On lower branch exact coherent structures in turbulent shear flows

Understanding the nature of transition to turbulence has been one of the most important problems in fluid dynamics that has attracted attention since Reynolds' first pipe flow experiments in 1883. It has received increasing attention in recent years with development in nonlinear dynamics and numerical solutions of PDEs. But the progress in understanding the transition threshold and controlling transition to turbulence has been slow due to the highly nonlinear nature and complexity of turbulent shear flows.; Our approach is through the exact coherent structures (ECS) in plane Couette flow. They come in pairs with upper and lower branches that bifurcate from a neutrally stable streaky flow. The lower branch ECS exhibit an asymptotic structure that consist of O(1) streaks sustained by O(R-1) streamwise rolls and a weak sinusoidal streak instability eigenmode that develops a critical layer structure. These unstable lower branch states have a one-dimensional unstable manifold and may be viewed as the 'backbone' of the phase space boundary separating the basin of attraction of the laminar point from that of the turbulent state. The very low dimensionality of the lower branch unstable manifold suggests new turbulence control strategies.