Information-theoretic characterization of turbulence intermittency
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arXiv
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| Format: | Preprint |
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2025
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| author | Sarkar, Shreyashri Das, Rishita |
| author_facet | Sarkar, Shreyashri Das, Rishita |
| contents | Small-scale intermittency is studied as the deviation of the probability distributions of pseudodissipation, dissipation and enstrophy in turbulence from those of a Gaussian random velocity field. This deviation is quantified using Kullback-Leibler (KL) divergence between the two distributions, directly measuring turbulence-induced intermittency separated from purely kinematic effects. Using direct numerical simulation data of forced isotropic turbulence over a wide range of Taylor Reynolds numbers ($Re_λ$), we characterize the $Re_λ$ dependence of small-scale intermittency via KL divergence and uncertainty via Shannon entropy, identifying distinct behavioral regimes. Small-scale uncertainty exhibits a non-monotonic dependence on $Re_λ$: despite continuously growing variability, entropy decays above a certain Reynolds number, suggesting a fundamental change in the statistical nature of the small scales. Turbulence-induced intermittency grows logarithmically with Reynolds number in contrast to the commonly reported power-law scaling, implying that turbulence shows a diminishing growth rate of intermittency at higher Reynolds numbers. Finally, we uncover an emergent symmetry: turbulence dynamics is shown to generate nearly equal intermittency in dissipation rate and enstrophy, challenging the prevailing assumption of asymmetry between strain-rate and vorticity dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Information-theoretic characterization of turbulence intermittency Sarkar, Shreyashri Das, Rishita Fluid Dynamics Data Analysis, Statistics and Probability Small-scale intermittency is studied as the deviation of the probability distributions of pseudodissipation, dissipation and enstrophy in turbulence from those of a Gaussian random velocity field. This deviation is quantified using Kullback-Leibler (KL) divergence between the two distributions, directly measuring turbulence-induced intermittency separated from purely kinematic effects. Using direct numerical simulation data of forced isotropic turbulence over a wide range of Taylor Reynolds numbers ($Re_λ$), we characterize the $Re_λ$ dependence of small-scale intermittency via KL divergence and uncertainty via Shannon entropy, identifying distinct behavioral regimes. Small-scale uncertainty exhibits a non-monotonic dependence on $Re_λ$: despite continuously growing variability, entropy decays above a certain Reynolds number, suggesting a fundamental change in the statistical nature of the small scales. Turbulence-induced intermittency grows logarithmically with Reynolds number in contrast to the commonly reported power-law scaling, implying that turbulence shows a diminishing growth rate of intermittency at higher Reynolds numbers. Finally, we uncover an emergent symmetry: turbulence dynamics is shown to generate nearly equal intermittency in dissipation rate and enstrophy, challenging the prevailing assumption of asymmetry between strain-rate and vorticity dynamics. |
| title | Information-theoretic characterization of turbulence intermittency |
| topic | Fluid Dynamics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2505.05304 |