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 ${Re}_{\lambda }$, we characterize the ${Re}_{\lambda }$ 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 ${Re}_{\lambda }$: 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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• Intermittency
• Isotropic turbulence
• Turbulence
• Direct numerical simulations
• Information theory