Directed percolation and the transition to turbulence

In pipe, channel and Couette flow turbulence does not arise from an instability of the laminar flow. Both states co-exist over a considerable Reynolds number range. Moreover the first turbulent structures that can be observed in experiments (depending on the flow referred to as puffs, spots or stripes) are essentially transients and decay after long times. Eventually however the proliferation of such turbulent patches outweighs their decay. At this point a non-equilibrium phase transition occurs which recently has been suggested to fall into the directed percolation universality class. In the light of the growth, decay and interaction mechanisms of turbulent patches in pipe, channel and Couette flow we discuss the correspondence to directed percolation and the conditions that must be fulfilled to fall into this universality class. In particular we discuss complications that arise in these flows and that are not part of simple percolation models, like for example puff-puff interactions. Finally we present data from a new pipe experiment, where the pipe length is order of 100 000 pipe diameters. The measured scaling of the turbulent fraction, the correlation length and correlation times are compared with the directed percolation predictions.