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

Abstract

Precursor peaks in the wavenumber k _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 = 1,000 perturbed Taylor–Green vortex realizations at N = 256 ³ and ν = 10 ⁻³ . For each run we extract k _peak ( t ), several definitions of the precursor time t _k , the dissipation-peak time t _ɛ , and run-wise extrema including K _max = max _t k _peak ( t ) and

, where

C ( k , t ) $\mathcal{C}\left(k,t\right)$

is the isotropic curl-of-vorticity spectrum. The distribution of Δ t _{ɛ , k} = t _ɛ − 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 = −Δ t _{ɛ , 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 ɛ _max and ensemble cross-correlations reveal a reproducible phase offset, consistent with an empirical association between high-curvature activity and dissipation bursts.