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

TL;DR

This study demonstrates that a curvature-weighted spectral precursor reliably predicts dissipation timing in decaying 3D turbulence across various initial conditions and viscosities, highlighting its robustness and practical utility.

Contribution

The paper extends previous work by validating the curvature-weighted spectral precursor across multiple initial flows and viscosity levels, clarifying its robustness and limitations.

Findings

The spectral precursor's characteristic time precedes dissipation peak across conditions.

The precursor persists at lower viscosities with sufficient resolution.

Higher viscosity weakens or breaks the precursor due to viscous damping.

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 $|\nabla\times \boldsymbol{\omega}|^2(k)$, 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 $|\nabla\times \boldsymbol{\omega}|^2(k)$ 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.