Turbulent drag reduction due to polymer additives, the Josephson-Anderson relation and Lighthill's mechanism

The Josephson-Anderson relation equates voltage-drop in superconductors and chemical-potential drop in superfluids to cross-stream vortex motion and it has been the key to "drag reduction" in superconductor technology by pinning of quantized vortices. This relation holds also in classical fluids and we apply it here to the explanation of the Toms effect of polymer drag reduction. Remarkably, drag-reduction by polymers in minute concentrations occurs only in turbulent flows, not in laminar, suggesting that turbulent-specific vortex dynamics is impeded. Lighthill has pointed out that classical turbulence in the vicinity of a solid wall produces a strong correlation between inflow to the wall and spanwise vortex-stretching. This mechanism counters strong viscous and turbulent diffusion away from the wall, leading to higher vorticity concentration near the wall than in laminar flows. We present direct numerical simulations of turbulent channel flow with FENE-P showing that polymers damp Lighthill's mechanism, explaining the more distributed mean vorticity profile. Smaller-scale "hairpin vortices" primarily responsible for outward transport are damped even more, however, explaining the net decrease in cross-stream vorticity flux and in pressure-drop. The Josephson-Anderson relation describes not only these time-average effects but also connects drag instantaneously to space-time intermittent vortex dynamics and sheds new light on the underlying rheological mechanisms.