Details on the intermittent transition to turbulence of a locally forced plane Couette flow G. Antar, S. Bottin, O. Dauchot, F. Daviaud, P. Manneville Abstract Experimental results are presented on the tran- sition to turbulence of a plane Couette flow locally and permanently forced by a small bead. The intermittent as- pect of this transition is investigated in a detailed analysis of the transition periods from coherent to turbulent and vice versa. A maximum number of transitions are achieved at a Reynolds number of about 310. It is shown that the breakdown of the flow coherence results from a complex succession of events occurring as follows. A secondary instability takes place leading to a drift of at least one vortex pair away from the excitation source. Consequently, the flow in the bead vicinity is laminar and a vortex pair is generated. Turbulence results from the interaction be- tween the newly born vortex and the one already active. As the fluctuation intensity decreases all over the flow, the laminar state is recovered in the bead vicinity from which two vortex pairs are regenerated. The second main con- tribution of this paper is the study of the turbulent state using spatio-temporal correlation. The role of lateral streaks and their properties in the turbulent state are in- vestigated. It is demonstrated that the turbulent spot is sustained by a vortex generation near the source followed by convection towards the boundaries. In both coherent and turbulent states, the flow near the bead is found to determine the plane Couette flow evolution. 1 Introduction Plane Couette flow (pCf) has received much attention mainly because of the apparent early discrepancy between theory and experiment. While, it was demonstrated that pCf is linearly stable for all Reynolds numbers (Darzin and Reid 1981), experimental investigations showed that tur- bulence appears at finite Reynolds numbers (Re) of less than 750 indicating that Couette flow is unstable for finite disturbances (Reichert 1956). Leutheusser and Chu (1971) using air with one fixed wall found a critical Reynolds number Rc=280. The first finite-amplitude solutions of a pCf were ob- tained by Nagata (1990) at Re‡500. He considered the problem of a circular Couette system between co-rotating cylinders with a narrow gap. By following a series of bi- furcation to the case with zero average rotation rate, he succeeded in determining steady solution in the form of co-flow modulated rolls. Later, these solutions were found unstable by Clever and Busse (1992). Recent investigations by Schmiegel and Eckhardt (1997) suggest that a chaotic repeller could underline the transition to turbulence and thus explain the unstable character of Nagata’s solutions. In parallel to Nagata’s work, several researchers (Butler and Farrell 1992; Farrell and Ioannou 1993; Trefethen et al. 1993; Schmid and Henningson 1992) emphasized the role of non-normality of the linear operator in the transition to turbulence. They considered the linearized Navier–Stokes incompressible equations of motion and obtained, in ad- dition to the Orr–Sommerfeld equation, another equation describing the evolution of wall normal vorticity. Ac- cordingly, the linear coupling between wall normal vor- ticity and the wall normal velocity could lead to an algebraic growth of the instability at Reynolds number much smaller than those predicted by the eigenvalue analysis. This is done by extraction of energy from the mean flow by structures such as streamwise vortices. A different approach based on extracting the mechanisms that sustain turbulence was performed by Waleffe (1995, 1996, 1998), and Hamilton et al. (1995). The model is based on a fundamental self-sustaining non-linear process consisting of an instability loop, according to which weak streamwise rolls disturb the streamwise velocity. The resultant inflections open up the possibility for three- dimensional fluctuations to develop, and the instability feeds back the energy to the original streamwise strolls. In this approach, it is the turbulent solution that is tracked instead of a fixed point as in Nagata’s case. A comparison among the various models of subcritical transition to turbulence can be found in Baggett and Trefethen (1996). On the other hand, the first numerical experiments performed by Orszag and Kells (1980) obtained a transi- tion to turbulence at Re1,000 where the essential three- dimensional effects were included. However, in this work Received: 28 February 2001 / Accepted: 30 September 2002 Published online: 6 December 2002 Ó Springer-Verlag 2002 G. Antar (&) University of California San Diego, Center for Energy Research, 9500 Gilman Drive, La Jolla, CA 92093-0417, USA E-mail: gantar@ferp.ucsd.edu S. Bottin, O. Dauchot, F. Daviaud Service de Physique de l’E ´ tat Condense ´, Centre d’E ´ tude de Saclay, 91191 Gif-sur-Yvette, France P. Manneville Laboratoire d’Hydrodynamique, E ´ cole Polytechnique, 91128 Palaiseau, France Experiments in Fluids 34 (2003) 324–331 DOI 10.1007/s00348-002-0560-2 324