Transition to turbulence.

Abstract

A few known types of transition to turbulence, as the cascade of period doubling and the intermittent transition, are reviewed. This happens in dynamical systems with a few degrees of freedom, as modelled by the iteration of nonlinear maps. Then specific transitions for systems with many degrees of freedom are presented. The occurrence of a low frequency broadband noise in large cells at the onset of Rayleigh-Benard convection and the transition by intermittent bursts in parallel flows are considered. In this last case, one is concerned with localized and finite amplitude perturbations. Simple geometric arguments show that these fluctuations, when they are isolated and with a well defined relative speed, exist for a single value of the Reynolds number only. (English abstract)