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

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 Physical Review Fluids on the Taylor--Green vortex, we analyze direct numerical simulations using the curl-of-vorticity spectrum $|\nabla\times \boldsymbolω|^2(k)$, 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 $|\nabla\times \boldsymbolω|^2(k)$ 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.