On the mechanism of turbulent drag reduction in dilute polymer solutions: dynamics of vortex filaments

Abstract

The localized-induction approximation (LIA) is generalized in the framework of the quasi-one-dimensional approach to include the effect of polymer additives on stretching of thin vortex filaments. It is shown that in dilute polymer solutions vorticity diffusion is negligible for vortices with longwave perturbations, and their strength remains constant in spite of the fact that high longitudinal stress and elongational viscosity may be generated in the course of vortex stretching in shear flow. General governing equations for vortex filaments in a background flow of dilute polymer solution are proposed. Their numerical solution is obtained. It shows that interaction between a spanwise perturbed vortex filament and a background shear flow leads to strong vortex stretching and to emergence of configurations similar to horseshoe or hairpin vortices. In dilute polymer solutions, strong stretching of vortex filaments yields high longitudinal stress (high elongational viscosity). The latter retards or completely arrests vortex stretching, which is similar to the findings of [1] that frequency of turbulence generation in ‘bursts’ decreases in dilute polymer solutions. Therefore, a more gentle mean velocity profile is expected in the boundary layer, which results in drag reduction.