The phenomenon of polymer-induced drag reduction describes the effect that even minute quantities of a high molecular weight polymer can have, of the order of ppm by weight, when added to a low molecular weight solvent, such as water or crude oil, in reducing considerably the turbulent drag. Despite a voluminous amount of research from its original discovery in the late 40s by Mysels and Tomms, unresolved issues still remain. Here I will describe the recent progress achieved thanks to Direct Numerical Simulations (DNS) of the turbulent channel flow of a dilute polymer solution modeled from first principles with various constitutive equations such as (FENE-P), (Giesekus), or others.

The main effect of viscoelasticity is shown to be the strengthening of the largest size turbulent structures which become much more coherent with a dynamics that changes at an appreciably lower rate than for the equivalent Newtonian structures. Our parametric study strongly suggests that this feature develops due to an enhanced resistance to extensional deformation induced due to viscoelasticity and it results to a lower energy transfer from the wall to the turbulent core, thus explaining the drag reduction. Recent developments in numerical methods allowed us to obtain accurate and stable simulations up to highly drag reduced (more than 60%) turbulent channel flows of dilute polymer solutions. The most recent data confirm earlier results in our group at lower drag reduction values whereby the primary mechanism for drag reduction is the decreased intensity of the wall eddies which is the result of a significant increase to extensional deformations contributed by the polymer additives, exactly as proposed earlier by Metzner and Lumley.

Recent work has been able to more systematically investigate the changes to the flow structure affected due to the polymers, and in particular to the coherent structures, using Karhunen-Loeve (KL) or Proper Orthogonal Decomposition (POD) analysis of the DNS data. This demonstrated a dramatic decrease in the K-L dimension of the flow (an order of magnitude) with viscoelasticity versus the Newtonian flow. Moreover, the time-dependent dynamic analysis of the solution in terms of the K-L modes a reduction in the velocity data has confirmed the increased time scales encountered with viscoelasticity but also the sensitivity of the polymer conformation data and stress to many scales of the velocity field. It also underscores the tremendous difficulty underling any effort towards a low-dimensional modeling of turbulent flows, given the large extent of scales of length and time characterizing turbulent dynamics.