’) of the vorticity maximum ‘simulating’ a finite-time singularity [@KM86; @KM87; @BP94].

Attention was focused on a time interval leading to the peak of $\|\pmb{\omega}(t)\|_\infty$, and the aim was to investigate a possibility of a power-law dependence between the actual geometric scale of sparseness $r(t)$ and the diffusion scale $d(t)=\frac{\nu^\frac{1}{2}}{\|\pmb{\omega}(t)\|_\infty^\frac{1}{2}}$ of the form $r \sim d^\alpha$ (recall that $d$ is a lower bound on the radius of spatial analyticity). A presence of a power-law scaling would indicate that the scale of sparseness $r$ is a *bona fide* small scale in the sense of turbulence phenomenology. In addition–since both $d$ and $r$ are valued between 0 and 1–detecting a power law with an exponent $\alpha 