Turbulence as Information

A message of any sort can be regarded as a source of information. Claude. E. Shannon showed in the last century that information ("what we don't already know") is equivalent to the entropy as defined in statistical mechanics. A string of experimental observations is like a succession of words; they both convey information and can be characterized by their entropy. For the fluid flow measurements and simulations to be discussed here (pipe and soap film flow, GOY model), the entropy depends on controllable parameters such as the Reynolds number. The information theory approach is applicable to measurements of any type including those governed by intractable equations or systems where the governing equations are not known. This contribution is dedicated to the memory of Leo Kadanoff, an inspiring teacher and one of the most important scientific leaders of the last half century.