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Updated: Jul 9, 2026

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
Published on: February 27, 2016
Curvature-weighted spectra anticipate dissipation peaks in decaying three-dimensional turbulence
1Research Center for Advanced Science and Technology, The University of Tokyo, Tokyo, Japan. tsuzukisatori@g.ecc.u-tokyo.ac.jp.
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 shell-summed curl-of-vorticity spectrum, denoted here by [Formula: see text] and equivalent to a [Formula: see text]-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 [Formula: see text] 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-[Formula: see text]/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.
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