https://doi.org/10.1007/s100510050536
Statistical analysis of the transition to turbulence in plane Couette flow
CEA — Service de Physique de l'État Condensé,
Centre d'Études de Saclay, 91191 Gif-sur-Yvette, France
Received:
10
April
1998
Revised:
22
June
1998
Accepted:
24
June
1998
Published online: 15 November 1998
We argue on general grounds that the transition to turbulence in plane Couette flow is best studied experimentally at a statistical level. We present such a statistical analysis of experimental data guided by a parallel investigation of a simple coupled map lattice model for spatiotemporal intermittency. We confirm that this generic type of spatiotemporal chaos is relevant in the context of plane Couette flow, where the linear stability of the laminar regime at all Reynolds numbers insures the necessary local subcriticality. Using large ensembles of similar experiments, we show the existence of a well-defined threshold Reynolds number above which a unique, turbulent, intermittent attractor coexists with the laminar flow. Furthermore, our data reveals that this transition to spatiotemporal intermittency is discontinuous, i.e. akin to a first-order phase transition.
PACS: 47.20.-k – Hydrodynamic stability / 47.20.Ky – Nonlinearity (including bifurcation theory) / 47.27.Cn – Transition to turbulence / 05.45.+b – Theory and models of chaotic systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998