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Abstract

The purpose of this contribution is to summarize and discuss recent advances regarding the onset of turbulence in shear ows. The absence of a clear-cut instability mechanism, the spatio-temporal intermittent character and extremely long lived transients are some of the major di culties encountered in these ows and have hindered progress towards understanding the transition process. We will show for the case of pipe ow that concepts from nonlinear dynamics and statistical physics can help to explain the onset of turbulence. In particular, the turbulent tructures (pu s) observed close to onset are spatially localized chaotic transients and their lifetimes increase super-exponentially with Reynolds number. At the same time uctuations of individual turbulent pu s can (although very rarely) lead to the nucleation of new pu s. 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.