(244i) Laminar-Turbulent Boundary and Its Implication for Friction Drag Reduction in Newtonian and Viscoelastic Turbulent Flows

Maximum drag reduction (MDR), the universal upper bound for polymer-induced turbulent drag reduction, has remained an unsolved problem despite decades of research. Recent advances revealed that dynamics at MDR are likely dominated by a class of weak turbulent states. These states exist in both Newtonian and viscoelastic turbulence and polymer additives do not seem to alter their behaviors. The nature of these states however remains unknown. The current study takes an a priori approach and explores the domain of weak turbulence near the boundary separating laminar and turbulent states. Dynamical trajectories along this boundary can be numerically computed through a pair of direct numerical simulation (DNS) solutions that tightly pinch the boundary. Trajectories on this boundary converge to an asymptotic “edge state”. Edge states are found for Newtonian and viscoelastic systems at a range of parameters. It is observed that viscoelasticity has a negligible effect on the statistics of these solutions. This confirms the existence of weak turbulent states that cannot be suppressed by polymer additives, explaining why polymer-induced drag reduction must be bounded by an upper limit. Dependence of these states on the Reynolds number (Re) is more complex: although at one low Re the mean velocity profiles correspond closely to experimental observations for polymer solutions in the MDR regime, at higher Re, these profiles are higher than that of MDR. The quantitative origin of MDR may lie in a domain between the edge state and the turbulent basin.