On the decay of turbulence in plane Couette flow (long version)

Abstract

Upon decreasing the Reynolds number, plane Couette flow first forms alternately turbulent and laminar oblique bands out of featureless turbulence below some upper threshold R_t. These bands exist down to a global stability threshold R_g below which laminar flow ultimately prevails. We study the fragmentation and decay of these bands in systems that are extended enough for several bands to exist. We use direct numerical simulations appropriately tailored to deal with such large systems during long enough durations. We point out a two-stage process involving the rupture of a band and next its slow shrinking. Previous interpretations of turbulence decay in wall-bounded flows within the chaotic transient or spatiotemporal intermittency paradigms are discussed.