Localized edge states nucleate turbulence in extended plane Couette cells

Abstract

We study the turbulence transition of plane Couette flow in large domains where localized perturbations are observed to generate growing turbulent spots. Extending previous studies on the boundary between laminar and turbulent dynamics we determine invariant structures intermediate between laminar and turbulent flow. In wide but short domains we find states that are localized in spanwise direction, and in wide and long domains the states are also localized in downstream direction. These localized states act as critical nuclei for the transition to turbulence in spatially extended domains.