Universal mean velocity profile in polymeric flows at maximum drag reduction

For a sufficient concentration of long-chain polymers in a Newtonian solvent, turbulent wall-bounded flows reach a universal state known as maximum drag reduction (MDR). Through direct numerical simulations of MDR pipe flows at Reτ = 310 and Wi = 104, we show that the wall-normal kinetic energy flux characterizing Newtonian wall-bounded turbulence is suppressed, and that polymers primarily sustain velocity fluctuations. We derive an expression for the mean velocity profile that aligns with experimental data and is no longer dependent on characteristic quantities of wall-bounded turbulence. For a sufficiently high concentration, MDR flows achieve an asymptotic universal profile, Uα = ln yα, consistent with Virk’s law at large Reynolds number.