Deterministic and stochastic aspects of the transition to turbulence

The purpose of this contribution is to summarize and discuss recent advances regarding the onset of turbulence in shear flows. The absence of a clear-cut instability mechanism, the spatio-temporal intermittent character and extremely long lived transients are some of the major difficulties encountered in these flows and have hindered progress towards understanding the transition process. We will show for the case of pipe flow that concepts from nonlinear dynamics and statistical physics can help to explain the onset of turbulence. In particular, the turbulent structures (puffs) observed close to onset are spatially localized chaotic transients and their lifetimes increase super-exponentially with Reynolds number. At the same time fluctuations of individual turbulent puffs can (although very rarely) lead to the nucleation of new puffs. The competition between these two stochastic processes gives rise to a non-equilibrium phase transition where turbulence changes from a super-transient to a sustained state.