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

Abstract

iTo my parents, my brother, and my best friend who contributed to this work in ways they did not realize ii Nonlinear traveling waves that are precursors to laminar-turbulent transition and cap-ture 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 poly-mer additives on these “exact coherent states ” (ECS) in the plane Poiseuille geometry, using the FENE-P constitutive model for polymer solutions. 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. The changes to the velocity field for the viscoelastic nonlinear traveling waves qualitatively capture many of those experimentally observed in fully tur-bulent flows of polymer solutions at low to moderate levels of drag reduction: drag i