Coherent structures in stably stratified plane Couette flow

A large body of recent work in wall-bounded, unstratified shear flow has been dedicated to finding Exact Coherent Structures (ECS) (e.g. see the review Kawahara et al. (2012)). These are fully non-linear, invariably unstable, exact solutions which help understand how turbulence arises. The growing consensus is that the existence of these solutions is a necessary (but not sufficient) condition for turbulent dynamics to be possible in parameter space. Plane Couette flow a fluid sheared between two parallel, differentially moving plates is an exemplar of this in that the flow is linearly stable for all Reynolds numbers Re yet turbulence can occur at a finite Re beyond that where ECS disconnected from the basic sheared state start to exist. In this presentation we add extra physics in the form of stable stratification (gravity perpendicular to the plates) to plane Couette flow to explore this hypothesis further and to investigate transition in a stably stratified shear flow.