Spectrum of the Curl of Vorticity as a Precursor to Dissipation in 3D Taylor--Green Turbulence

Abstract

Predicting when a three-dimensional turbulent flow reaches its dissipation peak is essential for both theory and adaptive algorithms in simulations and experiments. Using direct numerical simulations (DNSs) of the Taylor--Green vortex (TGV) at resolutions of $256^3$--$1024^3$, we introduce and test a small-scale weighted diagnostic: the spectrum of $|\nabla \times \mathbf{\omega }{|}^2$ (with $\mathbf{\omega }=\nabla \times \mathbf{u}$), which, for incompressible flow, is equivalent to a $k^4$-weighted energy spectrum. We show that the peak wavenumber of this spectrum, $k_{\mathrm{peak}}[|\nabla \times \mathbf{\omega }{|}^2]$, advances rapidly to intermediate-small scales and then levels off before the dissipation rate $\epsilon (t)={\sum }_{k}2\nu k^{2}E(k)$ reaches its maximum. Across all resolutions, we observe robust temporal ordering $t_k<t_{\epsilon }<t_{\Pi }$, where $t_k$ marks the onset of the rapid rise of $k_{\mathrm{peak}}[|\nabla \times \mathbf{\omega }{|}^2]$, $t_{\epsilon }$ is the time of the maximal $\epsilon (t)$, and $t_{\Pi }$ is when the cumulative flux $|\Pi (K)|$ attains its largest peak scale. This early-warning signal correlates with the morphological transition to filament-dominated structures visible in $Q$-criterion isosurfaces and is consistent with integral-scale trends ($L_{\mathrm{int}},\lambda ,\eta$). The diagnostic is simple to compute from standard DNS data and highlights the incipient formation of high-curvature structures, where viscosity acts most strongly.

References in corpus (1)

• Modeling and Simulation of Transitional Taylor-Green Vortex Flow with PANS

Cited by in corpus (2)

• Distinct transverse-response signatures of retained-spin, eliminated-spin, and polynomial Burnett-type surrogate closures
• Extreme-value statistics of curl-of-vorticity precursor peaks in perturbed Taylor-Green vortex turbulence