Information Content of Turbulence

This work is one of the few attempts to treat turbulence as an information source that can be controlled experimentally. As the Reynolds number $Re$ is increased, more degrees of freedom are excited and participate in the turbulent cascade. One might therefore expect that on raising $Re$, the system becomes more random, thereby increasing the Shannon entropy $H$. However, because the excited modes are correlated, $H$ is a {\em decreasing} function of $Re$, as is experimentally shown in a study of turbulence in a flowing soap film. A parallel analysis was made of the logistic map, where $H$ is calculated as a function of the control parameter $r$ in the equation $x_{n+1} =r x_n(1 - x_n)$. There, as expected, $H$ is an increasing function of $r$. This work is supported by NSF grant No. 1044105, a Mellon fellowship, and the Okinawa Institute of Science and Technology.