Revision 1

Accepted · first revision · record

Title: Origin and universality of the maximum drag reduction asymptote
Plain: Polymers can cut pipe friction a great deal, but adding more stops helping beyond a limiting friction curve that is the same for all polymers. Why this limit exists and is universal is not understood.
Precise: In turbulent pipe flow of polymer solutions, the Fanning friction factor f approaches Virk's maximum drag reduction asymptote $1/\sqrt{f} = 19.0\operatorname{log10}(\mathrm{Re}\sqrt{f}) - 32.4$, independent of polymer species. Identify the flow state that realizes it (elasto-inertial turbulence driven by polymer stress, or marginally sustained Newtonian-like turbulence), derive the asymptote, and explain why friction can fall below it toward laminar values.
Settled by: A derivation of the asymptote from the dynamics of the identified flow state, confirmed by DNS of a constitutive model reproducing the measured friction curve.
Kind: phenomenon
Answer type: mechanism
References: (empty)
Literature status: contested
Status note: Elasto-inertial turbulence (Samanta et al. 2013) and friction below the asymptote after relaminarization (Choueiri, Lopez, Hof 2018) favour an elasto-inertial origin; a predictive derivation is lacking.
Posed since: (empty)