Curvature-weighted spectra anticipate dissipation peaks in decaying three-dimensional turbulence

Abstract

We investigate the robustness of a curvature-weighted spectral precursor to dissipation in freely decaying three-dimensional incompressible turbulence. Building on our recent work in \emph{Physical Review Fluids} on the Taylor--Green vortex, we analyze direct numerical simulations using the shell-summed curl-of-vorticity spectrum, denoted here by ${\mathcal{C}}_4(k,t)$ and equivalent to a $k^4$-weighted energy spectrum in the modal incompressible sense. Extending the study across multiple initial conditions -- multi-mode ABC flows, a randomized low-wavenumber ABC field, the Taylor--Green vortex, and the Kida--Pelz flow -- we find a consistent temporal ordering: the characteristic time associated with the advance and saturation of the peak wavenumber of ${\mathcal{C}}_4(k,t)$ precedes the dissipation-peak time, which in turn precedes the characteristic time associated with the peak scale of the nonlinear energy-flux spectrum. We further probe Reynolds-number and scale-separation effects using Taylor--Green simulations at additional viscosities: the precursor ordering persists when adequate scale separation and resolution are maintained, but can change in the low-$R_{\lambda }$/limited-scale-separation regime. Throughout, we use explicit inspection of curvature-weighted spectra to distinguish physical peak evolution from cutoff-proximate artifacts. These results support robustness over the deterministic decaying-flow initial conditions examined here and clarify the practical role of Reynolds number, scale separation, and resolution when using curvature-weighted spectral diagnostics in decaying turbulence.