Information-theoretic characterization of turbulence intermittency

Abstract: We present a new characterization of small-scale intermittency of turbulence based on an information-theoretic measure, that inherently segregates turbulence intermittency from kinematic intermittency. Instead of the commonly studied higher-order moments, Kullback-Leibler (KL) divergence is used to quantify the deviation of turbulence pseudodissipation rate (or dissipation rate/enstrophy) from that of a Gaussian random velocity field as an accurate measure of the small-scale intermittency arising from turbulence dynamics. In addition, Shannon entropy is used to assess the uncertainty of these turbulence small-scale quantities. Analysis of direct numerical simulation data of forced homogeneous isotropic turbulent flow reveals the existence of two critical Taylor Reynolds numbers where the variation of uncertainty changes. The KL-divergence measure reveals two striking results about intermittency: (i) intermittency grows logarithmically with Reynolds number and (ii) dissipation rate and enstrophy are equally intermittent in a turbulent flow of any Reynolds number, if one considers only the intermittency arising from turbulence dynamics.