A curvature-weighted spectral precursor to dissipation in decaying three-dimensional turbulence: robustness across initial conditions and viscosity effects

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 curl-of-vorticity spectrum $\mathrm{\mid }\mathrm{\nabla }\times \mathit{\omega }{\mathrm{\mid }}^2(k)$, equivalent to a $k^4$-weighted energy spectrum for solenoidal flow. 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 $\mathrm{\mid }\mathrm{\nabla }\times \mathit{\omega }{\mathrm{\mid }}^2(k)$ 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 viscosity effects in Taylor–Green turbulence: the precursor persists at lower viscosity when adequate resolution is employed, but weakens and can break at higher viscosity, consistent with stronger viscous damping of curvature-dominated small-scale content. Throughout, we use explicit inspection of curvature-weighted spectra to distinguish physical peak evolution from cutoff-proximate artifacts. These results establish robustness across initial conditions and clarify the practical role of viscosity and resolution for deploying curvature-weighted spectral precursors in decaying turbulence.