On higher-order derivative ratios in turbulent flows
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| Format: | Preprint |
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2026
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| _version_ | 1866911703225073664 |
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| author | Grujić, Zoran Mohebujjaman, Muhammad |
| author_facet | Grujić, Zoran Mohebujjaman, Muhammad |
| contents | A computational study of higher-order derivative ratios on a time interval leading to the enstrophy peak is presented in the case of the 3D Taylor-Green vortex, a benchmark problem in the simulation of turbulent flows. The main finding is that the power law relating the ratios at time $t$ to $T^*-t$ where $T^*$ is the peak enstrophy time is of a form that allows the machinery of dynamic interpolation-sparseness to produce a lower bound on the radius of spatial analyticity sufficient to overcome an upper bound on the scale of sparseness of the super-level sets in view. As a consequence, the mechanism of turbulent dissipation engages via the harmonic measure maximum principle, furnishing a rigorous explanation for the subsequent slump of the enstrophy. This indicates that the higher-order derivative ratios -- which could be viewed as higher-order analogs of the classical Taylor and Kraichnan scales in turbulence phenomenology -- may be reasonable identifiers of the peak of the energy dissipation rate. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_21501 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On higher-order derivative ratios in turbulent flows Grujić, Zoran Mohebujjaman, Muhammad Analysis of PDEs Mathematical Physics Fluid Dynamics A computational study of higher-order derivative ratios on a time interval leading to the enstrophy peak is presented in the case of the 3D Taylor-Green vortex, a benchmark problem in the simulation of turbulent flows. The main finding is that the power law relating the ratios at time $t$ to $T^*-t$ where $T^*$ is the peak enstrophy time is of a form that allows the machinery of dynamic interpolation-sparseness to produce a lower bound on the radius of spatial analyticity sufficient to overcome an upper bound on the scale of sparseness of the super-level sets in view. As a consequence, the mechanism of turbulent dissipation engages via the harmonic measure maximum principle, furnishing a rigorous explanation for the subsequent slump of the enstrophy. This indicates that the higher-order derivative ratios -- which could be viewed as higher-order analogs of the classical Taylor and Kraichnan scales in turbulence phenomenology -- may be reasonable identifiers of the peak of the energy dissipation rate. |
| title | On higher-order derivative ratios in turbulent flows |
| topic | Analysis of PDEs Mathematical Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2605.21501 |