Plane Couette flow is the shear flow that, ideally, develops between two infinite parallel plates moving at the same speed U in opposite directions.Experimentally, as sketched in Fig.1, it can be achieved using rotating a belt with small enough gap 2h between the two facing parts of the belt (large aspect-ratio).The laminar solution is known to be stable against infinitesimal perturbations for any Reynolds number R =Uh/v, where v is the kinematic viscosity of the fluid.A subcritical transition to turbulence is nevertheless achieved at moderate values of R.Coexisting turbulent and laminar domains with complex spatiotemporal dynamics are observed in some range [Rg, Rt], with Rg ≈325 and Rt≈405; see refs.[1,2].