principle, be an indication of the build-up of a scaling-invariant singularity. Nevertheless, the simulations consistently showed an eventual disruption in the (approximately) self-similar, critical scaling, a formation of the peak, and a subsequent dissipation of the flow, prompting them to conclude that “However, the increase in peak vorticity stops at a certain time, possibly due to viscous dissipation effects” [@BP94].

As noted in the previous subsection, the analysis of the data sourced from an interval leading to the peak of the vorticity maximum within the $Z_\alpha$ framework demonstrated that the flow entered a regime beyond the critical diffusion class $Z_\frac{1}{2}$. In other words, sparseness of the super-level sets of the vorticity components was sufficient for the harmonic measure maximum principle to engage and prevent a further growth of the vorticity maximum, providing a rigorous justification of the observed ‘slump’ and dissipation. Nevertheless, it is worth noticing that the exponent observed in our analysis (1.098(9)) is only slightly larger than the critical exponent (1), confirming a close proximity to the criticality.

On simulation, data collection and analysis
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The Kida vortex initial configurations were introduced in [@K85]. The class features a high number of symmetries, all preserved by the Navier-Stokes flows. 