Information-theoretic characterization of turbulence intermittency

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 ($Re_{\lambda}$), 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 non-monotonic 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 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.