  We investigate the nature of information flow in turbulence from an
information-thermodynamic viewpoint. For the fully developed three-dimensional
fluid turbulence described by the fluctuating Navier-Stokes equation, we prove
that information of large-scale eddies is transferred to small scales along
with the energy cascade. We numerically illustrate our findings using a shell
model and further show that in the inertial range, the intensity of the
information flow is nearly constant and can be scaled by the large-eddy
turnover time. Our numerical results also suggest that the corresponding
information-thermodynamic efficiency is quite low compared to other typical
information processing systems such as Maxwell's demon. These findings provide
a new perspective on how universality and intermittency of turbulent
fluctuations emerge at small scales.
