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The present work analyzes the statistics of finite scale local Lyapunovexponents of pairs of fluid particles trajectories in fully developedincompressible homogeneous isotropic turbulence. According to the hypothesis offully developed chaos, this statistics is here analyzed assuming that theentropy associated to the fluid kinematic state is maximum. The distribution ofthe local Lyapunov exponents results to be an unsymmetrical uniform function ina proper interval of variation. From this PDF, we determine the relationshipbetween average and maximum Lyapunov exponents, and the longitudinal velocitycorrelation function. This link, which in turn leads to the closure of vonK\`arm\`an-Howarth and Corrsin equations, agrees with results of previousworks, supporting the proposed PDF calculation, at least for the purposes ofthe energy cascade main effect estimation. Furthermore, through the propertythat the Lyapunov vectors tend to align the direction of the maximum growthrate of trajectories distance, we obtain the link between maximum and averageLyapunov exponents in line with the previous results. To validate the proposedtheoretical results, we present different numerical simulations whose resultsjustify the hypotheses of the present analysis.

Statistics of finite scale local Lyapunov exponents in fully developed homogeneous isotropic turbulence