HRT

Abstract

Coherent states found numerically in plane Couette turbulence (Kawahara & Kida, J. Fluid Mech. 449, 2001; Kawahara, Phys. Fluids 17, 2005) and square duct turbulence (Uhlmann, Pinelli, Kawahara & Sekimoto, J. Fluid Mech. 588, 2007) are reviewed to discuss the role of coherent structures in wall-bounded turbulent flows at low Reynolds numbers. The coherent states in Couette flow are represented by unstable periodic solutions to the incompressible Navier-Stokes equation. The periodic solution, which exhibits a near-wall regeneration cycle of streamwise vortices and streaks, is shown to satisfy Prandtl's wall law, implying that the regeneration cycle has relevance to the statistical law of near-wall turbulent flow. The coherent states in marginally turbulent square duct flow are characterized by a four-vortex secondary flow and associated streaks. It is shown that at low Reynolds numbers streamwise vortices play a crucial role in the appearance of secondary flow of Prandtl's second kind.