Dynamics on the Laminar-Turbulent Boundary and the Origin of the Maximum Drag Reduction Asymptote

Abstract

Dynamical trajectories on the boundary in state space between laminar and turbulent plane channel flow—edge states—are computed for Newtonian and viscoelastic fluids. Viscoelasticity has a negligible effect on the properties of these solutions, and, at least at a low Reynolds number, their mean velocity profiles correspond closely to experimental observations for polymer solutions in the maximum drag reduction regime. These results confirm the existence of weak turbulence states that cannot be suppressed by polymer additives, explaining the fact that there is an upper limit for polymer-induced drag reduction.