  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. We study the
effect of polymer additives on these "exact coherent states" (ECS), in the
plane Poiseuille geometry. Many key aspects of the turbulent drag reduction
phenomenon are found, including: delay in transition to turbulence; drag
reduction onset threshold; 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. Specifically, at sufficiently high wall shear rates, viscoelasticity is
found to completely suppress the normal (i.e. streamwise-vortex-dominated)
dynamics of the near wall region, indicating that the maximum drag reduction
regime is dominated by a distinct class of flow structures.
