Spectrum of the Curl of Vorticity as a Precursor to Dissipation in 3D Taylor--Green Turbulence
Authors
Satori Tsuzuki
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 $|\nabla \times \boldsymbolω|^2$ (with $\boldsymbolω=\nabla \times \mathbf{u}$), which, for incompressible flow, is equivalent to a $k^4$-weighted energy spectrum. We show that the peak wavenumber of this spectrum, $k_{\rm peak}[\,|\nabla \times \boldsymbolω|^2\,]$, advances rapidly to intermediate-small scales and then levels off before the dissipation rate $\varepsilon(t)=\sum_k 2νk^2 E(k)$ reaches its maximum. Across all resolutions, we observe robust temporal ordering $t_k
