Scale-to-scale information flow amplifies turbulent fluctuations

In three-dimensional turbulence, information of turbulent fluctuations at large scales is propagated to small scales. Here, we investigate the relation between the information flow and turbulent fluctuations described by a shell model. We first establish a connection between the information flow and phase-space contraction rate. From this relation, we then prove an inequality between the information flow and turbulent fluctuations, which suggests that the information flow from large to small scales amplifies turbulent fluctuations at small scales. This inequality can also be interpreted as a quantification of Landau's objection to the universality of turbulent fluctuations. We also discuss differences between the information flow and the Kolmogorov-Sinai entropy.