Information content of turbulence.

We treat a turbulent velocity field as a message in the same way as a book or a picture. All messages can be described by their entropy per symbol h, defined as in Shannon's theory of communication. In a turbulent flow, as the Reynolds number Re increases, more correlated degrees of freedom are excited and participate in the turbulent cascade. Experiments in a turbulent soap film suggest that the spatial entropy density h is a decreasing function of Re, namely h[proportionality]-logRe + const. In the logistic map, also analyzed here, increasing the control parameter r increases h. A modified logistic map with additional coupling to past iterations suggests the significance of correlations.