Information theory used to study the turbulent cascade

The simplest picture of turbulence is the one imagined by Richardson and Kolmogorov. In their theory there is a cascade of energy from large scales to small scales. Here we present a new tool to study this picture using simple ideas borrowed from information theory. We use the conditional entropy (conditioned uncertainty) of velocity fluctuations on one scale conditioned on another larger or smaller scale. By varying the scale of the velocity fluctuations used in the conditioning, we can test both direction and locality. The ideas are tested on both experimental and numerical simulation data. This tool can be applied to 3D turbulence or 2D turbulence and because it has nothing to do with the Navier-Stoke's equation, it can be used for any other system where there is a similar cascade-like phenomenon.