Small-scale intermittency in isotropic and anisotropic turbulent flows using Kullback-Leibler divergence

Small-scale intermittency is typically quantified by examining the deviation of higher order moments of dissipation rate, enstrophy and pseudodissipation rate from Gaussianity. We employ the information-theoretic measure of Kullback-Leibler (KL) divergence to present a more comprehensive characterization of intermittency. KL divergence of the probability distributions of these quantities in turbulent flows compared to those in a Gaussian random velocity field (GRF) is used as the measure of small-scale intermittency. The choice of the GRF as baseline allows us to distinguish between the different sources of intermittency. In homogeneous isotropic turbulence, KL divergence relative to an isotropic GRF allows us to separate contributions arising from kinematic constraints and those attributable to turbulence dynamics. In turbulent channel flows, KL divergence with respect to an anisotropic GRF is used to further segregate anisotropy-driven kinematic intermittency from turbulence intermittency. Our results demonstrate that turbulence-induced intermittency grows logarithmically with Taylor Reynolds number above 10, in contrast to the widely accepted power law scaling. We further show that dissipation rate and enstrophy are equally intermittent, considering only the contribution from turbulence dynamics. In channel flow, anisotropy is shown to influence near-wall intermittency and logarithmic growth of intermittency similar to isotropic turbulence is observed only in the log layer.