Turbulent drag reduction due to polymer additives, vorticity dynamics, and Lighthill mechanism

Turbulent drag reduction by polymer additives in channels is widely attributed to weakening of coherent vortices and reducing their number, especially quasi-streamwise hairpin vortices in the buffer layer. Drag is due to the wall-normal flux of spanwise vorticity, with constant mean across the channel, and polymers must reduce this flux at all wall distances. However, another polymer effect is that the mean vorticity profile becomes more distributed, whereas it is strongly concentrated at the wall in Newtonian turbulence. Lighthill explained the latter by strong up-gradient vorticity transport (into the wall), due to correlated inflow and spanwise stretching. This transport is due to pancake-type detached eddies [1]. The net down-gradient transport (out from the wall) is due to even stronger transfer by viscous diffusion and turbulent advection. If the only polymer effect were to reduce the latter, however, then the mean vorticity profile would concentrate even more sharply at the wall! Direct numerical simulations of turbulent channel flow with FENE-P show that the polymer damps out Lighthill’s up-gradient transport, explaining the more distributed mean vorticity profile. The smaller-scale down-gradient vortices are damped out even more, however, explaining the net decrease in vorticity flux and drag. These effects are demonstrated by the 2D co-spectra of the nonlinear vorticity flux.

[1] S Kumar, C Meneveau & G Eyink, JFM; arXiv:2302.03738