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

Abstract

Precursor peaks in the wavenumber $k_{\mathrm{peak}}(t)$ 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 $ν=10^{-3}$. For each run we extract $k_{\mathrm{peak}}(t)$, several definitions of the precursor time $t_k$, the dissipation-peak time $t_\varepsilon$, and run-wise extrema including $K_{\max}=\max_t k_{\mathrm{peak}}(t)$ 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 $Δt_{\varepsilon,k}=t_\varepsilon-t_k$ 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 $X=-Δt_{\varepsilon,k}$ and $M_{\max}$; the negative shape estimates are consistent with effective bounded tails under the present finite-resolution sampling protocol and provide protocol-dependent endpoint estimates. Finally, $M_{\max}$ correlates strongly with $\varepsilon_{\max}$ and ensemble cross-correlations reveal a reproducible phase offset, consistent with an empirical association between high-curvature activity and dissipation bursts.