Viscoelastic exact coherent states in plane shear flows.

摘要

The recently discovered, traveling-wave solutions to the Navier-Stokes equations in plane shear flows provide an excellent model flow for the study of turbulent drag reduction by polymer additives. These solutions, or “exact coherent states” (ECS), qualitatively capture the dominant structure of the near-wall buffer region of shear turbulence, i.e. , counter-rotating pairs of streamwise-aligned vortices flanking a low-speed streak in the streamwise velocity. We develop a structural mechanism for polymer drag reduction by studying the effects of viscoelasticity on the ECS. The changes to the velocity field for the viscoelastic ECS mirror the modifications seen in experiments of fully turbulent flows of polymer solutions. These modifications to the ECS are due to the suppression of the streamwise vortices. The polymer molecules become highly stretched in the wavy, streamwise streaks then relax as they move from the streaks into a vortex. The relaxation of the polymer in a vortex produces a force that directly opposes the fluid motion in the vortex and weakens it. For the viscoelastic ECS, we also find that after the onset of drag reduction there is a dramatic increase in the critical wall-normal length scale at which the ECS can exist. This sharp increase in length scale mirrors experiments and might be the cause of the delay in the transition to turbulence seen in polymer solutions. Most importantly, this effect of polymers on the ECS may be relevant to the maximum drag reduction asymptote, which is the universal limit on polymer drag reduction.