Characteristics of significant and insignificant regions in isotropic turbulence

Significant and insignificant regions of isotropic turbulence are classified based on their sensitivity to localized perturbations.

The growth of the perturbations is assessed by running a massive amount of simulations $(\sim\mkern-5mu 10^6)$ with perturbed initial conditions at different locations.

The regions of the flow where perturbations lie in the top 5\% of amplification after a given time are labeled as `significant' and those in the bottom 5\% as `insignificant'.

The properties of both regions are studied, uncovering several differences between both regions. First, significant regions are found to have intense kinetic energy, enstrophy and dissipation. The converse applies for insignificant regions which are weak compared to the background flow. Studying their topology shows that in significant regions, the rate of strain dominates the vorticity, which results in the invariants of the velocity gradient tensor, $Q$ and $R$, leaning towards the Vieillefosse tail. Insignificant regions are dominated by vorticity, and thus dominated by positive $Q$ and neutral $R$. In conclusion, it is shown that straining motions are more efficient at propagating perturbations than vortical ones.