  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. We first establish a
connection between the information flow and phase-space contraction rate. From
this relation, we then prove a universal inequality between the information
flow and turbulent fluctuations, which states 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 the difference
between the information flow and the Kolmogorov-Sinai entropy.
