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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.19921 |
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| _version_ | 1866916028211003392 |
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| author | Dey, Anwesha Mukherjee, Ritwik Banerjee, Aikya Ray, Samriddhi Sankar |
| author_facet | Dey, Anwesha Mukherjee, Ritwik Banerjee, Aikya Ray, Samriddhi Sankar |
| contents | We investigate two-point velocity-gradient correlation functions in homogeneous isotropic turbulence using exact relations and direct numerical simulations. The second-order gradient correlation is shown to be exactly related to the Laplacian of the velocity correlation, implying inertial-range scaling $C_2^{1,1}(r)\sim r^{-4/3}$. At higher orders, we uncover a parity-dependent organization of gradient correlations: odd-odd correlations exhibit scaling close to $r^{-4/3}$ with weak dependence on order, whereas even-even correlations display systematically different exponents. We show that this distinction originates from the sign structure of the gradient field: sign decorrelation suppresses intermittent contributions in odd-odd sectors, while even-even correlations retain them and remain sensitive to the spatial organization of intense structures. The measured even-even exponents are quantitatively consistent, across two Reynolds numbers, with independently measured box-counting dimensions of intermittent gradient structures. These results identify parity under sign reversal as a fundamental organizing principle for higher-order turbulent correlations and establish a direct connection between sparse intermittent geometry and scaling exponents in turbulence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19921 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parity-Dependent Scaling of Velocity-Gradient Correlations in Turbulence Dey, Anwesha Mukherjee, Ritwik Banerjee, Aikya Ray, Samriddhi Sankar Fluid Dynamics We investigate two-point velocity-gradient correlation functions in homogeneous isotropic turbulence using exact relations and direct numerical simulations. The second-order gradient correlation is shown to be exactly related to the Laplacian of the velocity correlation, implying inertial-range scaling $C_2^{1,1}(r)\sim r^{-4/3}$. At higher orders, we uncover a parity-dependent organization of gradient correlations: odd-odd correlations exhibit scaling close to $r^{-4/3}$ with weak dependence on order, whereas even-even correlations display systematically different exponents. We show that this distinction originates from the sign structure of the gradient field: sign decorrelation suppresses intermittent contributions in odd-odd sectors, while even-even correlations retain them and remain sensitive to the spatial organization of intense structures. The measured even-even exponents are quantitatively consistent, across two Reynolds numbers, with independently measured box-counting dimensions of intermittent gradient structures. These results identify parity under sign reversal as a fundamental organizing principle for higher-order turbulent correlations and establish a direct connection between sparse intermittent geometry and scaling exponents in turbulence. |
| title | Parity-Dependent Scaling of Velocity-Gradient Correlations in Turbulence |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2605.19921 |