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Localized edge states for the transition to turbulence in shear flows

In parallel shear flows like pipe flow or plane Couette flow, laminar and turbulent dynamics coexist. The boundary between the two types of dynamics shows up clearly in studies that monitor the life time of a perturbation, i.e. the time it takes to relaminarize. Initial conditions that neither become fully turbulent nor return to the laminar state live in the boundary between laminar and turbulent flow. They typically approach a relative attractor called the edge state. The edge state together with its stable manifold then defines the boundary between laminar and turbulent motion. Edge states determined in small domains are infinitely extended when extrapolated to larger domains and are not compatible with the observation that a local perturbation suffices to produce turbulence. Studies of pipe flow, however, show that in long domains also localized edge states can exist. We here present results from direct numerical simulations of plane Couette flow which show that in narrow but long domains the edge states are localized and similar to the ones found in pipe flow. © 2010 Springer Science+Business Media B.V.

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