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Information-theoretic characterization of turbulence intermittency

Shreyashri Sarkar and Rishita Das*

  • *Contact author: rishitadas@iisc.ac.in
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Phys. Rev. Fluids 11, 084605 – Published 13 August, 2026

DOI: https://doi.org/10.1103/bzy7-p57q

Abstract

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 Reλ, we characterize the Reλ dependence of small-scale intermittency via KL divergence and uncertainty via Shannon entropy, identifying distinct behavioral regimes. Small-scale uncertainty exhibits a nonmonotonic dependence on Reλ: 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, as characterized by KL divergence, grows logarithmically with Reynolds number in contrast to the commonly reported power-law scaling of individual moments, implying that turbulence shows a diminishing growth rate of intermittency at higher Reynolds numbers. 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.

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Outline

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Phys. Rev. Fluids 11, 084605– Published 13 August, 2026
  • Received 9 May 2025
  • Revised 9 August 2025
  • Accepted 15 July 2026
Article part of CHORUS
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