Intermittent fluctuations determine the nature of chaos in turbulence
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arXiv
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| Format: | Preprint |
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2025
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| author | Banerjee, Aikya Mukherjee, Ritwik Murugan, Sugan Durai Bhattacharjee, Subhro Ray, Samriddhi Sankar |
| author_facet | Banerjee, Aikya Mukherjee, Ritwik Murugan, Sugan Durai Bhattacharjee, Subhro Ray, Samriddhi Sankar |
| contents | We adapt recent ideas for many-body chaos in nonlinear, Hamiltonian fluids [Murugan \textit{et al.}, Phys. Rev. Lett. 127, 124501 (2021)] to revisit the question of the Reynolds number Re dependence of the Lyapunov exponent $λ\propto{\rm Re}^α$ in fully developed turbulence. The use of such decorrelators allow us to investigate the interplay of the competing effects of viscous dissipation and nonlinearity. We obtain a precise value of $α= 0.59 \pm 0.04$ and show that departure from the Kolmogorov mean field result $λ\propto \sqrt{\rm Re}$ is a consequence of the intermittent fluctuations in the velocity-gradient tensor. The robustness of our results are further confirmed in a local, dynamical systems model for turbulence. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_09538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intermittent fluctuations determine the nature of chaos in turbulence Banerjee, Aikya Mukherjee, Ritwik Murugan, Sugan Durai Bhattacharjee, Subhro Ray, Samriddhi Sankar Fluid Dynamics Statistical Mechanics Chaotic Dynamics We adapt recent ideas for many-body chaos in nonlinear, Hamiltonian fluids [Murugan \textit{et al.}, Phys. Rev. Lett. 127, 124501 (2021)] to revisit the question of the Reynolds number Re dependence of the Lyapunov exponent $λ\propto{\rm Re}^α$ in fully developed turbulence. The use of such decorrelators allow us to investigate the interplay of the competing effects of viscous dissipation and nonlinearity. We obtain a precise value of $α= 0.59 \pm 0.04$ and show that departure from the Kolmogorov mean field result $λ\propto \sqrt{\rm Re}$ is a consequence of the intermittent fluctuations in the velocity-gradient tensor. The robustness of our results are further confirmed in a local, dynamical systems model for turbulence. |
| title | Intermittent fluctuations determine the nature of chaos in turbulence |
| topic | Fluid Dynamics Statistical Mechanics Chaotic Dynamics |
| url | https://arxiv.org/abs/2505.09538 |