Abstract

In the present study we investigate turbulence using information theory. We propose a methodology to study mutual information, entropy and complexity utilizing data from direct numerical simulations. These quantities are defined in their continuous form and estimated using the Kozachenko–Leonenko and Kraskov–Stögbauer–Grassberger estimators, for entropy and mutual information, respectively. To validate our tools and methodology, we compare the entropy of three direct numerical simulations of forced isotropic turbulence at different Reynolds numbers (Re?=433, Re?=648 y Re?=1300) with results previously reported in the literature. The main body of the study is the analysis of the transition to turbulence in a transitional boundary layer, our results show that the mutual information between the velocity field and temporal velocity increments reaches a maximum close to the transition to turbulence followed by a decrease during the transition, while at the same time there is a change in entropy due to both, the change in variance of the velocity field and the deformation of the probability density function. Finally, we examine the vertical profiles of the information-theoretic quantities in a turbulent channel flow (Re?=5200). Here we study spatial velocity increments and observe an increase of the entropy due to the deformation of the probability density function of the velocity field, as it becomes more Gaussian away from the wall. © 2023 Elsevier B.V.