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

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 Physical Review Fluids on the Taylor–Green vortex, we analyze direct numerical simulations using the shell-summed curl-of-vorticity spectrum, denoted here by and equivalent to a -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 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-/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.