Plane Couette flow, the flow between two parallel plates moving in opposite directions, belongs to the group of shear flows where turbulence occurs while the laminar profile is stable. Experimental and numerical studies show that at intermediate Reynolds numbers turbulence is transient and that the lifetimes are distributed exponentially. However, these studies have remained inconclusive about a divergence in lifetimes above a critical Reynolds number. The extensive numerical results for flow in a box of width 2 and length 8 presented here cover observation times up to 12 000 units and show that while the lifetimes increase rapidly with Reynolds number, they do not indicate a divergence and therefore no transition to persistent turbulence. DOI: 10.1103/PhysRevE.81.015301 PACS number͑s͒: 47.27.Cn, 05.45.Ϫa, 47.27.ed, 47.52.ϩj Plane Couette flow ͑pCf͒, the flow driven by two parallel plates moving in opposite direction, belongs to a class of shear flows where transition to turbulence may be observed at flow speeds where the laminar profile is linearly stable against infinitesimal perturbations ͓1͔. In these systems, which also include pressure driven plane Poiseuille and pipe flow, laminar and turbulent dynamics coexist for the same flow speed ͓2͔. Linear stability of the laminar flow implies that a finite amplitude perturbation is needed to drive the system out of the laminar fixed point's basin of attraction and to trigger turbulence.In the transition region the reverse process, whereby the turbulent flow relaminarizes without external stimulus or any noticeable precursor, has been seen both experimentally and numerically ͓3,4͔. Therefore, the turbulent state must be associated not with a turbulent attractor but rather with a turbulent saddle. An important question is whether there is a critical Reynolds number above which the lifetimes diverge and the system undergoes a transition to an attractor ͓5͔. Previous evidence in pCf indicated a divergence ͓3,6͔, but the reanalysis of data in ͓7͔ failed to reproduce the divergence. Pipe flow is another flow where the situation is undecided ͓7-12͔. Beyond the immediate interest of the transition to turbulence in linearly stable shear flows, these studies may also contribute to our understanding of transiently chaotic systems in general ͓13͔.The critical Reynolds number in pCf has long been studied experimentally. Ever present fluctuations and perturbations in the flow can trigger a "natural" transition without explicit external stimulus. Experiments such as ͓14͔ indicate that this happens near Re= 370, with the usual definition of the Reynolds number as Re= U 0 h / with U 0 is the half the velocity difference between the plates, h half the gap width and the kinematic viscosity of the fluid. However, since the "natural" transition depends on uncontrolled background fluctuations, experiments with reproducible finite amplitude perturbations were developed. Early experiments ͓15͔ using a jet injection perturbation give Re c = 370Ϯ 10 above which turbulent spots are repo...
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