Lower branch coherent states in shear flows: transition and control

Abstract

Lower branch coherent states in plane Couette flow have an asymptotic structure that consists of O(1) streaks, $O(R^{-1})$ streamwise rolls and a weak sinusoidal wave that develops a critical layer, for large Reynolds number $R$. Higher harmonics become negligible. These unstable lower branch states appear to have a single unstable eigenvalue at all Reynolds numbers. These results suggests that the lower branch coherent states control transition to turbulence and that they may be promising targets for new turbulence prevention strategies.