Two-Dimensional Turbulence: a survey, a new result, speculations
Prof. Dr. Theo Odijk (Lorentz Institute for Theoretical Physics, University of Leiden, Netherlands)

Even though turbulence is basically still an enigma, several key analytical results are known when it is two dimensional (2D).
I present a short survey for those who are not familiar with the subject. Next, a novel asymptotically rigorous result is discussed based on an analogy between 2D nematics and` 2D turbulence in the inertial Kraichnan regime at high Reynolds numbers.The behaviour of a polymer chain dissolved in the former is similar to that of a material line in the latter.This reasoning leads to a relatuin between the material line correlations and those of the underlying bulk liquid under conditions of complete slaving.
The non-trivial exponent for the former seems to bear on important soap film experiments carried out by Amarouchene and Kellay a decade ago. I also present speculations on how a complete theory of 2D turbulence could look like.