Spectrum of the Curl of Vorticity as a Precursor to Dissipation in 3D Taylor--Green Turbulence
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909999529197568 |
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| author | Tsuzuki, Satori |
| author_facet | Tsuzuki, Satori |
| contents | 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 $t_k<t_\varepsilon<t_Π$, where $t_k$ marks the onset of the rapid rise of $k_{\rm peak}[\,|\nabla \times \boldsymbolω|^2\,]$, $t_\varepsilon$ is the time of the maximal $\varepsilon(t)$, and $t_Π$ is when the cumulative flux $|Π(K)|$ 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 ($L_{\rm int},λ,η$). The diagnostic is simple to compute from standard DNS data and highlights the incipient formation of high-curvature structures, where viscosity acts most strongly. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_05728 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectrum of the Curl of Vorticity as a Precursor to Dissipation in 3D Taylor--Green Turbulence Tsuzuki, Satori Fluid Dynamics 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 $t_k<t_\varepsilon<t_Π$, where $t_k$ marks the onset of the rapid rise of $k_{\rm peak}[\,|\nabla \times \boldsymbolω|^2\,]$, $t_\varepsilon$ is the time of the maximal $\varepsilon(t)$, and $t_Π$ is when the cumulative flux $|Π(K)|$ 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 ($L_{\rm int},λ,η$). The diagnostic is simple to compute from standard DNS data and highlights the incipient formation of high-curvature structures, where viscosity acts most strongly. |
| title | Spectrum of the Curl of Vorticity as a Precursor to Dissipation in 3D Taylor--Green Turbulence |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2510.05728 |