Polymer induced drag reduction in exact coherent states of plane Poiseuille flow

Nonlinear traveling waves that are precursors to laminar-turbulent transition and capture the main structures of the turbulent buffer layer have recently been found to exist in all the canonical parallel flow geometries. The present work examines the effect of polymer additives on these "exact coherent states" (ECS) in the plane Poiseuille geometry, using the FENE-P constitutive model for polymer solutions, focusing on Reynolds numbers slightly above transition. In experiments with a given fluid, Reynolds and Weissenberg numbers are linearly related (i.e., Wi/Re=const). In this situation, we study the effects of viscoelasticity on velocity field and polymer stress field along some experimental paths, which represent different flow behaviors as Re (and Wi) increases. Many key aspects of the turbulent drag reduction phenomenon are found, including delay in transition to turbulence, drag reduction onset threshold, and diameter and concentration effects. Furthermore, examination of the ECS existence region leads to a distinct prediction, consistent with experiments, regarding the nature of the maximum drag reduction regime: at sufficiently high wall shear rates, viscoelasticity is found to completely suppress the streamwise vortices of the near-wall region, suggesting that the maximum drag reduction regime is dominated by a distinct class of flow structures. In order to test the scenario that we infer from these results, we next implement direct numerical simulation (DNS), studying the transient and statistically converged flow dynamics in a "minimal channel" (the smallest box that can sustain turbulence in our DNS study) using ECS as initial conditions to better understand these saddle-points that underlie the strange-attractor of near-wall turbulence. Our results indicate that turbulent flows can sustain in the "minimal channel" even at low Reynolds number considered here and many observations about fully turbulent flows of dilute polymer solutions are captured. The quantitative methods implemented here further characterize the effect of viscoelasticity on flow structures in "minimal channel flow", suggesting the existence of other coherent traveling wave states.