Experimental evidence of a phase transition to fully developed turbulence in a wake flow

Abstract

The transition to fully developed turbulence of a wake behind a circular cylinder is investigated with respect to its statistics. In particular, we evaluated the probability density functions of velocity increments on different length scales $r$. Evidence is presented that the $r$-dependence of the velocity increments can be taken as Markov processes in the far field, as well as, in the near field of the cylinder wake. With the estimation of the deterministic part of these Markov processes, as a function of the distance from the cylinder, we are able to set the transition to fully developed turbulence in analogy with a phase transition. We propose that the appearing order parameter corresponds to the presence of large scale coherent structures close to the cylinder.