Extreme-value statistics of curl-of-vorticity precursor peaks in perturbed Taylor-Green vortex turbulence

Precursor peaks in the wavenumber $k_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}(t)$ maximizing the curl-of-vorticity spectrum have been observed to precede the dissipation peak in decaying turbulence. Because small perturbations in the initial condition can shift peak times, the associated lead time should be characterized statistically. We perform a pseudospectral DNS ensemble of $N_s=1000$ perturbed Taylor–Green vortex realizations at $N={256}^3$ and $\nu ={10}^{-3}$. For each run we extract $k_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}(t)$, several definitions of the precursor time $t_k$, the dissipation-peak time $t_{\epsilon }$, and run-wise extrema including $K_{\max }={\max }_t{k}_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}(t)$ and $M_{\max }={\max }_t{\max }_k\mathcal{C}(k,t)$, where $\mathcal{C}(k,t)$ is the isotropic curl-of-vorticity spectrum. The distribution of $\mathrm{\Delta }{t}_{\epsilon ,k}=t_{\epsilon }-t_k$ shows that the precursor typically leads, while rare lagging realizations occur and are strongly conditioned on $K_{\max }$. Using peaks-over-threshold extreme-value theory, we fit generalized Pareto models to the right tails of $X=-\mathrm{\Delta }{t}_{\epsilon ,k}$ and $M_{\max }$; negative shape parameters indicate bounded tails and enable worst-case lag and endpoint estimates. Finally, $M_{\max }$ correlates strongly with ${\epsilon }_{\max }$ and ensemble cross-correlations reveal a reproducible phase offset, supporting a dynamical coupling between high-curvature activity and dissipation bursts.